bluuebunny/crossref_metadata_2025 huggingface dataset:
A design optimization procedure to minimize fillet bending stresses in an epicyclic gear system
Authors: Andrews J. D.
Published: August 2005

This paper presents the development of a design algorithm for epicyclic gear systems. The criterion on which the design performance is assessed is the maximum tensile stress induced in the fillets of the sun, planet and annulus gears. From an initial set of prescribed real and integer design parameters the finite element method is used to determine the maximum tensile fillet stresses in each gear. An objective function is formulated to represent the total stress in the system by combining the maximum fillet stresses in each component. A sequential procedure is then used to minimize the objective function subject to equality, inequality and integer function constraints.

The finite element method is used to evaluate the stresses in the gear teeth and iterative application of the analysis and optimization stages converges to produce a design vector such that the maximum stress produced in all components of the system is minimized.

Since the effectiveness of each design is assessed using the finite element method, the factorized stiffness matrix is reused to calculate the design derivatives. This makes the processes very efficient in its use of computer resources.
Closed form stiffness matrices and error estimators for plane hierarchic triangular elements
Authors: Lawrence Kent L. , Nambiar Rajiv V. , Bergmann Brad
Published: August 2005

Closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.
A critical analysis of quadratic beam finite elements
Authors: Rakowski Jerzy
Published: August 2005

A 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

The 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

The 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

An 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

Numerical 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

For 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

A 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

A 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

The 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

The 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

Iterative 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

The 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

In 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

A 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

The 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

The 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

A 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

An 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

A 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

This 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

The 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

The 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.
Time finite element methods for structural dynamics
Authors: Hulbert Gregory M.
Published: August 2005

Time finite element methods are developed for the equations of structural dynamics. The approach employs the time‐discontinuous Galerkin method and incorporates stabilizing terms having least‐squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time‐discontinuous Galerkin and least‐squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.
Static and vibration analysis of laminated composite beams with an interlaminar shear stress continuity theory
Authors: Lee Chun‐Ying , Liu Dahsin , Lu Xianqiang
Published: August 2005

A finite element method for stress and vibration analysis of laminated composite beams was investigated. The analysis was based on a multilayered theory presented by Lu and Liu. This theory accounts for the continuity of interlaminar shear stress. The principle of minimum potential energy was used in the finite element formulation. The interlaminar shear stress was obtained directly from the constitutive equations. It was verified that the present technique was able to give excellent results for displacements, stresses and vibration frequencies for both thin and thick composite beams. The effects of the number of layers and the number of elements on the convergence were also discussed.
Plane strain finite element simulation of shear band formation during metal forming
Authors: Heinstein Martin W , Yang Henry T. Y.
Published: August 2005

A plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic‐plastic formulation includes a 5‐node 10‐degree‐of‐freedom (d.o.f.) ‘crossed‐triangle’ element, a 4‐node 8‐d.o.f. element with selective reduced integration, an 8‐node 16‐d.o.f. element and a 4‐node 8‐d.o.f. element with an embedded shear band. The formulation includes an elastic‐plastic material model with a modified Gurson yield function and combined isotropic‐kinematic hardening. The solution procedure is based on a Newton–Raphson incremental‐iterative method with an orthogonal projection of zero or negative eigen‐modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4‐node quadrilaterals are comparable to the 5‐node crossed‐triangle element as well as the 8‐jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet‐stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182‐O sheet. The load vs. extension history and the through‐thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight‐sided dies is presented and characteristic features of the formation of dead metal zone are observed.
On the multi‐grid technique for solving three‐dimensional boundary value engineering problems
Authors: Bulgakov V. E. , Belyi M. V.
Published: August 2005

The paper proposes an iterative technique with a similar multi‐grid operator for solving complex spatial bounctary value problems. The description of the method and efficient vectorial algorithms based on a simple ctata structure applicable to solving three‐dimensional engineering problems are presented. The discussion of the method's convergence includes theoretical grounds and practical aspects. We give a general proof of convergence and consider the model cases to estimate the rate of convergence. We also address the histories of convergence derived from the numerical tests and consider two examples of practical problems.
Assessment of discretized errors and adaptive refinement with quadrilateral finite elements
Authors: Liu Y. C. , Elmaraghy H. A.
Published: August 2005

This paper studies discretized errors, and their estimation in conjunction with quadrilateral finite element meshes which are generated by the intelligent mesh generator XFORMQ.1 The exact energy error is used to evaluate the distortion effect of the quadrilateral mesh. The Zienkiewicz–Zhu2 error estimate and actaptive procedure are applied to the short cantilever and the square plate problems using the quadrilateral mesh generator XFORMQ. It is shown that the multistage quadrilateral element refinement produces results superior to the triangular element refinement in the test cases.
On the coupled thermomechanical treatment of necking problems via finite element methods
Authors: Wriggers P. , Miehe C. , Kleiber M. , Simo J. C.
Published: August 2005

The necking process of a bar in an uniaxial tension test is influenced by the heat production due to inelastic deformations. Thus, for an analysis of this problem the thermomechanical coupling has to be considered. A finite element model and an associated algorithm are developed for this purpose. This computational tool allows the study of adiabatic processes as well as processes with heat flux. The analysis of the necking process of a perfectly cylindrical specimen shows that, in contrast to isothermal and adiabatic cases, no bifurcation occurs in the case where heat flux is considered.
A three‐dimensional BEM solution for plasticity using regression interpolation within the plastic field
Authors: Gupta Anil , Delgado Hugo E. , Sullivan John M.
Published: August 2005

This paper presents an improved solution of three‐dimensional plasticity problems using the boundary element method (BEM). The BEM formulation for plasticity requires volume as well as boundary discretizations. An initial stress formulation is used to satisfy the material non‐linearity. Conventionally, the plastic field in the volume element (or cell) is interpolated based on the value of plastic stress at the nodes of the cell. In this paper, the distribution of the plastic field in the cell is based on a number of points interior to the cell. The plastic field is described using regression interpolation polynomials through these interior points. The constitutive relation is satisfied at each interior point. The number of points can be varied in each cell, thus allowing for adaptive volume cells. The plastic stresses are computed at the interior points only, therefore, the need for surface stress computation (which uses numerical derivatives at the surface) is completely eliminated. Three‐dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto‐plasticity problems. In all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation method.
An inverse method for determining elastic material properties and a material interface
Authors: Schnur D. S. , Zabaras Nicholas
Published: August 2005

A numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two‐dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg‐Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.
Adaptive solution strategy for solving large systems of p‐type finite element equations
Authors: Morris R. B. , Tsuji Y. , Carnevali P.
Published: August 2005

A solution strategy is proposed and implemented for taking advantage of the hierarchical structure of linear equation sets arising from the p‐type finite element method using a hierarchical basis function set. The algorithm dynamically branches to either direct or iterative solution methods. In. the iterative solution branch, the substructure of the finite element equation set is used to generate a lower order preconditioner for a preconditioned conjugate gradient (PCG) method. The convergence rate of the PCG algorithm is monitored to improve the heuristics used in the choice of the preconditioner. The robustness and efficiency of the method are demonstrated on a variety of three dimensional examples utilizing both hexahedral and tetrahedral mesh discretizations. This strategy has been implemented in a p‐version finite element code which has been used in an industrial environment for over two years to solve mechanical design problems.
Axisymmetric thermoelastic shape sensitivity analysis and its application to turbine disc design
Authors: Lee Boo Youn , Kwak Byung Man
Published: August 2005

A general method for shape design sensiti vityi analysis (SDSA) as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method. The sensitivity of a general functional composed of thermal and mechanical quantities is considered. The method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. It is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary. Results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading. The sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences. Optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only, clearly showing the practical importance of the SDSA of thermoelastic systems.
Postbuckling analysis of layered composites using p‐ version finite strips
Authors: Kasagi Akihito , Sridharan Srinivasan
Published: August 2005

This paper presents the results of a study on the buckling and postbuckling analyses of layered shear‐deformable composite plates using p‐version finite strips. The plates are considered to be sufficiently long so that the effect of boundary conditions along the shorter edges is of little significance; this makes it possible to use the ‘exact’ trigonometric functions in the longitudinal direction. The displacement field in the transverse direction is discretized by p‐version finite strips and convergence is studied by p‐extension, i.e. keeping the number of strips relatively small whilst increasing the polynomial order till convergence of the buckling load or the postbuckling stiffness is achieved.

Detailed convergence studies are presented and comparison with results of earlier investigations are shown wherever appropriate. The results demonstrate the superior convergence characteristics of the p‐version approach.
Least squares element method for boundary eigenvalue problems
Authors: Rothe Kai
Published: August 2005

Linear and non‐linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non‐linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non‐linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples.
A structural mapping technique for geometric parametrization in the optimization of magnetic devices
Authors: Weeber Konrad , Ratnajeevan S. , Hoole H.
Published: August 2005

The continuity and differentiability of object functions is a basic prerequisite for the application of gradient methods in optimization. However, for parameters defining the shape of an electromagnetic device, the finite element discretization in the field analysis introduces discontinuities into the object function which slow down the convergence rate. Additionally, depending on the geometric parametrizaiion employed, the optimization frequently yields shape contours that are impracticable for manufacturing purposes. This paper investigates the problems inherent in geometric parametrization and shows that the discontinuities in the object function are caused by changes in mesh topology as the geometric parameters vary; these changes inevitably follow from the use of free meshing algorithms. As a solution to these shortcomings a structural mapping technique is outlined that maps surface displacements onto the parameters of the finite element mesh and obtains the parameter dependent geometric variations without a change in mesh topology. This resulting geometric parametrization yields continuous object functions without artificial local minima and results in smooth surface contours of the optimized device. Using this new parametrization technique, design sensitivity analysis, is shown to be a reliable and essential part in the efficient application of gradient methods for shape optimization.
An application of preconditioned conjugate gradients to relative placement in chip design
Authors: Kredler Christian , Zillober Christian , Johannes Frank , Sigl Georg
Published: August 2005

In distance geometry problems and many other applications, we are faced with the optimization of high‐dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well‐known preconditioning techniques for the conjugate gradient method remain applicable. Very‐large‐scale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
Interpolation of curved shell geometries by low order finite elements—errors and modifications
Authors: Gebhardt H. , Schweizerhof Karl
Published: August 2005

Low order finite elements are of vital interest for practical applications in linear and non‐linear structural analysis. The possible discretization errors, when Reissner‐Mindlin shell elements with bilinear shape functions are used, and modifications to prevent these errors are presented. On some numerical examples the influence of these errors and of various modifications on the results is shown. Finally, the case of membrane locking with low order Reissner‐Mindlin elements for particular assumptions concerning the base vectors and methods to prevent this locking are discussed.
Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution
Authors: Flores Fernando G. , Godoy Luis A.
Published: August 2005

The general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non‐axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluated.
The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier‐Stokes equations
Authors: Dutto Laura C.
Published: August 2005

We investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non‐linear GMRES algorithm, for solving the Navier‐Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non‐linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill‐McKee and snake, and consider preconditionings without fill‐in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non‐linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.

We also consider the effect of orderings when an incomplete factorization which allows some fill‐in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill‐in.

Finally, following the principal ideas of non‐linear GMRES algorithm, we suggest other inexact Newton methods.
An algorithm for adaptive refinement of triangular element meshes
Authors: Nambiar R. V. , Valera R. S. , Lawrence K. L. , Morgan Robert B. , Amil David
Published: August 2005

A simple algorithm is developed for adaptive and automatic h refinement of two‐dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.
Boundary element solution of heat conduction problems in multizone bodies of non‐linear material
Authors: Bialecki Ryszard , Kuhn Günther
Published: August 2005

A novel algorithm for handling material non‐linearities in bodies consisting of subregions having different, temperature dependent heat conductivities is developed. The technique is based on Kirchhoff's transformation. The material non‐linearity is reduced to a solution dependent function of unified form added to unknown nodal Kirchhoff's transforms. Assembling of element contributions brings the non‐linearity to the right hand sides of the global set of equations. The first step of the solution of this set is the Gaussian pre‐elimination (condensation) of linear degrees of freedom. At this stage efficient block solvers can be used. Then, a set of non‐linear equations is extracted from the condensed one and solved employing the Newton‐Raphson technique. The iteratively solved set consists of the least possible number of equations and its Jacobian matrix is calculated efficiently by taking advantage of the specific form of the equations.
Superconvergent extraction techniques for finite element analysis
Authors: Niu Qingxiang , Shephard Mark S.
Published: August 2005

A class of extraction techniques is developed to recover stresses as well as displacements from finite element solutions. Particular emphasis is placed on the extraction of boundary stresses along slope continuous portions of the boundary. The techniques are superconvergent in that the convergence of the recovered quantities is equal to that of the strain energy. Numerical examples are used to demonstrate that the techniques are efficient and reliable, and can be easily implemented in the finite element analysis environment.
Explicit time‐domain transmitting boundary for dam‐reservoir interaction analysis
Authors: Yang R. , Tsai C. S. , Lee G. C.
Published: August 2005

An explicit time‐domain transmitting boundary for the analysis of dam‐reservoir interactions is presented. This transmitting boundary is a semi‐analytical solution of the governing wave equation of the far field of the reservoir. By using this transmitting boundary, the radiation condition and water compressibility can readily be incorporated in the time‐domain analysis of dam‐reservoir systems. Therefore, the finite element method can be used to accurately analyse a dam‐reservoir system including the semi‐infinite reservoir while maintaining its efficiency in time‐domain analysis. Numerical results have excellent agreement with the available analytical solution. Results also show that the proposed explicit transmitting boundary is more efficient computationally than the implicit transmitting boundary presented by Tsai and Lee.