bluuebunny/crossref_metadata_2025_split huggingface dataset:
Fast decomposition of matrices generated by the boundary element method
Authors: Rezayat Mohsen 
Published: August 2005

AbstractA new method to reduce the solution time of matrices generated by the Boundary Element Method is presented here. The method involves converting the fully populated system into a banded system by lumping certain coefficients of the matrix into fictitious nodes and then constraining these nodes to accurately represent each coefficient. The major advantages of lumping over the substructuring method are that lumping can be applied to arbitrarily shaped geometries and infinite‐domain problems and that it preserves the diagonal‐dominance of the matrix. It is shown here that the proposed algorithm reduces the rate of increase of solution time t of an n‐degree‐of‐freedom problem from t ∝ n3 to t ∝ n2. Although the algorithm is for thermal problems, its extension to mechanical problems is straightforward. The procedure can easily be incorporated into existing boundary‐element‐based packages.
An optimal method for the solution of the constrained eigenvalue/response problem for large structures comprising rigidly‐connected substructures
Authors: Garvey S. D. , Penny J. E. T. 
Published: August 2005

AbstractDynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating‐point operations which must take place and the on‐board computer memory required. The proposed method makes use of a stable co‐ordinate transformation which reduces the mass matrix for the constrained composite‐system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite‐system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.
Tetrahedral elements for fluid flow
Authors: Bertrand F. H. , Gadbois M. R. , Tanguy P. A. 
Published: August 2005

AbstractSeveral old and new tetrahedral elements are tested and compared to some classical hexahedral elements for the solution of three‐dimensional incompressible fluid flow problems. The proposed elements are created by adding velocity degrees of freedom to the basic trilinear velocity, constant pressure tetrahedron so as to satisfy the Brezzi condition. Numerical tests carried out for an artificial divergence‐free flow problem and the lid‐driven cubic cavity up to a Reynolds number of 400 are used to compare the proposed elements and assess their accuracy.
The dual boundary element method: Effective implementation for crack problems
Authors: Portela A. , Aliabadi M. H. , Rooke D. P. 
Published: August 2005

AbstractThe present paper is concerned with the effective numerical implementation of the two‐dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed‐mode crack problems can be solved with a single‐region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite‐part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack‐edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J‐integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed‐mode conditions.
Memory and operations count scaling of coupled finite‐element and boundary‐element systems of equations
Authors: Paulsen Keith D. , Liu Weiping 
Published: August 2005

AbstractMemory and operations count scaling for the solution of coupled finite‐element and boundary‐element systems of equations is considered. Three algebraic approaches for solving the hybrid set of equations are studied using both direct and iterative matrix methods. Results show that once the matrix solution technique is chosen, a single hybrid algebra emerges as a clear favourite. Interestingly, the most computationally attractive hybrid algebra under assumptions of direct solution becomes the least desirable approach when iterative methods are applied. The analysis has been carried out using a range of mesh‐dependent parameters which have been empirically derived through practical experience; however, the scaling expressions presented are valid for any mesh once these critical parameters have been determined.
The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
Authors: Zienkiewicz O. C. , Zhu J. Z. 
Published: August 2005

AbstractIn this second part of the paper, the issue of a posteriori error estimation is discussed. In particular, we derive a theorem showing the dependence of the effectivity index for the Zienkiewicz–Zhu error estimator on the convergence rate of the recovered solution. This shows that with superconvergent recovery the effectivity index tends asymptotically to unity. The superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the Zienkiewicz–Zhu error estimator to demonstrate accurate estimation of the exact error attainable. Numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient (stress) error estimation. Several examples of the performance of the error estimator in adaptive mesh refinement are also presented.
On the three‐dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds
Authors: McGee O. G. 
Published: August 2005

AbstractThe natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the Ritz method. The present work is the first known three‐dimensional study of the problem. Assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. Reasonably accurate natural frequencies are calculated for low aspect ratio, thick parallelepipeds having arbitrary degrees of twist and skewness. Detailed numerical studies show that a three‐dimensional analysis is essential in monitoring complicated coupled‐mode sensitivities in the variation of non‐dimensional natural frequencies with increasing skew and twist angles and thickness ratio. Results obtained using the present method are compared with those obtained in a detailed three‐dimensional finite element analysis, where the suitability and limitations of s‐version solid element discretizations are clearly brought out.
An assessment of four‐noded plate finite elements based on a generalized third‐order theory
Authors: Averill R. C. , Reddy J. N. 
Published: August 2005

AbstractPlate finite elements based on the generalized third‐order theory of Reddy and the first‐order shear deformation theory are analysed and compared on the basis of thick and thin plate modelling behaviour, distortion sensitivity, overall accuracy, reliability and efficiency. In particular, several four‐noded Reddy‐type elements and the nine‐noded Lagrangian and heterosis (Mindlin‐type) plate elements are analysed to assess their behaviour in bending, vibration and stability of isotropic and laminated composite plates. A four‐noded Reddy‐type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general‐purpose finite element program.
A finite element formulation for highly anisotropic incompressible elastic solids
Authors: Brádaigh Conchúr M. Ó , Pipes R. Byron 
Published: August 2005

AbstractA numerical approach is developed for the solution of problems of materials with extremely strong directions. Small deformations of a transversely isotropic linear elastic solid, reinforced by a single family of inextensible fibres, are considered. The kinematic constraint equations of incompressibility and inextensibility in the fibre direction lead to the appearance of an arbitrary hydrostatic pressure and an arbitrary tension stress in the constitutive equations. A Galerkin approach is used to discretize the virtual work and weak form of the constraint equations. Independent interpolation of the displacement, pressure and tension fields leads to a mixed system of equations, with characteristic zero‐diagonal terms. The assumption of plane stress conditions in the plane of the fibres results in a simplified displacement‐tension formulation, analogous to the primitive‐variable formulation of Stokes flow. A mixed penalty approximation is then employed to solve for displacement and tension stress fields. Computations are carried out using a biquadratic displacement element with discontinuous bilinear tension stress interpolation. The formulation is used to solve a number of simple beam problems and the results compared to closed‐form solutions.
On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure
Authors: Gupta K. K. , Lawson C. L. , Ahmadi A. R. 
Published: August 2005

AbstractThe paper first presents the details of the development of a new six‐noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution effort is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.
Local error indicator in finite element analysis of Laplacian fields based on the green integration formula
Authors: Adamiak Kazimierz 
Published: August 2005

AbstractThe paper presents a simple and practical method for the local error assessment In the finite element solution of fields in linear media governed by the Laplace equation. The local error is estimated for each node or element of the mesh model by applying the Green integration formula, with the error distribution being used for the adaptive mesh refinement. Several alternatives of the local error estimation algorithm are compared and numerical examples are given for a typical ‘L’‐section potential problem. These confirm the efficiency of the proposed method.
Sensitivity analysis for non‐linear constrained elastostatic systems
Authors: Tortorelli Daniel A. 
Published: August 2005

AbstractAdjoint and direct differentiation methods are used to formulate design sensitivities for non‐linear constrained elastostatic systems. Variations of a general response functional are expressed in explicit form with respect to all design field variations, including shape. The response functional is expressed over the undeformed configuration; however, the displacement gradient is included so that field quantities that are defined over the deformed configuration, such as Cauchy stress, may be modelled. The finite element method is used to evaluate the sensitivities in an example problem.
p‐Version plate and curved shell element for geometrically non‐linear analysis
Authors: Sorem Robert M. , Surana Karan S. 
Published: August 2005

AbstractThis paper presents a p‐version geometrically non‐linear formulation based on the total Lagrangian approach for a nine node three dimensional curved shell element. The element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction. The element approximation functions and the corresponding nodal variables are derived from the Lagrange family of interpolation functions. The resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures C° continuity.The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete three dimensional stresses and strains are considered, hence the element is equally effective for very thin as well as extremely thick shells and plates.Incremental equations of equilibrium are derived and solved using the standard Newton–Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the literature.
A finite element formulation with stabilization matrix for geometrically non‐linear shells
Authors: Kim J. H. , Lee S. W. 
Published: August 2005

AbstractAn assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non‐linear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement‐dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine‐node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation.
Element by element a posteriori error estimation of the finite element analysis for three‐dimensional elastic problems
Authors: Ohtsubo Hideomi , Kitamura Mitsuru 
Published: August 2005

AbstractAn a posteriori error estimation method for finite element solutions for three‐dimensional elastic problems is presented based on the theory developed by the authors for two‐dimensional problems.1 The error is estimated for the finite element solutions obtained using three‐dimensional 8‐node elements with a linear interpolation function in an arbitrary hexahedron. The method is successfully applied to three‐dimensional elastic problems. In order to decrease computing time and memory use, the error is estimated element by element. The major difficulty in the element‐wise error estimation technique is satisfying the self‐equilibrium condition of applied forces, especially in three‐dimensional problems. These forces are mainly due to traction discontinuity on the element boundaries. The difficulty is circumvented by employing an element‐wise optimal procedure. It is also shown that a very accurate stress solution can be obtained by adding estimated error to the original finite element solutions.
The use of dynamic data structures in finite element applications
Authors: Hawken D. M. , Townsend P. , Webster M. F. 
Published: August 2005

AbstractThe derivation of more efficient algorithms for finite element applications is not the primary goal of this article, but rather the efficient implementation of existing algorithms using dynamic data structures. In some cases the algorithms may be far from optimal, but serve to illustrate the advantages of dynamic data structures. In the first section, a tree data structure termed a PATRICIA tree is described and is shown to be suitable for storing data associated with finite element meshes. The manner in which the tree is constructed guarantees to provide rapid data retrieval times, competitive with those associated with static array data structures, whilst providing the added advantages of a dynamic data structure. The second section introduces a list of lists (LOL) data structure which is used to produce an efficient implementation of an example of a bandwidth reduction algorithm. Furthermore, the LOL data structure is also shown to be appropriate for implementing a novel method for extracting the domain boundary, with its orientation, from a given finite element connectivity matrix.
Arbitrary Lagrangian‐Eulerian finite element analysis of large deformation in contacting bodies
Authors: Ghosh Somnath 
Published: August 2005

AbstractThe primary aim of this research is to implement the arbitrary Lagrangian–Eulerian finite element description to model large deformation of interacting bodies. A pure Lagrangian description is often incapable of representing their contact with sufficient precision. In this work, the arbitrary Lagrangian‐Eulerian (ALE) description has been extended to the surface nodes of interacting bodies to overcome these limitations. A penalty formulation has been implemented to account for the impenetrability constraint. The materials have been characterized as elastic‐viscoplastic. Implicit integration schemes have been used at the global and constitutive levels for'improved stability.
A finite element for variable order singularities based on the displacement formulation
Authors: Maiti S. K. 
Published: August 2005

AbstractAn element for analysis of variable order one point singularities in plane problems has been proposed. The element meets all the convergence requirements, viz. the rigid body mode, the constant strain condition and the interelement compatibility. It can be easily incorporated in any package based on the displacement formulation. Four examples from fracture mechanics are presented to demonstrate its performance. The examples involve mechanical or thermal loadings. The accuracy of results in all the examples is very good.
Unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems
Authors: Saetta Anna V. , Vitaliani Renato V. 
Published: August 2005

AbstractA new partitioned solution procedure for the direct time integration of second order coupled‐field systems is presented and it is applied to the problem of soil–pore fluid interaction. The necessary convergence analysis for the iterative method is carried out and the fulfilment of the convergence condition is achieved with the introduction of two suitable auxiliary matrices in the basic equations governing the dynamic phenomena. Numerical examples are presented to demonstrate the effectiveness and the versatility of the proposed solution procedure.
The problem of the selection of an a posteriori error indicator based on smoothening techniques
Authors: Babuška Ivo M. , Rodriguez Rodolfo 
Published: August 2005

AbstractThis paper addresses the problem of assessing the quality of an a posteriori error estimate of a finite element solution. An error estimate based on local L2‐projections is analysed in the case of translation‐invariant meshes. It is shown that for general meshes this technique does not lead to an asymptotically exact estimator. The problem is analysed in detail in the one‐dimensional setting. It is shown that an asymptotically exact estimator is not the optimal one when the solution is not sufficiently smooth. An optimal estimator for adaptively constructed meshes is given. Finally, a general mathematical framework for the quality assessment of estimators is introduced.
An augmented Lagrangian method for discrete large‐slip contact problems
Authors: Heegaard J.‐H. , Curnier A. 
Published: August 2005

AbstractAn augmented Lagrangian formulation is proposed for large‐slip frictionless contact problems between deformable discretized bodies in two dimensions. Starting from a finite element discretization of the two bodies, a node‐on‐facet element is defined. A non‐linear gap vector and its first variation are derived in terms of the nodal displacements. The relevant action and reaction principle is stated. The gap distance is then related to the conjugate pressure by a (multivalued non‐differentiable) unilateral contact law. The resulting inequality constrained minimization problem is transformed into an unconstrained saddle point problem using an augmented Lagrangian function. Large slip over several facets is possible and the effects of target convexity or concavity are investigated. A generalized Newton method is used to solve the resulting piecewise differentiable equations necessary for equilibrium and contact. The proper tangent (Jacobian) matrices are calculated. The primal (displacements) and dual (contact forces) unknowns are simultaneously updated at each iteration.
A bilinear shell element with the cross‐reduced integration technique
Authors: Zhong Zhi‐Hua 
Published: August 2005

AbstractA bilinear shell element is presented. The element is based on the concepts of laminas and fibres. A cross‐reduced integration technique is used to carry out the element integration. In this reduced integration technique, the Gauss points are chosen both on the reference lamina and along the central fibre. Spurious shear strains are averaged on the reference lamina to solve the shear locking problem and to eliminate any zero‐energy mode associated with the rotational degrees of freedom. Due to the integration on the reference lamina, zero‐energy modes associated with the translational degrees of freedom can also be removed. The behaviour of the element is examined in several numerical examples with various loading conditions and boundary conditions.
A rectangular finite element for analysing composite multilayered shallow shells in statics, vibration and buckling
Authors: Beakou A. , Touratier M. 
Published: August 2005

AbstractThis paper presents a new 32‐degree‐of‐freedom finite element of multilayered composite, moderately thick, shallow shells. The element is a four‐node C1 rectangular element and is built from standard interpolations but with a new kind of kinematics which allows us to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of a laminated structure and the boundary conditions at the upper and lower surfaces of the shell. The transverse shear deformation which is represented by cosine functions is of a higher order and allows us to avoid shear correction factors. The element is evaluated on standard problems and in comparison with exact three‐dimensional and analytical solutions for multilayered plates and shells in statics, vibrations and stability.