bluuebunny/crossref_metadata_2025 huggingface dataset:
Boundary formulations for shape sensitivity of temperature dependent conductivity problems
Authors: Kane James H. , Wang Hua
Published: August 2005

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a non‐linear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of non‐linear equations and the computational performances examined in detail. Multi‐zone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized non‐iinear boundary conditions or regions of geometric insensitivity to design variables. A series of non‐linear example problems is presented that have closed form solutions. Exact anaytical expressions tor the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.
Time dependent axisymmetric thermoelastic boundary element analysis
Authors: Dargush G. F. , Banerjee P. K.
Published: August 2005

A boundary element method is developed for problems of quasistatic axisymmetric thermoelasticity. Unlike previous approaches, this new time domain formulation is written exclusively in terms of surface quantities, thereby eliminating the need for volume discretization. Furthermore, since the exact three‐dimensional infinite space fundamental solutions are employed, very accurate solutions are obtainable, including the determination of surface stresses.

In the integral formulation, the fundamental solutions are separated into steady‐state and transient components. The steady‐state portion, which contains all of the singularities, is integrated analytically in the circumferential direction, yielding the familiar axisymmetric kernels. The remaining non‐singular transient integrands are treated by a combination of analytical and numerical quadrature.

The method is implemented in a general purpose boundary element code, which includes multiregion capability along with higher order conforming surface elements. Several numerical examples are provided to illustrate the validity of the formulation and the attractiveness of this approach for practical engineenring analysis.
Coupled bending–torsional dynamic stiffness matrix for axially loaded beam elements
Authors: Banerjee J. R. , Fisher S. A.
Published: August 2005

Analytical expressions for the coupled bending–torsional dynamic stiffness matrix elements of an axially loaded uniform beam element are derived in an exact sense by solving the governing differential equations of motion of the beam. The influence of axial force on the coupled bending–torsional frequencies of a cantilever and hinged–hinged beam of thin‐walled section is demonstrated by numerical results. Application of the developed theory includes coupled bending–torsional frequency and mode calculations of helicopter, turbine and propeller blades, plane and space frames, and grillages consisting of axially loaded beam elements with non‐coincident mass centre and shear centre.
Vibration of shear‐deformable beams using a spline‐function approach
Authors: Dawe D. J. , Wang S.
Published: August 2005

B‐spline functions are used as trial functions in a Rayleigh‐Ritz analysis of the free vibration of shear‐deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross‐sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear‐locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B‐spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear‐locking difficulty is completely eliminated. This has clear significance for the analysis of shear‐deformable plates and shells when using B‐spline functions.
Large displacement analysis of thin‐walled beams with generic open section
Authors: Conci Aura
Published: August 2005

A finite element formulation for geometric non‐linear analysis of elastic straight thin‐walled beams is presented. The updated Lagrangian procedure is used for a stiffness matrix derivation‐to analyse large displacements or buckling behaviour of space frames. The stiffness matrix is developed for a generic cross‐section and is equally efficient for symmetric, monosymmetric or asymmetric open sections. Some non‐linear strain terms usually neglected in the literature have been considered, resulting in a formulation which also includes the initial bimoment and torsion effect for all cross‐sections analysed. The proposed method has been implemented and the results of sample problems are presented.
Boundary element analysis of two‐dimensional elastoplastic contact problems
Authors: Karami G.
Published: August 2005

In this paper a boundary element method for two‐dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic‐perfectly plastic or work‐hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three‐noded line elements are used to represent the boundary and eight‐noded quadrilateral or six‐noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.
Non‐singular boundary integral equation implementation
Authors: Cruse T. A. , Aithal R.
Published: August 2005

The basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non‐singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non‐singular and is shown to be amenable to simple, low‐order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi‐analytical BIE implementation reported herein.
Application of block Lanczos method for analysis of cyclic symmetric structures
Authors: Balasubramanian P. , Jagadeesh J. G. , Suhas H. K. , Ramamurti V.
Published: August 2005

In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.
An efficient implementation of stress resultant plasticity in analysis of Reissner‐Mindlin plates
Authors: Ibrahimbegović Adnan , Frey François
Published: August 2005

An efficient solution procedure for elasto‐plastic analysis of Reissner‐Mindlin plates has been proposed in this work. The main ingredients which render efficiency are: what appears to be an optimally tuned four‐node plate element with assumed shear strains and incompatible bending modes; an elasto‐plastic constitutive model given directly in terms of stress resultants; and efficient computation of plastic flow which simplifies to a solution of a single scalar equation and remaining state update computation. The performance of the element has been proved very satisfying in both elastic singularity‐dominated and elasto‐plastic problems.
Solution of the Helmholtz eigenvalue problem via the boundary element method
Authors: Kirkup S. M. , Amini S.
Published: August 2005

The numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non‐linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non‐linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. The method is applied to the test problems of a three‐dimensional sphere with an axisymmetric boundary condition and a two‐dimensional square.
Quartz resonator frequency shifts computed using the finite element method
Authors: Clayton Larry D. , Eernisse Errol P.
Published: August 2005

A new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by Tiersten.36The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT‐ and SC‐cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution technique.
A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt by using the boundary‐fitted co‐ordinate system
Authors: Saitou Masatoshi , Hirata Akira
Published: August 2005

A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt is proposed. The boundary‐fitted co‐ordinate system is applied to a treatment for the moving solid‐liquid interface in cylindrical co‐ordinates with a symmetry axis. An alternating‐direction‐implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
Boundary element method solutions for elastic wave scattering in 3D
Authors: Schafbuch P. J. , Rizzo F. J. , Thompson R. B.
Published: August 2005

Time‐harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three‐dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.
An approach to optimal design of structures with non‐linear response
Authors: Oblak M. M. , Kegl M. , Butinar B. J.
Published: August 2005

A commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems, where each of these is obtained as an approximation of the original problem. Considering structures with linear response, this procedure works very well and can be implemented quite straightforwardly. However, considering structures with non‐linear response, the situation is more sophisticated since structural stability properties have to be taken into account.

The paper presents an approach to optimal design of statically loaded structures with non‐linear response. It is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained. These similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level, which is lower or at most equal to the critical load level. By this approach, the structural stability requirements are taken into account in an effective manner. The efficiency is illustrated with several examples involving kinematic as well as material non‐linear effects.
Boundary stress calculation using regularized boundary integral equation for displacement gradients
Authors: Matsumoto Toshiro , Tanaka Masataka , Hirata Hideki
Published: August 2005

Accurate computation of boundary stress components is important in stress‐base shape optimization. The boundary element method usually gives us more accurate solutions of them compared with those obtained by the finite element method. In the present paper we propose a new approach to calculate the boundary stress components by using the regularized boundary integral equation relating the boundary displacement gradients to the tractions. Although the original integral equation must be evaluated in the sense of the Cauchy principal value, it can be regularized by subtracting and adding the displacement gradients at the source point from and to the original integral equation. When the displacement gradients satisfy the Hölder continuity at the source point, the regularized integral equation becomes non‐singular and can be evaluated numerically by using the standard Gaussian quadrature formula. The numerical implementation of the proposed integral equation is presented and the effectiveness of the approach is also discussed through some numerical demonstrations.
Finite element simulation of adaptive bone remodelling: A stability criterion and a time stepping method
Authors: Harrigan Timothy P. , Hamilton James J.
Published: August 2005

Adaptive bone remodelling simulations which use finite element analysis can potentially aid in the design of orthopedic implants and can provide examples which test specific bone remodelling hypotheses in a quantitative manner. By concentrating on remodelling algorithms in which the geometry is fixed but the tissue stiffness changes based on strain energy density, we have predicted stability conditions for bone remodelling and we have tested the applicability of these conditions using numerical simulations. The stability requirements arrived at using a finite element formulation are similar to the requirements arrived at in an earlier analytical study. In order to test the stability conditions, we have developed an Euler backward time stepping technique which uses the derivation for stability. These simulations arrived at solutions which were impossible using Euler forward time stepping as applied in this study. Cases in which a simplified version of the derived Euler backward method are unstable or marginally stable have also been seen, but when the Euler backward method is applied using the full derived matrices, no instabilities are apparent. The results of the stability tests indicate that the converged density distributions in the examples studied are stable. Although a priori conditions which ensure stability are not found, a test for stability is provided, given an assumed density distribution.
An ALE hydrodynamic lubrication finite element method with application to strip rolling
Authors: Hu Yu‐Kan , Liu Wing Kam
Published: August 2005

A method that incorporates the hydrodynamic lubrication analysis into the arbitrary Lagrangian Eulerian (ALE) finite element analysis is developed for steady‐state strip rolling simulation. By employing the ALE formulation, only part of the workpiece, which is subjected to large plastic deformation within the roll‐bite region, is modelled, so that the computational cost is substantially reduced. In the hydrodynamic lubrication formulation, the effect of surface roughness on the lubricant flow is taken into consideration by the use of an average flow model. The friction stress is expressed in terms of forming variables such as surface roughness, lubricant and workpiece properties, film thickness, forming speed and process geometry. Furthermore, the elastic deformation of rolls is also analysed by the boundary element method to avoid the finite element discretization inside the rolls. Two numerical examples, aluminium and steel strip rolling processes, are presented to demonstrate the merits of the proposed method.
Elastic stability of skew laminated composite plates subjected to biaxial follower forces
Authors: Liao C.‐L. , Lee Z.‐Y.
Published: August 2005

The present study investigates the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces by the finite element method. The plate is assumed to follow first‐order shear deformation plate theory (FSDPT). The kinetic and strain energies of skew laminated composite plate and the work done by the biaxial inplane follower forces are derived by using tensor theory. Then, by Hamilton's principle, the dynamic mathematical model to describe the free vibration of this problem is formed. The finite element method and the isoparametric element are utilized to discretize the continuous system and to obtain the characteristic equations of the present problem. Finally, natural vibration frequencies, buckling loads (also the instability types) and their corresponding mode shapes are found by solving the characteristic equations. Numerical results are presented to demonstrate the effects of those parameters, such as various inplane force combinations, skew angle and lamination scheme, on the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces.
Three‐dimensional analysis of thermally loaded cracks
Authors: Raveendra S. T. , Banerjee P. K. , Dargush G. F.
Published: August 2005

The stress intensity factors for cracks in three‐dimensional, thermally stressed structures are computed by using the boundary element method. While many boundary and volume‐integral‐based formulations are available for the treatment of thermoelastic problems in solids, the present analysis is based on a recently developed boundary‐only formulation. The accuracy of the solutions in the present work is improved by using special elements at the crack front that accurately model the variation of displacement, temperature fields and singularity of traction, flux fields.
Construction of stiffness matrices to maintain the convergence rate of distorted finite elements
Authors: Ingber M. S. , Schreyer H. L.
Published: August 2005

High‐order elements are an option for providing an enhanced rate of convergence. However, it is not widely known that if a high‐order element based on a mapping from a master‐element space is distorted by displacing one of the side nodes slightly from the traditional midside position then the rate of convergence drops one order. The proof for a three‐node element in one dimension has been given previously. Here, a numerical demonstration is presented to show how quickly the rate is lost as the second node is moved from the midpoint. For a six‐node triangular element, a similar convergence study is performed in two dimensions in which one of the side nodes is moved off centre along a straight line joining the vertices of the triangle. Again, a loss in the order of convergence is shown although the loss is only apparent for sufficiently small element size. To prevent this drop in the rate of convergence as a side node is displaced, a procedure is given for developing the element stiffness matrix without formulating element basis functions. For the six‐node triangle, a complete quadratic representation is retained, but at the expense of element compatibility between nodes. The numerical investigation shows that convergence appears to be retained but that the error associated with the incompatibility is greater than the error obtained with the use of distorted isoparametric elements. The results of this study are particularly appropriate for domains with curved boundaries and for non‐linear problems in which node positions are updated according to the deformation history.
State‐space representation and optimal control of non‐linear material deformation using the finite element method
Authors: Grandhi Ramana V. , Kumar Anand , Chaudhary Anil , Malas James C.
Published: August 2005

A state‐space model for representing the non‐linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal‐forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state‐space model from non‐linear finite element formulation, optimal control strategy and numerical example cases with discussions.
Lagrangian finite‐element analysis of time‐dependent viscous free‐surface flow using an automatic remeshing technique: Application to metal casting flow
Authors: Muttin F. , Coupez T. , Bellet M. , Chenot J. L.
Published: August 2005

The Navier‐Stokes incompressible model is used to describe two‐dimensional metal casting flow. Such flows involve moving free boundaries. A new numerical algorithm has been developed using the Lagrangian finite‐element method. It allows treatment of flows with moderate Reynolds numbers. The main feature is to avoid the calculation of the convective term, together with an automatic remeshing technique, to cure the mesh distortions. The problem of the free oscillation of a liquid is treated to verify the formulation. An application of this method to the computation of an industrial metal casting flow situation is presented.
A new approach to 2‐D eigenvalue shape design
Authors: Melnikov Y. U. A. , Titarenko S. A.
Published: August 2005

A new approach to solve problems in the optimal shape design of eigenvalues is presented. The idea behind the approach is based on a combination of the known material derivative method4,7 and a specially adapted Green's functions formulation.14 In the current study, numerical testing has been limited to two‐dimensional shape optimization. The two test cases involve the first eigenvalues of boundary value problems which model (i) free vibrations of a fixed membrane and (ii) natural frequencies of clamped thin plates. The basic algorithm can easily be adapted to serve other types of boundary value problems dealing with the highest eigenvalues that occur in applied mechanics. Computational aspects of the proposed approach, such as accuracy of the obtained sensitivities, cost of computation and so on are discussed in References 16 (in preparation).
A new approach to magnetic field analysis by the dual reciprocity boundary element method
Authors: Yamada T. , Wrobel L. C.
Published: August 2005

This paper presents an application of the dual reciprocity boundary element method to non‐linear magnetic field analysis. Advanced techniques employed in the procedure include discontinuous elements, quasi‐singular and hyper‐singular integration schemes and the Galerkin formulation. Numerical results are included to show the performance of the proposed approach.
High‐order integration of smooth dynamical systems: Theory and numerical experiments
Authors: Austin Mark
Published: August 2005

This paper describes a new class of algorithms for integrating linear second‐order equations and those containing smooth non‐linearities. The algorithms are based on a combination of ideas from standard Newmark integration methods and extrapolation techniques. For the algorithm to work, the underlying Newmark method must be stable, second‐order accurate, and produce asymptotic error expansions for response quantities containing only even‐ordered terms. It is proved that setting the Newmark parameter γ equal to 1/2 gives a desirable asymptotic expansion, irrespective of the setting for β. Numerical experiments are conducted for one linear and two non‐linear applications.
Fundamental frequency analysis of laminated rectangular plates by differential quadrature method
Authors: Farsa Jalaleddin , Kukreti Anant R. , Bert Charles W.
Published: August 2005

In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.
Shape optimization using adaptive shape refinement
Authors: Kohli H. S. , Carey G. F.
Published: August 2005

A large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.
Application of singular quadratic distorted isoparametric elements in linear fracture mechanics
Authors: Lim I. L. , Johnston I. W. , Choi S. K.
Published: August 2005

The understanding of the performance of the quarter‐point and transition elements is of considerable importance as these singular elements are widely used in linear elastic fracture mechanics (LEFM) analyses. However, a number of issues remain unresolved although numerous investigations into their performance have been conducted. In particular is the question of optimum quarter‐point element and transition element size. This study examines several aspects in relation to the size effect by performing a large number of numerical analyses on several standard problems. Interpretation of the numerical results was aided by the use of two concepts, the ‘zones of dominance’ and ‘zones of representation’. This study proposes a means of explaining the errors in stress intensity factor computation through the interaction between both types of zones. Consequently, a number of new and significant observations were made regarding the singular elements' performance. This study concludes with some recommendations for the application of these elements.
A direct application of higher‐order parametric programming techniques to structural optimization
Authors: Ohsaki M. , Arora J. S.
Published: August 2005

Computational methods based on a sequence of parametric programming problems are presented for solving constrained optimization problems (COP) without any parameter. An auxiliary parametric programming problem (APPP) is formulated in order to solve COP. The procedure is started with an arbitrary initial solution which is the trivial solution of APPP corresponding to the initial value of the parameter. Then the optimal solution for the final value of the parameter, which is the optimal solution of COP, is estimated by Taylor's expansion with respect to the parameter where higher‐order terms are incorporated. It is shown that the incorporation of the higher‐order terms indeed leads to a faster convergence of the solution. As an extension of the method, a general algorithm is presented for optimum design problems with state variable constraints which are implicit functions of the design variables. Logarithmic penalty functions are incorporated and the weight coefficients for the penalty terms are updated continuously. The derivatives of the state variables with respect to the parameter and their sensitivity coefficients are expressed explicitly in terms of those of the design variables. Finally, a method of simultaneous analysis and optimization is developed for trusses with geometrical non‐linearity.
Design optimization of non‐linear structures with rate‐dependent and rate‐independent constitutive models
Authors: Jao S. Y. , Arora J. S.
Published: August 2005

A design optimization process for non‐linear structures with history‐dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material non‐linear effects is used. Shape, non‐shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non‐shape design parameters are treated in the example problems.
Detecting symmetry‐breaking bifurcation points of symmetric structures
Authors: Carstensen C. , Wagner W.
Published: August 2005

In engineering applications often problems with symmetric system and symmetric loading occur. It is well known that these symmetry conditions can be used to reduce the computational effort. Thus, only a symmetric reduced system is treated with sufficient boundary and loading conditions. Especially for non‐linear problems this procedure is very effective. Such a strategy allows the computation of solution paths with the constraint that the solution has to be symmetric. Consequently in a stability analysis, only limit points and bifurcation points with associated symmetrical eigenvectors can be found. Often the stability behaviour is dominated by symmetry‐breaking bifurcation points which cannot be detected considering only the tangent stiffness matrix of the reduced system. Hence, in case of stability considerations a calculation of the complete system is necessary. This paper introduces a special form of stability analysis of the complete system using only certain matrices known from the symmetric reduced system, and some transformations concerning the topology of the total system. The proposed methods base on a substructure technique for symmetry under reflections and rotations, and are formulated for the finite element method. Numerical examples are given to show the efficiency of the proposed procedures and algorithms.
Linked interpolation for Reissner‐Mindlin plate elements: Part I—A simple quadrilateral
Authors: Zienkiewicz Olgierd C. , Xu Zhongnian , Zeng Ling Fu , Samuelsson Alf , Wiberg Nils‐Erik
Published: August 2005

In most plate elements using the Reissner‐Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables.

Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed).

In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.
A general methodology for structural shape optimization problems using automatic adaptive remeshing
Authors: Bugeda G. , Oliver J.
Published: August 2005

The proposed methodology is based on the use of the adaptive mesh refinement (AMR ) techniques in the context of 2D shape optimization problems analysed by the finite element method. A suitable and very general technique for the parametrization of the optimization problem, using B‐splines to define the boundary, is first presented. Then mesh generation, using the advancing frontal method, the error estimator and the mesh refinement criterion are studied in the context of shape optimization problems In particular, the analytical sensitivity analysis of the different items ruling the problem (B‐splines. finite element mesh, structural behaviour and error estimator) is studied in detail. The sensitivities of the finite element mesh and error estimator permit their projection from one design to the next one leading to an a priori knowledge of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the mesh refinement criterion permits one to build up a finite element mesh on the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked by means of several examples.
Adaptive multivlevel methods in three space dimensions
Authors: Bornemann Folkmar , Erdmann Bodo , Kornhuber Ralf
Published: August 2005

We consider the approximate solution of self‐adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non‐uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real‐life problem arising from hyperthermia, a recent clinical method for cancer therapy.
Dynamic optimization of structures with non‐linearities
Authors: Liu Xiaojian
Published: August 2005

Dynamic optimal design of structural systems with local non‐linearities is proposed and the corresponding mathematical programming is established in this paper. A predictor‐corrector method is presented for state and sensitivity analysis of the systems which is based on partitioning and interface prediction of linear and non‐linear regions. The non‐linear programming problem is linearized and solved by a coarse search SLP approach. A model of an automatic weapon is optimized and some interesting results are given to illustrate the effectiveness of the present method.
An alternative pseudoperipheral node finder for resequencing schemes
Authors: Souza Luiz T. , Murray David W.
Published: August 2005

Many resequencing algorithms for reducing the bandwidth, profile and wavefront of sparse symmetric matrices have been published. In finite element applications, the sparsity of a matrix is related to the nodal ordering of the finite element mesh. Some of the most successful algorithms, which are based on graph theory, require a pair of starting pseudoperipheral nodes. These nodes, located at nearly maximal distance apart, are determined using heuristic schemes. This paper presents an alternative pseadoperipheral node finder, which is based on the algorithm developed by Gibbs, Poole and Stockmeyer. This modified scheme is suitable for nodal reordering of finite meshes and provides more consistency in the effective selection of the starting nodes in problems where the selection becomes arbitrary due to the number of candidates for these starting nodes. This case arises, in particular, for square meshes. The modified scheme was implemented in Gibbs‐Poole‐Stockmeyer, Gibbs‐King and Sloan algorithms. Test problems of these modified algorithms include: (1) Everstine's 30 benchmark problems; (2) sets of square, rectangular and annular (cylindrical) finite element meshes with quadrilateral and triangular elements; and (3) additional examples originating from mesh refinement schemes. The results demonstrate that the modifications to the original algorithms contribute to the improvement of the reliability of all the resequencing algorithms tested herein for the nodal reordering of finite element meshes.
Finite element analysis of laminated composites with contact constraint by extended interior penalty methods
Authors: Kim Seung Jo , Kim Jin Hee
Published: August 2005

In this paper the extended interior penalty methods are applied to solve the bolted joint problems of the laminated composite plates. The conventional interior penalty methods have the weak point such that the searches for optimized solution in the neighbourhood of the constraint surfaces are difficult since the values of penalty term in the infeasible domain are infinity. To improve the weak point, the extended interior penalty formulation is proposed. In this work mathematical analysis on the characteristics of the solutions is attempted and the convergence of the penalized solutions is estimated. As a numerical example, first, the case of single bolted joint is solved for a variety of lamination angles of the composite plates. The computed results are compared with the previous works and are proved to agree well. Next the problem of the two bolt holes in series and in parallel are treated in a similar manner. It is concluded that the formulations for the class of the problems by the extended interior penalty methods are mathematically sound and numerically efficient.
A continuum‐based finite element formulation for the implicit solution of multibody, large deformation‐frictional contact problems
Authors: Laursen T. A. , Simo J. C.
Published: August 2005

In this paper, a formulation is presented for the finite element treatment of multibody, large deformation frictional contact problems. The term multibody is used to mean that when two bodies mechanically contact, both may be deformable. A novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first, before deriving the corresponding finite element equations This feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general. In particular, the approach yields a characterization of the frictional constraint (assuming a Coulomb law) suitable for arbitrary discretizations in either two or three dimensions. A geometric framework is constructed within which both frictionless and frictional response are naturally described, making subsequent finite element discretization a straightforward substitution of finite‐dimensional solution spaces for their continuum counterparts. To our knowledge, this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature.

The development includes exact linearization of the statement of virtual work, which enables optimal convergence properties for Newton‐Raphson solution strategies, and which appears to be highly desirable (if not essential) for the general robustness of implicit finite element techniques. Since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur, the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non‐linear behaviour. This assertion is substantiated through presentation of a variety of examples in both two and three dimensions.
Two‐dimensional elastoplasticity: Approximation by mixed finite elements
Authors: Weissman Shmuel L. , Jamjian Michel
Published: August 2005

Two‐dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non‐linear regime. In particular, four‐node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress, plane strain, axisymmetric and (shear‐deformable) plate bending problems. The excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature. In addition, agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements.
Incremental kinematics for finite element applications
Authors: Rashid M. M.
Published: August 2005

A kinematical algorithm is proposed in which the input is the incremental deformation gradient corresponding to an increment in motion for a time step, and the output is a constant rate‐of‐stretching tensor and a rotation tensor. The concept of algorithmic objectivity is discussed, with a stronger statement of objectivity than those advanced in previous works being set forth. The importance of strong objectivity is illustrated for applications in which moderately large rotation increments are to be expected. Accuracy of the proposed algorithm is discussed and illustrated with example calculations, and it is shown that the accuracy of the algorithm may be extended to arbitrary order. Also, the computational effort associated with the proposed algorithm is seen to compare favourably to that of other algorithms.
A new first‐order interior feasible direction method for structural optimization
Authors: Stander Nielen , Snyman J. A.
Published: August 2005

A new interior feasible direction method for optimization problems with linear objective functions but non‐linear constraints is proposed. The method is particularly suitable for weight minimization problems in structural design where the design variables are the cross‐sectional areas of members and arbitrary stress and displacement constraints are applied. Four truss structures are analysed and in each case the minimum weight consistent with or lower than that currently available in the literature is achieved. Although still expensive in its current version, the method is comparable in cost and robustness with other methods such as the ‘trust region’ multiplier method. Apart from one tolerance value, a reconnaissance parameter needs to be specified. The fact that the same value of the parameter was used for all the examples, and that the method is relatively insensitive to the choice thereof, confirms the robustness of the method.
Modelling edge effects with the C0 plate bending elements: Part 1. Analysis of the mechanism
Authors: Briassoulis D.
Published: August 2005

The behaviour of the C0 plate elements in modelling edge zone effects is analysed by utilizing the classical and a recently proposed formulation. Boundary layers are shown to develop under the activation of an edge zone moment redistribution mechanism, being part of a more generalized moment redistribution mechanism triggered by the in‐plane twisting stiffness of the model.
A finite volume format for structural mechanics
Authors: Oñate E. , Cervera M. , Zienkiewicz O. C.
Published: August 2005

A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non‐Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
Element‐free Galerkin methods
Authors: Belytschko T. , Lu Y. Y. , Gu L.
Published: August 2005

An element‐free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least‐squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least‐squares interpolants and the choices of the weight function are also discussed in this paper.