bluuebunny/crossref_metadata_2025_split huggingface dataset:
An alternative numerical procedure for simulating the dynamical response of non‐linear elastic rods
Authors: Da Gama Rogério martins Saldanha 
Published: August 2005

AbstractIn this paper there is presented an alternative numerical procedure for obtaining approximations to non‐linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress–strain relation is non‐linear). The above‐mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic‐non‐linear rod, fixed at its edges, that is left in a non‐equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.
A non‐proportional loading finite element analysis of continuum damage mechanics for ductile fracture
Authors: Wang June , Chow C. L. 
Published: August 2005

AbstractThis paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non‐proportional loading. The condition of non‐proportional loading is formulated by introducing a dynamic co‐ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.The finite element analysis developed under non‐proportional loading is applied to predict the crack initiation load of a centre‐cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre‐cracked thin plates made of aluminium alloy 2024‐T3. The analysis also reveals under non‐proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
The generalized boundary element approach to Burgers' equation
Authors: Kakuda Kazuhiko , Tosaka Nobuyoshi 
Published: August 2005

AbstractThe generalized boundary element method is presented for the numerical solution of Burgers' equation. The new method is based on the set of boundary integral equations derived for each subdomain by using the fundamental solution for the linearized differential operator of the equation. The resulting system of quasi‐non‐linear equations is solved implicitly with use of a simple iterative procedure. The adaptability and the accuracy of the proposed method are demonstrated by three examples and a comparison of the numerical results with the exact solution or other existing solutions is shown for the first example.
Higher derivative explicit one step methods for non‐linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods
Authors: Hoff C. , Taylor R. L. 
Published: August 2005

AbstractA generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor–corrector scheme suitable for arbitrary non‐linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non‐linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non‐linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.
Studies in anisotropic plasticity with reference to the Hill criterion
Authors: De Borst René , Feenstra Peter H. 
Published: August 2005

AbstractAlgorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso‐error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.
Inelastic transient dynamic analysis of three‐dimensional problems by BEM
Authors: Ahmad S. , Banerjee P. K. 
Published: August 2005

AbstractA direct Boundary Element formulation and its numerical implementation for inelastic transient dynamic analysis of three‐dimensional solids is presented. The formulation is based on an initial stress approach and is the first ever of its kind in the field of the Boundary Element Method. This formulation employs the Navier–Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution and the Divergence theorem, together with Kinematical and Constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity. The boundary integral equations are cast in an incremental form, in which elastoplastic relations of the incremental type are used for the material description. These equations are then solved using a time‐stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations. Higher order shape functions are used to approximate the field quantities in space as well as in time. Finally, the applicability of this methodology is demonstrated by presenting a few example problems.
Automatic step size correction for non‐associated plasticity problems
Authors: Van Langen H. , Vermeer P. A. 
Published: August 2005

AbstractThe finite element method is used in calculating accurate collapse loads. The behaviour of granular materials is described by the non‐associated Mohr–Coulomb model. The load–displacement path is traced up to and beyond limit points using an accelerated initial stiffness method. The convergence properties of this method are examined, both for associated and non‐associated plasticity.Step sizes in the incremental iterative procedure are adapted during the iteration process, depending on an estimated number of iterations. The automatic step size control thus obtained proves to be robust and particularly appropriate for non‐associated plasticity. Some soil collapse calculations are discussed to demonstrate the practical application of the method.
A new approach in non‐linear mechanics: The large time increment method
Authors: Boisse Ph. , Bussy P. , Ladeveze P. 
Published: August 2005

AbstractA new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non‐linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
A finite‐element model of two‐layer ocean circulation
Authors: Bermejo R. 
Published: August 2005

AbstractA mixed finite‐element formulation is applied to solve the quasi‐geostrophic equations in a two‐layer ocean domain enclosed by solid boundaries. A combination of leap‐frog and θ‐schemes is used to integrate the equations in time. Wood's formula of the wall vorticity is derived in our formulation for the case of square elements adjacent to the boundaries. Long‐term computations with and without lumping have been carried out.
The multigrid method in solid mechanics: Part I—Algorithm description and behaviour
Authors: Parsons I. D. , Hall J. F. 
Published: August 2005

AbstractA multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some two dimensional problems to evaluate its strengths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees‐of‐freedom in the discretization, characteristics of the algorithm, Poisson's ratio when it is close to 0·5, the amount of bending deformation in the problem under consideration, and the degree of non‐uniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees‐of‐freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees‐of‐freedom and still depends on the other factors listed above.
Contact problems of kinked cracks modelled by a boundary integral method
Authors: Zang W. L. , Gudmundson P. 
Published: August 2005

AbstractBased on the integral equation for the resultant forces along a crack, a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account. The method is demonstrated by a consideration of an elastic half‐plane containing a piece‐wise straight line crack. Two numerical examples are presented and compared to finite element calculations. The numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact.
A finite element formulation for the coupled thermoviscoelastic response of solid–fluid systems
Authors: Lévesque D. , Bertrand L. 
Published: August 2005

AbstractThe coupled thermoviscoelastic response of a solid–fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
Free vibration of axisymmetric solids by BEM using particular integrals
Authors: Wang Hui‐Ching , Banerjee Prasanta K. 
Published: August 2005

AbstractThe free vibration of solids of revolution had never been solved by the Boundary Element Method (BEM) until a previous paper10 by the authors, in which the BEM was combined with the method of particular integrals to solve axisymmetric free vibration problems. In this paper the previously developed analysis is extended to study the non‐axisymmetric free vibration of axisymmetric solids. The developed analysis has been implemented in a general purpose BEM system. Free vibrations of solid and hollow cylinders, a hyperbolic cooling tower and a gas turbine shell are used as examples, and their results are compared with those given by other methods. Except for low modes of very thin shells, good agreement can be seen.
Time‐domain radiation boundary for analysis of plane Love‐wave propagation problem
Authors: Anandarajah A. 
Published: August 2005

AbstractA new method of modelling the radiation effect in a time‐domain finite element analysis of semi‐infinite solids is proposed. The domain to be analysed is divided into a finite, interior region and a semi‐infinite, exterior region. The standard finite elements are used to model the interior region. An infinite element is used to model the semi‐infinite region. The main feature of the proposed method is the selection of semi‐infinite shape functions to develop the infinite element. A procedure is proposed whereby the necessary shape functions are derived directly from frequency‐domain analytical mode shapes. The interior and exterior regions are coupled by enforcing displacement continuity at the interface. The validity of the method is demonstrated in this paper by analysing a two‐dimensional, linear (damped), anti‐plane, shear‐wave (plane Love‐wave) propagation problem. The results obtained by the proposed method are compared with those obtained by direct finite element analysis with a fixed boundary placed sufficiently far from the location of loading to avoid wave reflections.
Automatic conversion of triangular finite element meshes to quadrilateral elements
Authors: Johnston Bruce P. , Sullivan John M. , Kwasnik Andrew 
Published: August 2005

AbstractA method is presented for the fully automatic conversion of a general finite element mesh containing triangular elements into a mesh composed of exclusively quadrilateral elements. The initial mesh may be constructed of entirely triangular elements or may consist of a mixture of triangular and quadrilateral elements. The technique used employs heuristic procedures and criteria to selectively combine adjacent triangular elements into quadrilaterals based on preestablished criteria for element quality. Additional procedures are included to eliminate isolated triangles. The methods operates completely without user intervention once the nodal co‐ordinates and element connectivity of the original mesh are supplied.
An adaptive descent method for non‐linear viscoplasticity
Authors: Eggert Geoffrey M. , Dawson Paul R. , Mathur Kapil K. 
Published: August 2005

AbstractA forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non‐linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate‐insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non‐linear solution algorithm has traditionally hampered their use.
Accurate integration of singular kernels in boundary integral formulations for Helmholtz equation
Authors: Ramesh P. S. , Lean M. H. 
Published: August 2005

AbstractBoundary integral formulations for the 2D Helmholtz equation involve kernels in the form of modified Bessel functions. Accurate schemes for evaluating integrals of the kernels and their derivatives are presented. Special attention is paid to integrals involving singular and near singular kernels. Both boundary and domain integrals are considered. It is shown that, with the use of series expansion functions for the modified Bessel functions, the boundary integrals can be evaluated analytically in the neighbourhood of the singularity. For domain integrals, the behaviour of the kernels in the vicinity of the singularity is used to construct accurate numerical quadrature schemes. A transient heat conduction problem is formulated as a Helmholtz equation, solved, and compared against analytic solution to demonstrate the effectiveness of these schemes in relation to traditional methods. References are made to previous work to advocate the utility of the boundary integral method for non‐linear and time‐transient problems.
Optimization analysis of the four‐level‐time schemes
Authors: Shayya Walid H. , Segerlind Larry J. , Bralts Vincent F. 
Published: August 2005

AbstractA procedure was implemented to determine some optimum values for the parameters of the four‐level‐time scheme which can be utilized for the numerical solution of a system of ordinary differential equations. A multi‐variable search method was employed to estimate these optimum parameters. Two different optimization studies were performed. The resultant optimum four‐level‐time schemes produced very accurate results, satisfied physical reality, and did not produce any oscillations for the specific problems that were studied. The optimum values for the three parameters α, β and γ in the four‐level‐time scheme were α = 16.72, β = 6.26 and γ = 2.46. The optimum value of θ for the Wilson‐θ method was θ = 1.42. The optimum schemes were compared to some existing four‐level‐time schemes. The outcome demonstrated that the optimum schemes were superior. The Houbolt method and the Galerkin weighting procedure were shown to have greater inaccuracies than the optimum schemes.
On a new iterative approach of component mode synthesis
Authors: Xu Keqin , Luo Zhenhuang , Han Zushun 
Published: August 2005

AbstractA wholly new concept of intermediate structure is developed in this paper. Based on this, a new component mode iteration (CMI), or subdomain subspace iteration method, is proposed.In the new CMI method, the ordinarily required step of ensuring interface compatibility is eliminated. An outstanding achievement of this method is that it retains the merit of the standard subspace iteration (SSI) technique concerning the number of vectors required in computation. In the present method iteraton is carried out at subdomain levels. On machines capable of parallel processing, this work can be performed simultaneously.Numerical examples clearly demonstrate the excellence of this new method.
Application of the boundary element method to transient heat conduction
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractAn advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher‐order conforming elements, self‐adaptive integration and a multiregion capability. Planar, three‐dimensional and axisymmetric analyses are all addressed with a consistent time‐domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM., Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain‐based methods.
Efficient evaluation of the flexibility of tapered I‐beams accounting for shear deformations
Authors: Vu‐Quoc L. , Léger P. 
Published: August 2005

AbstractThe principle of complementary virtual work is used to evaluate numerically the flexibility matrix of tapered I‐beams accounting for shear deformations. Equilibrium considerations of the top and bottom fibres reveal that the shear stress is not equal to zero at these locations. To correct for this non‐vanishing shear, a statically admissible shear stress field is considered by assuming a parabolic distribution of shear stress which takes non‐zero values at the top and bottom fibres such that the global equilibrium is satisfied within the assumed stress profile. The flexibility matrices of the proposed tapered I‐beam finite element with different slopes are generated using numerical integration based on Gauss quadrature. The results are compared to full‐blown shell finite element models, and stepped beam models constituted by a series of uniform beam elements, to illustrate the effectiveness of the proposed method.
Postintegration methods for numerical integration of non‐linear dynamic equations of motion
Authors: Langer Jan , Klasztorny Marian , El‐Bagalaty' Salah El‐Sayed 
Published: August 2005

AbstractThe paper presents a family of methods with postintegration, for numerical integration of non‐linear dynamic equations of motion of discrete systems. Both explicit and implicit algorithms of these methods are conditionally stable, but can give solutions of accuracy of a few orders higher than the known methods with preintegration, corresponding to them. A general analysis of stability and accuracy of single‐step methods is carried out. The postintegration methods have been tested on a single‐degree‐of‐freedom non‐linear system.
An integration scheme for Prandtl‐Reuss elastoplastic constitutive equations
Authors: Gratacos P. , Montmitonnet P. , Chenot J. L. 
Published: August 2005

AbstractWe investigate the Generalized Midpoint Rule for the time integration of elastoplastic constitutive equations for pressure‐independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation, the solution of which reduces to one single scalar equation in the plastic multiplier. The existence and uniqueness of an incremental solution is discussed. The pressure/deviator decomposition is the basis for reduced integration of the pressure term in the Principle of Virtual Work, in order to avoid locking and spurious pressure oscillations. It is also shown that an optimal choice of the parameter of the Midpoint Rule can be computed by reference to the analytical solution of the equations assuming no work hardening. A benchmark test shows that this choice allows increased time steps. This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen, and a comparison with the analytical solution is performed. Finally, the hypothesis which sustains these formulations of elastoplasticity (constant strain rate during an increment) is discussed with reference to elastic unloading and residual stress computation.
SIMD implementation of a non‐linear transient shell program with partially structured meshes
Authors: Belytschko Ted , Plaskacz Edward J. 
Published: August 2005

AbstractThe implementation of an explicit transient program for the three‐dimensional non‐linear finite element analysis of shells on a massively parallel SIMD computer, the CONNECTION Machine, is described. Particular emphasis is placed on interprocessor communication using router and NEWS schemes. A hybrid communication scheme, where NEWS is used within structured subdomains and the router is used to exchange nodal forces between subdomains, is examined. It is shown that the ‘mesh‐structure index’ of most large meshes is sufficient to make hybrid schemes effective and this is verified by computer runs. Some benchmark non‐linear calculations with 8K to 32K elements are also presented.
Eight nodes or nine?
Authors: Macneal Richard H. , Harder Robert L. 
Published: August 2005

AbstractThe chief advantage claimed for nine‐noded shell elements is that they can pass constant curvature patch tests with bilinear element geometry while eight‐noded shell elements cannot. It is shown that a simple modification of the shape functions of an eight‐noded element can make this advantage disappear. Test results confirm this result and show that the performance of a modified eight‐noded element is similar to that of recently reported nine‐noded elements.