bluuebunny/crossref_metadata_2025_split huggingface dataset:
A critical analysis of quadratic beam finite elements
Authors: Rakowski Jerzy 
Published: August 2005

AbstractA new methodology of evaluation of C0 beam elements is presented. It is shown that, knowing the stiffness matrix of an arbitrary type of element, it is possible to create equivalent equilibrium conditions expressed in the form of one difference equation for a regular beam discretized by these elements. The study of the convergence of one difference equation gives an interpretation of the source of troubles occurring in low‐order bending elements which is more convincing than the usually applied consideration of the conditioning of element stiffness matrices. A careful examination of quadratic Mindlin elements provides a very clear explanation of the shear locking essence in the Timoshenko beam. The presented method enables one to identify errors that appear also in the reduced integrated or constrained elements. For each type of analysed quadratic element an adequate difference equation is derived and compared with the exact one. Based on this comparison a simple method of corrections is proposed that completely eliminates the errors associated with the application of C0 bending elements.
Linear‐non‐linear dynamic substructures
Authors: Leung A. Y. T. , Fung T. C. 
Published: August 2005

AbstractThe dynamic substructure method is extended to linear and non‐linear coupling systems. Only those master co‐ordinates with non‐linear nature (non‐linear co‐ordinates) are retained. Other slave co‐ordinates relating to the linear part (linear co‐ordinates) are eliminated by the dynamic substructure method. The dynamic flexibility matrix associated with the linear co‐ordinates is first expanded in terms of the fixed interface natural modes. The condensed dynamic stiffness‐matrix associated with the non‐linear co‐ordinates is formed subsequently. The convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and Taylor series expansion. To find the steady state solutions, the non‐linear responses are expanded into a Fourier series. Responses of the linear co‐ordinates are related to the non‐linear co‐ordinates analytically. To solve for the unknown Fourier coefficients, the harmonic balance method gives a set of non‐linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients. A Newtonian algorithm is adopted to solve for the unknown Fourier coefficients iteratively. The computational cost of a non‐linear analysis depends heavily on the number of degrees of freedom encountered. In the method, the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced.
Delaunay versus max‐min solid angle triangulations for three‐dimensional mesh generation
Authors: Joe Barry 
Published: August 2005

AbstractThe Delaunay triangulation has been used in several methods for generating finite element tetrahedral meshes in three‐dimensional polyhedral regions. Other types of three‐dimensional triangulations are possible, such as a triangulation satisfying a local max‐min solid angle criterion. In this paper, we present experimental results to show that max‐min solid angle triangulations are better than Delaunay triangulations for finite element tetrahedral meshes, since the former type of triangulations contains tetrahedra of better shape than the latter type. We also describe how mesh points are generated and triangulated in our tetrahedral mesh generation method.
Buckling under combined loading of shear deformable laminated anisotropic plates using ‘infinite’ strips
Authors: Zeggane Madjid , Sridharan Srinivasan 
Published: August 2005

AbstractAn efficient formulation is presented to predict the buckling under combined loading of relatively long shear deformable laminated anisotropic plates. The numerical formulation is based on a semi‐analytical Reissner‐Mindlin ‘infinite’ strip. The effect of shear locking is eliminated by the use of higher Lagrangian polynomials. The deterioration of Kirchhoff theory (classical plate theory (CPT)) in the case of moderately thick anisotropic plate is highlighted. A complete convergence study of the present theory was carried out and the accuracy of the method is demonstrated by comparison with the published results.
Adaptive error analysis in seepage problems
Authors: Burkley V. J. , Bruch J. C. 
Published: August 2005

AbstractNumerical experiments in adapting variations of a computationally simple error estimator (the Zienkiewicz‐Zhu estimator) to an existing finite element code are shown. The error estimator used allows both overall and local errors to be estimated. From the local estimates of error, refinements of the mesh are calculated to reach a prescribed error tolerance. These calculated refinements are used by a mesh refiner to produce a modified mesh which lowers the overall error to the prescribed value while keeping the mesh as crude as possible. The physical example on which these numerical experiments are performed is that of free surface flow through an earth dam with a toe drain. It is also shown how the problem formulation affects the error analysis and how the choice of computational scheme affects the mesh adaptation.
Self‐adaptive space and time grids in device simulation
Authors: Nanz G. , Kausel W. , Selberherr S. 
Published: August 2005

AbstractFor the solution of the three basic semiconductor equations in two space dimensions fully self‐adaptive grids are a powerful tool to optimize the ratio between the number of unknowns and the accuracy of the solution. For the method of finite differences hardly any mathematically founded criterion for automatic grid control can be given which can be implemented in a computer program with acceptable effort. Therefore most of the strategies for self‐adaptive grid control are totally heuristic or derived from physical properties.In this paper we present criteria for the design of an initial space grid. We discuss some conventional strategies for the automatic control of space grids (e.g. equidistribution of the local discretization error) and present new criteria (e.g. degree of coupling of the equations, physical properties like net generation rate). For the time grid an automatic step length control algorithm is presented and the interaction between space and time grid is analysed. Throughout the paper the results are illustrated by realistic examples.
Linearization of dynamic equations of flexible mechanisms—a finite element approach
Authors: Jonker Ben 
Published: August 2005

AbstractA finite element based method is presented for evaluation of linearized dynamic equations of flexible mechanisms about a nominal trajectory. The coefficient matrices of the linearized equations of motion are evaluated as explicit analytical expressions involving mixed sets of generalized co‐ordinates of the mechanism with rigid links and deformation mode co‐ordinates that characterize deformation of flexible link elements. This task is accomplished by employing the general framework of the geometric transfer function formalism. The proposed method is general in nature and can be applied to spatial mechanisms and manipulators having revolute and prismatic joints. The method also permits investigation of the dynamics of flexible rotors and spinning shafts. Application of the theory is illustrated through a detailed model development of a four‐bar mechanism and the analysis of bending vibrations of two single link mechanisms in which the link is considered as a rotating flexible arm or as an unsymmetrical rotating shaft, respectively. The algorithm for the calculation of the matrix coefficients is directly emenable to numerical computation and has been incorporated into the linearization module of the computer program SPACAR1.
Stabilization by non‐conforming modes: 9‐node membrane element with drilling freedom
Authors: Kebari H. , Cassell A. C. 
Published: August 2005

AbstractA simple technique of stabilizing spurious zero energy modes by non‐conforming modes is presented. The non‐conforming modes are derived by removing one or a number of nodes from the original element, and hence the associated stiffnesses are used to stabilize a uniform reduced integrated 9‐node element. Three models were pursued to control the communicable spurious modes. The proposed model has been on the basis of including drilling freedoms and retaining much of the excellent performance of the original 9‐node element with uniform reduced integration.The drilling freedoms are incorporated by constraining the true continuum mechanics definition of rotation at the reduced integration points by the penalty function method.A patch test was applied and a considerable number of problems were tested to investigate the performance of the new element.
Equivalent homogeneous finite element for composite materials via reissner principle. Part I: Finite element for plates
Authors: Peseux B. , Dubigeon S. 
Published: August 2005

AbstractThe stiffness matrix in the finite element method for multi‐layered materials is generally computed by expressing the strain energy in each layer and adding them together. In order to lower the computing time, which may be prohibitive if the number of layers is high, and to get accurate information on the stresses, especially on transverse shear stresses, we present a new finite element using the Reissner principle. In the first part the case of plates will be detailed: extensions to shell problems will be presented in the second part. The efficiency of the method is tested on a special analytic solution, and some examples are given.
Equivalent homogeneous finite element for composite materials via reissner principle. Part II: Finite element for shells
Authors: Peseux B. , Dubigeon S. 
Published: August 2005

AbstractThe lateral hulls of multi‐shelled ships such as Catamarans or Trimarans can be considered as rigid solids, or compared to thin walled beams in multi‐layered materials for the global statical or dynamical behaviour of the ship. Unfortunately this approximation no longer hold after a detailed study of the hulls.Working in these problems we proceed to a fine analysis of the stress field at the neighbourhood of the linkage shell‐arm or of the holes for access input to the hull itself. Analysis with a beam model is inadequate and the shell theory must be more appropriate. Numerous papers have been devoted to shell elements, see References 1 to 8 to mention just a few. Some of them require a reduced or selective integration scheme.9‐12 We choose to start from the Ahmad element, 13, 14 which is suitable for moderate thick shells.15.16 The final aim of this paper is to explain how to build up a multi‐layered equivalent homogeneous shell element which is both economical and accurate. Some examples will be given and compared with those obtained with the Ahmad finite element.
Iterative solution techniques in boundary element analysis
Authors: Kane J. H. , Keyes D. E. , Prasad K. Guru 
Published: August 2005

AbstractIterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single‐ and multi‐zone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multi‐zone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods. To characterize the potential of these iterative techniques, we discuss accuracy, storage and timing statistics in comparison with analogous information from direct, sparse blocked matrix factorization procedures. Matrix populations that experience block fill‐in during the direct decomposition process are included. With different degrees of preconditioning, iterative equation solving is shown to be competitive with direct methods for the problems considered.
Shifted integration technique in one‐dimensional plastic collapse analysis using linear and cubic finite elements
Authors: Toi Yutaka 
Published: August 2005

AbstractThe present study is concerned with the physical explanations of the linear and the cubic finite elements for beams and axisymmetric shells through comparisons of their strain energy approximations with those of the Rigid Bodies‐Spring Models which are discrete elements suitable for plastic collapse analysis using the concepts of plastic hinges and hinge lines. The established conditions for the equivalence between these two modellings, which are given as the relations between the locations of the numerical integration points and those of the occurrence of plastic hinges, can be conveniently used in the economical plastic collapse analysis of framed structures and axisymmetric shells where the locations of plastic hinge formations are controlled by the movement of numerical integration points. Some numerical results are shown in order to prove numerically the obtained relations and to verify the validity of the proposed shifting technique of numerical integration points, which is identified as ‘the shifted integration technique’ in the present paper.
Characteristics of subspace in reduced basis technique
Authors: Tao Dahong , Ramm Ekkehard 
Published: August 2005

AbstractIn the reduced basis technique the coefficients of global shape functions are taken as generalized degrees of freedom. The non‐linear system is solved iteratively in a reduced subspace using considerably less unknowns. This paper investigates the characteristics of the reduced system, the relationship between the reduced system and the main system, the criterion to judge the critical point with reduced quantities and the criterion of convergence in the reduced subspace.
A boundary element method for steady incompressible thermoviscous flow
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractA boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modelling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.
On first‐ and second‐order moderate rotation theories of laminated plates
Authors: Sacco E. , Reddy J. N. 
Published: August 2005

AbstractThe first‐ and second‐order, small strain and moderate rotation, theories of anisotropic laminated plates are developed and numerically evaluated. Beginning with an assumed displacement field and introducing various order‐of‐magnitude assumptions, the governing equilibrium equations of laminated plates are derived from the principle of virtual displacements. The finite‐element formulation for the second‐order moderate rotation theory is developed, and numerical results are presented to evaluate the new plate theories in comparison with the von Kàrmàn plate theory with shear deformation. For comparison purposes, the 2‐D elasticity theory with full non‐linearity is also analysed using the finite element method. It is found that the second‐order theory with moderate rotations is closest to the 2‐D finite elasticity theory.
On grid refinement at point singularities for h‐p methods
Authors: Chen A. T. , Rice J. R. 
Published: August 2005

AbstractThe h‐p method for solving partial differential equations uses discretizations where the grid size h and the polynomial degree p are varied to obtain the most efficiency in the computing of approximate solutions. It has been known for many years that increasing p can dramatically improve efficiency and that the current common practice of keeping p = 1 is a particularly poor choice. For problems with singularities, good efficiency requires that the grid be refined near the points with singularities so the h‐p method also requires a grid refinement scheme. We compare two such schemes here which we call E‐Refinement (proposed by Babuska and colleagues recently) and Q‐Refinement (proposed by Rice in the 1960's). Both of these schemes have been shown to have asymptotically optimal order of convergence.The actual behaviours of these two schemes are quite different in practice and the mechanisms for choosing good values of h, p and the grid refinement parameters are also quite different. This paper presents the results of a systematic experimental study of these two methods and discusses the difficulty of choosing highly efficient h, p and grid refinement parameters. Our study confirms that these two refinements are of approximately equal efficiency given such good choices. The data suggest that the Q‐Refinement is more efficient but the advantage is not dramatic given the uncertainties inherent in choosing numerical methods for practical applications. We conclude that it is substantially simpler to make good choices for the Q‐Refinement than for the E‐Refinement.
Treatment of internal constraints by mixed finite element methods: Unification of concepts
Authors: Weissman Shmuel L. , Taylor Robert L. 
Published: August 2005

AbstractA general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented. The assumed fields are constructed in such a way that internal constraints are satisfied a priori. Consequently, the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided. To this end, the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations, thus avoiding Fraeijs de Veubeke's limitation principle. Results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated.
Numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points
Authors: Chrysakis A. C. , Tsamasphyros G. 
Published: August 2005

AbstractAn integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of order n (hence of polynomial accuracy 2n− 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄k, determined as roots of appropriate transcedental functions, in order to retain the 2n − 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so that xk may be arbitrary and yet the high (2n − 1) accuracy of the Gaussian quadrature is retained.
Stabilized rapidly convergent 18‐degrees‐of‐freedom flat shell triangular element
Authors: Fish Jacob , Belytschko Ted 
Published: August 2005

AbstractA rank‐sufficient flat triangular shell element with drilling degrees‐of‐freedom is described. A variational basis for this element has been provided by a three‐field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling problems.
Integration of Tresca and Mohr–Coulomb constitutive relations in plane strain elastoplasticity
Authors: Sloan S. W. , Booker J. R. 
Published: August 2005

AbstractThis paper considers the problem of integrating the constitutive relations for Tresca and Mohr–Coulomb materials under conditions of plane strain. In the case of a Tresca material, we show that the constitutive law may be integrated exactly by assuming the strain rates dϵ/dλ to be constant. We also derive a semi‐analytic method for integrating both types of constitutive law which assumes that the quantities dϵ/dλ are constant. This approach is motivated by the fact that the exact variation of the strains during a time interval is unknown and leads to a single non‐linear equation in λ which can be solved efficiently to yield the unknown stresses. Finally, we compare the results from the analytic and semi‐analytic methods with those from a variety of numerical integration schemes.
Computational structural mechanics and optimal control—the simulation of substructural chain theory to linear quadratic optimal control problems
Authors: Wanxie Zhong , Jiahao Lin , Chunhang Qiu 
Published: August 2005

AbstractThe theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co‐ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half‐size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.
Optimization of mechanical systems: On strategy of non‐linear first‐order approximation
Authors: Kegl M. S. , Butinar B. J. , Oblak M. M. 
Published: August 2005

AbstractThe paper presents an extended approach to non‐linear first‐order approximation of non‐linear programming problems and it explains how to transform an approximate problem into a strictly convex one. The essence of the proposed approximation technique is to rewrite each given function hj as a composite gj o Ψj. The function Ψj has to be chosen—the paper explains how to do this—while gj is linear approximated with gj. The approximation of hj is then obtained as gj o Ψj.This approach enables one to obtain approximate functions with variable conservativeness, which implies an adjustable approximate problem. A solution procedure, which replaces the original problem with a sequence of approximate problems, can therefore adjust each succeeding approximate problem to improve the convergence properties.The theory is illustrated with a three parameters controlled approximation. This technique represents, together with an optimality criteria based solution procedure, a powerful and economic tool for solving nonlinear programming problems. The three parameters, which influence to a great extent the conservativeness of the approximate functions, are under full control of the optimizer. They are varied automatically during the process of optimization to speed‐up the convergence or to prevent oscillations.The benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system.