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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite volumes ; finite elements ; compressible flows ; unstructured grids ; hybrid grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.
    Additional Material: 16 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: porous media ; mixture theories ; fluid-saturated binary model ; incompressible constituents ; non-linear elasticity ; dynamic loading ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.
    Additional Material: 9 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: induction heating ; coupled problem ; three-dimensional analysis ; eddy current temperature analysis ; thin conducting sheet model ; eddy current boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a special finite element formulation for the computer simulation of an inductive heating device for thin moving metal strips. The calculation includes both the electromagnetic field and the temperature distribution resulting from the losses of the induced currents. The electromagnetic field is described by an electric vector potential and a magnetic scalar potential, the induced eddy currents are represented by a special boundary condition for the magnetic scalar potential along the surface of the current-carrying strip. This avoids the necessity to discretize the thin secondary region. The thermal model includes the movement of the strip as well as convection and radiation as its surfaces. The field equations are discretized using the Galerkin variant of the Method of Weighted Residuals. The mutually coupled electromagnetic and temperature fields are then calculated using an iterative, staggered solution scheme. Comparisons between calculated and measured temperature profiles show the validity of the presented approach.
    Additional Material: 17 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
    Additional Material: 6 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
    Additional Material: 21 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: helical spring ; free vibration ; frequency ; transfer matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of 12 partial differential equations pertaining to helical springs is solved for free vibrations by the transfer matrix method. The dynamic transfer matrix including the axial and the shear deformations and the rotational inertia effects for any number of coils is numerically determined up to any desired precision in an efficient way. It is proved that the coefficients of the characteristic determinant of the dynamic differential matrix, [D], with odd-numbered subscripts are equal to zero which is based on the peculiarity that the traces of the same matrix with odd powers are all equal to zero. This important property of [D] has been the essence of the developed solution algorithm. The validity of the computer program coded in Fortran-77 has been verified by means of comparisons with the results given in literature. Next, the effects of the helix angle, the boundary conditions, the number of coils, and the ratio of (cylinder diameter/wire diameter) on the free vibration frequencies are investigated.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: spectral method ; Chebyshev-collocation ; Galerkin-collocation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This investigation presents a fully spectral method for solving coupled hyperbolic partial differential equations. The spectral method is based on the Galerkin-collocation technique. Two different preconditioners, the Preissmann and upwind schemes, are evaluated for their performance in solving the discretized equations. It has been found, for the cases considered, that the upwind scheme is a viable preconditioner for the fully spectral discretization of hyperbolic PDEs. Its performance as a preconditioner is in every way superior to that of the Preissmann scheme. It is established that the relative accuracy of different numerical solutions is reliably indicated by the root-mean-square average of their residuals obtained by the discretization. It is also established that the scheme gives much better accuracy than the finite-difference Preissmann scheme, for the same amount of computational effort, for both linear and non-linear problems.
    Additional Material: 8 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary element methods ; subdomain technique ; viscous fluid flow ; iterative methods ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of Navier-Stokes equations of time-dependent incompressible viscous fluid flow in planar geometry by the Boundary Domain Integral Method (BDIM) is discussed. The introduction of a subdomain technique to fluid flow problems is considered and improved in order to maintain the stability of BDIM. To avoid problems with flow kinematics computation in the sudomain mesh, a segmentation technique is proposed which combines the original BDIM with its subdomain variant and preserves its numerical stability. In order to reduce the computational cost of BDIM, which greatly depends on the solution of systems of linear equations, iterative methods are used. Conjugate gradient methods, conjugate gradients squared and an improved version of the biconjugate gradient method BiCGSTAB, together with the generalized minimal residual method, are used as iterative solvers. Different types of preconditioning, from simple Jacobi to incomplete LU factorization, are carried out and the performance of chosen iterative methods and preconditioners are reported. Test examples include backward facing step flow and flow through tubular heat exchangers. Test computation results show that BDIM is an accurate approximation technique which, together with the subdomain technique and powerful iterative solvers, can exhibit some significant savings in storage and CPU time requirements.
    Additional Material: 13 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: hierarchic models ; laminated composites ; stress-based formulation ; complementary energy ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubeke's dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed.
    Additional Material: 14 Ill.
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  • 12
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: rigid body dynamics ; Coulomb friction ; inelastic impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new time-stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro-Marques, except that the numerical formulation used here ensures that there is no inter-penetration of rigid bodies, unlike their velocity-based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three-dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: renumbering ; profile ; wavefront ; matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective hybrid renumbering method for reducing the profile and wavefront of a sparse matrix is presented. The method is an innovative combination of the classical graph theory approach and the wavefront minimization technique. A rooted level structure is generated first and the level of each node is determined. Then, for each element, the element level is defined as the minimal level of the nodes the element is connected to. Using element levels as weighting factors, the node and element numbering are then reassigned by minimizing wavefront on an element-by-element basis. The method can be used to generate node or element numbering for efficient implementation of finite element analyses using active column solvers or frontal solvers. It can also be applied to sparse matrices with a symmetric pattern of zeros. Because of the use of element levels, the entire structure of the matrix to be renumbered is taken into account during the local element-based wavefront minimization process. Therefore, the algorithm presented here combines the effectiveness of wavefront minimization schemes in local renumbering with the reliability of classical graph theory methods for global renumbering.
    Additional Material: 16 Ill.
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  • 15
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: particle tracking ; Lagrangian-Eulerian finite element methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian-Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian- Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: post-buckling ; frictional contact ; complementarity ; arc-length method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear complementarity problem formulation combined with an arc-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The arc-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc-length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints.
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: multigrid ; shell ; unstructured mesh ; finite element ; solver ; acceleration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An accelerated multigrid method, which exploits shell element formulation to speed up the iterative process, is developed for inherently poor conditioned thin domain problems on unstructured grids. Its building blocks are: (i) intergrid transfer operators based on the shell element shape functions, (ii) heavy smoothing procedures in the form of Modified Incomplete Cholesky factorization, and (iii) various two- and three-parameter acceleration schemes. Both the flat shell triangular element and the assumed strain degenerated solid shell element are considered. Numerical results show a remarkable robustness for a wide spectrum of span/thickness ratios encountered in practical applications.
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  • 18
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: plasticity ; numerical integration algorithms ; consistent linearization ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a consistent algorithm, which combines the advantages of the exact time integration of Prandtl-Reuss elastoplastic models and the quadratic asymptotic convergence of Newton-Raphson iteration strategies. The consistent modulus is evaluated by a full linearization of the exact stress update procedure. Numerical tests for a thin wall tube subjected to combined loads of tension and torsion are performed to illustrate the accuracy and efficiency of the consistently linearized exact stress update algorithm described in the paper. For comparison purpose numerical results of the radial return method are also given.
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  • 19
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: iterative methods for linear systems ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: history ; finite elements ; structural mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents summaries of the works of several authors associated with the invention of the analysis technique now referred to as the finite element method. It stresses the notion of first development from which subsequent ideas evolved and gives what is believed to be an accurate record of the historical sequence of published papers in the international literature.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: co-rotational formulation ; continua ; incompatible modes ; incompressibility ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The co-rotational technique is described for the three-dimensional analysis of continua. The technique exploits the proven technology of the best continua elements for linear analysis which are embedded into a formulation that applies an element-attached local co-ordinate frame that continuously moves and rotates with the element. The geometric non-linearity is then incorporated via the rotation of this local system. The method uses similar procedures to those recently described for 2-D continua elements but introduces concepts from a more conventional ‘continuum mechanics’ approach. The general framework for the co-rotational procedure is kept. However, a much neater formulation is derived, which readily allows the extension from two to three dimensions.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: parallel computers ; parallel software ; finite difference ; heat and moisture transfer ; unsaturated soil ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New parallel software for the analysis of coupled heat and moisture transfer in unsaturated soil is developed. The model, written in a two-dimensional polar co-ordinate formulation, is based on a finite difference self-implicit method. The code is programmed in FORTRAN with message passing libraries PARMACS and executed on a ‘Paramid’ parallel supercomputer. The validity of the parallel code by comparison of simulation results with experimentally measured values obtained from a laboratory heating experiment is examined. An assessment of the algorithm's performance on a large network of processors is also explored. It was found that the simulation results compared very well with the experimental measurements. The efficiency of the parallel code was also revealed leading to the conclusion that the algorithm was highly efficient in nature. The new parallel code was also found to be more efficient when dealing with larger problems requiring more finite difference nodal points, on a larger network of processors.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: gradient plasticity ; strain localization ; mixed strain element method ; large strain ; consistent algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense.The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived.Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary element methods ; Cauchy principal-value integrals ; Hadamard finite-part integrals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hypersingular integrals are guaranteed to exist at a point x only if the density function f in the integrand satisfies certain conditions in a neighbourhood of x. It is well known that a sufficient condition is that f has a Hölder-continuous first derivative. This is a stringent condition, especially when it is incorporated into boundary-element methods for solving hypersingular integral equations. This paper is concerned with finding weaker conditions for the existence of one-dimensional Hadamard finite-part integrals: it is shown that it is sufficient for the even part of f (with respect to x) to have a Hölder-continuous first derivative - the odd part is allowed to be discontinuous. A similar condition is obtained for Cauchy principal-value integrals. These simple results have non-trivial consequences. They are applied to the calculation of the tangential derivative of a single-layer potential and to the normal derivative of a double-layer potential. Particular attention is paid to discontinuous densities and to discontinuous boundary conditions. Also, despite the weaker sufficient conditions, it is reaffirmed that, for hypersingular integral equations, collocation at a point x at the junction between two standard conforming boundary elements is not permissible, theoretically. Various modifications to the definition of finite-part integral are explored.
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: beams ; bending ; Chebyshev approximations ; quantifier elimination ; Sturm sequences ; tensionless elastic foundation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The well-known Sturm's theorem (based on Sturm's sequences) for the determination of the number of distinct real zeros of polynomials in a finite or infinite real interval has been already used in elementary quantifier elimination problems including applied mechanics and elasticity problems. Here it is further suggested that this theorem can also be used for quantifier elimination, but in more complicated problems where the functions involved are not simply polynomials, but they may contain arbitrary transcendental functions. In this case, it is suggested that the related transcendental equations/inequalities can be numerically approximated by polynomial equations/inequalities with the help of Chebyshev series expansions in numerical analysis. The classical problem of a straight isotropic elastic beam on a tensionless elastic foundation, where the deflection function (incorporating both the exponential function and trigonometric functions) should be continuously positive (this giving rise to a quantifier elimination problem along the length of the beam) is used as an appropriate vehicle for the illustration of the present mixed (symbolic-numerical) approach. Two such elementary beam problems are considered in some detail (with the help of the Maple V computer algebra system) and the related simple quantifier-free formulae are established and seen to coincide with those already available in the literature for the same beam problems. More complicated problems, probably necessitating the use of more advanced computer algebra techniques (together with Sturm's theorem), such as the Collins well-known and powerful cylindrical algebraic decomposition method for quantifier elimination, can also easily be employed in the present approximate (because of the use of Chebyshev series expansions) symbolic-numerical computational environment.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: elastic plastic design ; contact constraints ; multilevel models ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we study the rich class of formulations that arise in the limit analysis and design of elastic/plastic structures in the presence of contact constraints. It is well-known that in the absence of contacts, both the limit analysis and limit design problems can be written as linear programs. However, when contact constraints are present, the structure effectively exhibits both softening and stiffening behaviour under monotonically increasing loading. The resulting limit analysis and limit design problems are non-convex and are difficult to solve due to the presence of complementary type of equality constraints. We show that by using a mixed form of the minimum principle, we can restate the limit analysis and limit design problems as two- and three-level formulations, respectively. Further, under a strong assumption on the problem and solution data, we can take advantage of the underlying convexity to reduce both these multilevel formulations to equivalent linear programs. While it may not be possible to always verify this assumption in practice, we show that a two-step iterative procedure is effective in reaching a solution to the limit design problem.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: singular value decomposition ; finite difference method ; modified Timoshenko equation ; dynamic model ; gear dynamics ; gear tooth testing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A piece wise continuous closed-form dynamic model of spur gear teeth meshing, using the modified Timoshenko beam equation for a stubby cantilever beam of varying cross-sectional area, is presented. The kinematics and kinetic relationships of a shaft-driven spur gear are used to determine the force on the involute surface of the gear tooth. A convenient set of equations, used to locate this force, is presented. The co-ordinates of this force are given with respect to a gear fixed coordinate system, located at the base of the gear tooth. The governing equations of motion were then numerically solved, and dynamic simulations of the gear tooth response at different gear speeds were performed. This model was then compared with the empirical data from research performed at the NASA Lewis Research Center.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: modified effective capacitance ; solidification ; tetrahedral elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new formulation for modelling solidification is discussed. The formulation has similar features to both the apparent and effective heat capacitance methods used for solidification problems where conduction predominates over other heat transfer mechanisms. The main feature of the new method is that a modified form of effective heat capacitance is calculated from the solution of non-linear equations that describe the energy loss for linear tetrahedral finite elements. This approach ensures that the predicted temperature field corresponds exactly with the energy loss and so providing an extremely stable formulation. The method is tested against a range of problems including some with non-linear liquid fractions. The predictions are compared against known analytical solutions and the method is shown to provide reasonable accuracy even for relatively large time-steps. A comparison is made between the method and the well-known temporal and spatial approximations of apparent heat capacitance, and effective capacitance. Accuracy is maintained over a greater variation in time-step and mesh density with comparable computational requirements. In addition, the method lends itself to the use of relatively simple bisection techniques for the solution of the non-linear finite element equations. Also demonstrated is the method's innate ability to predict energy loss to a high degree of accuracy for large time steps.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: optimal slewing ; finite elements ; flexible beam ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computational approach to modelling and control of a flexible beam is proposed. The structural modelling and the control design problems are formulated in a unified mathematical framework that allows simultaneous structural and control design iterations that result in an optimal overall system performance. The method employs the space-time spectral elements for simultaneous space and time discretizations of a Timoshenko beam model. Dimensionless equations of motion are derived using Hamilton's principle of variable action and an integral formulation in the framework of space-time spectral elements is introduced. An optimal control problem formulated for the continuum model is transformed by the space-time spectral element formulation into an optimization problem in a finite-dimensional parameter space. Dynamic programming is then used to obtain both open and closed loop control laws. A simulation study shows good performance of the control law applied to the nominal model. It is also demonstrated that proper discretization yields performance robustness of the system with respect to modal truncation.
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  • 32
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: shotcrete ; tunnelling ; cap model ; New Austrian Tunnelling Method (NATM) ; finite element method ; viscoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the parameter identification, verification and selected applications of a 3D viscoplastic material model for shotcrete proposed by Meschke. The performance of the shotcrete model is evaluated by means of reanalyses of short-term and creep tests on shotcrete specimen. The most essential items of a viscoplastic cap model used for the representation of soil including the determination of the model parameters are also presented. Both models are employed in a 3D finite element simulation of the excavation of a single-track tunnel driven according to the New Austrian Tunnelling Method. Comparisons between in situ measurements and numerical results are presented.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: sheet metal forming ; stress resultant ; plastic anisotropy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on Hill's quadratic orthotropic yield function, a yield function in the stress resultant space is approximated in quadratic form for sheets with planar isotropy and normal anisotropy. An equivalent stress resultant is defined and the equivalent work-conjugate generalized plastic strain rate is then derived. A power-law hardening rule between the equivalent stress resultant and generalized plastic strain is obtained under proportional straining conditions. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by finite element methods based on the stress resultant constitutive law. The results of these finite element simulations are in good agreement with those using the through-the-thickness integration method. The results also indicate that the computational time of the simulations based on the stress resultant constitutive law is much shorter than that based on the through-the-thickness integration method.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite element methods ; p-version ; singular points ; stress intensity factors ; flux intensity factors ; complementary energy ; fracture mechanics ; bi-material interfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for the computation of the generalized flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs, computed in a companion paper, characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs/GSIFs.This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.
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    Keywords: Engineering ; Engineering General
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary strip ; elastostatics ; potential problems ; BEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper develops the idea of the boundary strip method, and presents its fundamentals, merits, applications and also some closed-form or non-element solutions based on it. The present approach combines the Boundary Integral Equation Method (BIEM) and the finite strip method, taking the advantages of both. The finite strip method is installed into the BIEM by expanding the unknown parameters of problems in terms of trigonometric series. This combination creates a new powerful numerical method with three advantages over other numerical methods, namely, a shorter computation time, a better accuracy and a reduction of one and a half dimensions in mesh generation. Applications in two-dimensional potential and field problems demonstrate the efficiency and the accuracy of the proposed method. Finally, closed-form presentations for Laplace equation and elastostatics are given, along circular segments.
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    Keywords: Engineering ; Engineering General
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    Keywords: Engineering ; Engineering General
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; viscous compressible flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of generating general tetrahedral meshes suitable for use in viscous flow simulations is proposed. The approach which is followed consists of the initial generation of a number of unstructured layers of highly stretched elements, in the vicinity of solid walls, followed by the discretisation of the remainder of the domain, by a standard advancing front procedure. The numerical performance of the proposed methodology is demonstrated by the generation of meshes suitable for viscous flow analysis over a number of three-dimensional aerodynamic configurations of current practical interest.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: inverse heat conduction problem ; heat capacity determination ; non-linear problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An inverse analysis utilizing the conjugate gradient method and the minimization of adjoint equation is used successfully to estimate the temperature dependent heat capacity per unit volume in a homogeneous medium.No prior information is available on the functional form of the unknown heat capacity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that an excellent estimation on the heat capacity per unit volume can be obtained by using just boundary measurements (i.e. internal measurements are unnecessary) and the CPU time used in VAX-9420 computer is less than one second.The advantages of applying this algorithm in inverse analysis can greatly simplify the experimental set-up, diminish the sensitivity to the measurement errors and reduce the CPU time in inverse calculation, while the reliable predictions can still be achieved.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: stress elements ; Trefftz method ; fracture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation based on the approximation of the stress field is used to compute directly the stress intensity factors in crack problems. The boundary displacements are independently approximated. In each finite element, the assumed stresses may model multipoint singularities of variable order. The differential equilibrium equations are locally satisfied as solutions of the governing differential system are used to build the stress approximation basis. The approximation on the boundary displacements is constrained to satisfy locally the kinematic boundary conditions. The remaining fundamental conditions, namely the differential compatibility equations, the constitutive relations and the static boundary conditions are enforced through weighted residual statements. The approximation criteria are so chosen as to ensure that the finite element model is described by a sparse, adaptive and symmetric governing system described by structural matrices with boundary integral expressions. Numerical applications are presented to show that accurate solutions can be obtained using structural discretizations based on coarse meshes of few but highly rich elements, each of which may have different geometries and alternative approximation laws.
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    Keywords: large displacements ; finite volumes ; mixed formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses the problem of the numerical solution of beam statics undergoing large displacements. A kinematic analysis outlines the beam geometrical model through the definition of its Lagrangian co-ordinate and strain parameters. A definition of the stress parameters, a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain. The equations governing the beam equilibrium are introduced and their weak form is derived. These equations are then proved to be equivalent to the primal and mixed form of Principle of Virtual Work. The numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form. The weak-weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain. Some numerical examples prove the capability of present formulation in handling actual problems.
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    Keywords: time domainBEM ; wave equation ; space and time derivatives ; initial conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The complete expressions corresponding to space and time derivatives of Volterra's integral representation of the time-dependent scalar wave equation are presented in this paper. The concept of finite part of an integral is used in order to compute boundary kernels contributions. Time integration of boundary kernels is performed analytically for linear and constant time approximations for the potential and its normal derivative, respectively. The new integral representations presented in this text are quite general, as contributions due to the initial conditions have also been included. Two examples are presented in order to assess the accuracy of the formulation.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: consistent boundary ; far field ; radiation condition ; similarity ; soil-structure interaction ; unbounded domain ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of unbounded medium-structure interaction, the consistent infinitesimal finite-element cell method is developed for the three-dimensional vector wave equation. This is a boundary finite-element procedure. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is rigorous in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure-medium interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed. The derivation is based on the finite-element formulation and on similarity.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: eigenvalue problem ; conjugate gradient method ; Rayleigh quotient ; asymptotic analysis ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is shown that with a generally selected preconditioning matrix the actual performance of the PCG scheme may not be superior to an accelerated inverse power method. Finally, some test problems in the finite element simulation of 2-D and 3-D large scale structural models with up to 20200 unknowns are performed to examine and demonstrate the performances.
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    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: variational methods ; hybrid finite elements ; geometrical non-linearity ; shells ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear hybrid nine-node finite 2D-shell element is presented. The theoretical formulation is based on a Reissner functional in strains and displacements. The increments of which are interpolated with respect to different spatially fixed triads: both the displacement and rotation increments in the material frame (global rectangular Cartesian) and the Green-Lagrange-strain increments in a suitably chosen local rectangular Cartesian in the centroid of the considered element in the reference configuration. Corresponding transformations then deliver the components on the shell mid-surface. Although a single element possesses one spurious zero-energy mode, an assemblage performs excellently (also in comparison with a full-rank element).
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    Keywords: energy-conservation ; dynamics ; beams ; co-rotation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes an energy-conserving procedure for the implicit non-linear dynamic analysis of planar beam structures. The method is based on a form of co-rotational technique which is ‘external to the element’. A range of numerical results are presented which clearly demonstrate the improved numerical performance in comparison with more conventional techniques.
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    Chichester [u.a.] : Wiley-Blackwell
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    Keywords: transport problems ; control volumes ; finite elements ; conservation properties ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A physical approach, based on energy balances at element and at node levels, is utilized to derive both control volume and Galerkin finite element formulations of convection-type problems. This direct approach leads to the same systems of differential equations yielded by conventional formulations, but allows us to demonstrate that there are no differences in conservation properties between the two methods. Besides, we provide reliable physical interpretations for all the steps involved in standard mathematical procedures of discretization.
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    Keywords: Engineering ; Engineering General
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    Chichester [u.a.] : Wiley-Blackwell
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    Keywords: finite elements ; free-edge effects ; global-local analyses ; hierarchical displacement fields ; layerwise theory ; mesh superposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A displacement-based variable kinematic global-local finite element model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. The displacement field hierarchy contains both a conventional plate expansion (2-D) and a full layerwise (3-D) expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. The VKFE is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm. These models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free-edge effects).
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  • 54
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    Chichester [u.a.] : Wiley-Blackwell
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    Keywords: elastic buckling ; space frames ; open thin-walled cross-sections ; bending ; torsion ; warping ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A so-called exact static stiffness matrix for a uniform beam element with open thin-walled cross-section carrying an axial compressive load is derived. This stiffness matrix is useful in an accurate calculation of bifurcation loads and corresponding buckling modes of space frames built up of such beam elements. One may also calculate displacements and sectional forces caused by external joint loads taking into account the second-order effect of the axial beam loads. The exact stiffness matrix is derived by use of the general solution to a set of three coupled differential equations. This means that no preselected shape functions need be introduced and that discretization errors are avoided. The differential equations model coupled Euler-Bernoulli bending in the two principal planes and Saint-Venant/Vlasov torsion and warping with respect to the shear centre axis. No cross-sectional symmetries are assumed. Numerical examples are given. One application will be to loaded pallet racks. The ‘effective length’ for a rack column is calculated.
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    Keywords: elastoplastic ; high-accuracy ; locking-free ; low-order ; nonlinear ; three-field functional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a family of low-order high-accuracy three-dimensional brick elements. The elements are formulated via a three-field variational principle. The assumed (independent) strain field is constructed from two disjointed distributions. The first contains the lower-order distribution and its dimension is the minimum required to satisfy stability requirements. An energy constraint, which is enforced weakly at the element level, is used to relate the second distribution to the first. The stress field is chosen to a priori satisfy a similar energy constraint. As a result, internal constraints (e.g. incompressibility) are automatically satisfied by these fields, and locking behaviour is avoided. A J2-plasticity model illustrates the proposed elements' performance in nonlinear solids. The excellent performance of the proposed elements is demonstrated with numerous challenging examples, including many that are usually modelled by shell elements.
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    Keywords: Voronoi cell finite element model ; porous and composite materials ; elastoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Voronoi Cell Finite Element Model (VCFEM) has been successfully developed for materials with arbitrary microstructural distribution. In this method, the finite element mesh evolves naturally by Dirichlet Tessellation of the microstructure. Composite VCFEM for small deformation plasticity has been developed by expressing the element stresses in terms of polynomial expansions of location co-ordinates. Though this works well for discrete composites with inclusions, its effectiveness diminishes sharply for porous materials with voids. The effect worsens sharply with voids of arbitrary shapes. To overcome this limitation, a new way of defining stress functions is introduced in this paper. Based on a transformation method similar to the Schwarz-Christoffel conformal mapping, it introduces reciprocal stress functions that are derived to incorporate shape effects. Several numerical experiments are conducted to establish the strength of this formulation. The effect of various microstructural morphologies on the overall response and local variables are studied.
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    Chichester [u.a.] : Wiley-Blackwell
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    Keywords: B-spline ; finite element ; adaptable element ; membrane vibration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptable curved quadrilateral element based on quadratic B-splines is developed for finite element analysis of membrane vibration problems. The approximated displacement field in each element is divided into corners, edges and internal modes. The number of knots on the edges of elements are distinct in any integer power of 2. The elements of different resolutions can be thus connected smoothly under the constraint from the ‘two-scale relation’ of splines bases. The displacement compatibility on the interconnected edges between adjacent elements is satisfied along the whole edge. The advantages of the proposed element also result in a more adaptable element meshing strategy for structural discretization. Some numerical examples are studied as verification and demonstration of the present work.
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    Keywords: finite elements ; shell ; shell element ; warped configuration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A reformulated four-node shell element, based on the analysis of the moment redistribution mechanism development by C0 plate bending and shell elements, is presented. The moment redistribution mechanism of a finite shell element model is shown to be predominantly activated by the membrane flexural action of the shell. This action is triggered through the membrane strain components which participate in the moment equilibrium equations of the finite element assembly system. An equivalent elastic foundation action, along with the activation of the in-plane twisting stiffness of the shell, may also contribute to the moment redistribution mechanism of the finite shell element model. The proposed shell element formulation aims at retaining the non-spurious contribution of the transverse shear/membrane strain energy to the flexural behaviour of the shell, through the activation of the moment redistribution mechanism. Yet, any potentially spurious, whether locking or kinematic, mechanism is rejected. In warped configurations, the element activates appropriate coupling mechanisms of the bending terms to nodal translations. The so-obtained reformulated four-node shell element exhibits an excellent behaviour without experiencing any locking phenomena or zero-energy modes, while its formulation is kept simple, based on physical considerations. The proposed formulation performs equally well in flat as well as in warped shell element applications.
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Keywords: higher-order continua ; plasticity ; localization ; mixed elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Improved algorithms are proposed for a gradient plasticity theory in which the Laplacian of an invariant plastic strain measure enters the yield function. Particular attention is given to the type of finite elements that can be used within the format of gradient-dependent plasticity. Assuming a weak satisfaction of the yield function, mixed finite elements are developed, in which the invariant plastic strain measure and the displacements are discretized. Two families of finite elements are developed: one in which the invariant plastic strain measure is interpolated using C1-continuous polynomials, and one in which penalty-enhanced C0-continuous interpolants are used. The performance of both families of finite elements is assessed numerically in one-dimensional and two-dimensional boundary value problems. The regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated, both for mesh refinement and for the directional bias of the grid lines.
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 62
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary elements ; interelement stress ; error bounds ; post-processing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The conventional boundary element method employs piecewise shape functions which lead to stress discontinuity at the interelement boundary. This paper derives formulae for boundary stress and boundary stress gradient based on boundary element solutions, and discusses error propagation in stress evaluation due to errors in the displacement boundary values. The nature of stress discontinuity is investigated. A simple post-processing scheme is presented using continuities of stress and stress gradient along a traction boundary as two extra conditions, so that a high-order shape function can be employed for the evaluation of stress and stress gradient on the interelement boundary. Four numerical examples are used to demonstrate the accuracy of the proposed post-processing scheme. The numerical results show that as compared with the conventional method, the post-processing method can significantly improve the stress and stress gradient on the traction boundaries, especially in the area of stress concentration.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 63
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: refined nonconforming element method ; hybrid element method ; quadrilateral axisymmetric element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general approach for constituting non-conforming displacement function has been developed for axisymmetric finite element analysis and a pure non-conforming quadrilateral axisymmetric element, from a non-conforming displacement function and without any reduced integration technique, is given.Based on a proposed functional for formulating axisymmetric element and the orthogonal approach, a quadrilateral axisymmetric refined hybrid element has been presented which can be used to achieve superior performances such as higher accuracy and free from locking.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 64
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: boundary element method ; elastohydrodynamic lubrication ; layered contact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a numerical routine to compute the contact characteristics of elastomer layered cylinders lubricated by isoviscous liquids. The indentation of the elastic layer is calculated from boundary integral equations which are solved by linear and quadratic boundary element methods for a finite plane model and a circular representation of the junction. The hydrodynamic equation is also transformed into a boundary integral equation and solved by Simpson's rule. Some factors which possibly affect numerical accuracy are examined. Examples for finite plane and circular layer are analysed with reference to parameters for printing press roller contact, in which results are obtained for the indentation, film thickness and liquid pressure, as well as internal stresses through the simultaneous solution of the elasticity and hydrodynamic equations. The results show that high precision is easily achieved and the method is efficient for such layered problems.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 65
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: 3-D boundary element method ; elastoplastic analysis ; hypersingular formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3-D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.
    Additional Material: 16 Ill.
    Type of Medium: Electronic