bluuebunny/crossref_metadata_2025 huggingface dataset:
Design sensitivity analysis of elastoplastic structures
Authors: Ohsaki M. , Arora J. S.
Published: August 2005

An iterative and incremental algorithm is presented for the Design Sensitivity Analysis (DSA) of elastoplastic structures. Geometrical non‐linearity is included in the formulation, and the structure may be subjected to a cyclic loading. The key concept is discussed using an elastoplastic truss. It is shown that the Design Sensitivity Coefficients (DSCs) are path‐dependent and discontinuous at the time at which yielding takes place in a member (yield time). In the proposed algorithm, the yield time is considered to be a function of the design variables. In this way, the discontinuity in the DSCs at the material transition points can be overcome in a simple and routine way. Incremental response analysis and DSA are carried out simultaneously using the Newton–Raphson type iterative procedure. Since the proposed algorithm is completely consistent with the analysis procedure, it can be implemented into an existing code for structural analysis. Application to distributed parameter structures with kinematic and/or isotropic hardening is discussed using the von Mises yield condition and the elastic‐predictor radial‐return method. DSA is carried out for a ten‐bar truss with a piecewise linear constitutive relation. It is shown that the DSCs found using the proposed method agree quite well with those calculated by the central difference method. Finally, an alternate method without any iteration for DSA is proposed and the results from the two methods are compared.
An approach to refining three‐dimensional tetrahedral meshes based on Delaunay transformations
Authors: Golias N. A. , Tsiboukis T. D.
Published: August 2005

A technique for refining three‐dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non‐convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi–Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3‐D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.
Validation of a posteriori error estimators by numerical approach
Authors: Babuška I. , Strouboulis T. , Upadhyay C. S. , Gangaraj S. K. , Copps K.
Published: August 2005

A numerical methodology which determines the quality (or robustness) of a posteriori error estimators is described. The methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems, namely, the local geometry of the grid and the structure of the solution. The methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations.
A consistent formulation for the integration of combined plasticity and creep
Authors: Duxbury Paul , Crook Tony , Lyons Paul
Published: August 2005

Within the context of the consistent tangent update, this paper outlines a stress update algorithm for combined creep and plasticity. The algorithm is implicit, providing unconditional stability, and utilizes local Newton iteration to solve SCALAR forms of the coupled constitutive equations for the creep and plastic strain increments. The tangent for the local iteration is obtained accurately providing quadratic convergence at the Gauss point level. Quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep. Further, combination with an automatic time‐stepping scheme provides an efficient, stable, accurate and robust computational algorithm. The algorithm has been implemented in the general purpose FE package LUSAS1.
An effective two‐dimensional frictional contact model for arbitrary curved geometry
Authors: Saleeb A. F. , Chen K. , Chang T. Y. P.
Published: August 2005

A finite element model is developed on the basis of a variational formulation of the perturbed Lagrange type and the classical Coulomb law of friction, for the analysis of frictional contact problems in two dimensions. The model accounts for all geometric/kinematic non‐linearities associated with large sliding motions as well as arbitrary contact‐surface curvatures. Explicit forms for the contact force and tangent stiffness operators and a penalty‐type format is utilized in the implementation. An extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model.
Topology design with optimized, self‐adaptive materials
Authors: Jog C. S. , Haber R. B. , Bendsøe M. P.
Published: August 2005

Significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems. We study the optimal shape design of a two‐dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material. The macroscopic version of this problem is not well‐posed if no restrictions are placed on the structure topoiogy; relaxation of the optimization problem via quasiconvexification or homogenization methods is required. The effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material.

A combined analytical‐computational approach is proposed to solve the relaxed optimization problem. Both stress and displacement analysis methods are presented. Since rank‐2 layered composites are known to achieve optimal energy bounds, we restrict the design space to this class of microstructures whose effective properties can easily be determined in explicit form. We develop a series of reduced problems by sequentially interchanging extremization operators and analytically optimizing the microstructural design fields. This results in optimization problems involving the distribution of an adaptive material that continuously optimizes its microstructure in response to the current state of stress or strain. A further reduced problem, involving only the response field, can be obtained in the stress‐based approach, but the requisite interchange of extremization operators is not valid in the case of the displacement‐based model.

Finite element optimization procedures based on the reduced displacement formulation are developed and numerical solutions are presented. Care must be taken in selecting the discrete function spaces for the design density and displacement response, since the reduced problem is a two‐field, mixed variational problem. An improper choice for the solution space leads to instabilities in the optimal design similar to those encountered in mixed formulations of the Stokes problem.
On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua
Authors: Perić Djordje , Yu Jianguo , Owen D. R. J.
Published: August 2005

The a posteriori error estimates based on the post‐processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J2‐elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post‐instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h‐refinement and almost uniform error distribution in all considered error norms.
Solution techniques for the p‐version of the adaptive finite element method
Authors: Papadrakakis Manolis , Babilis George P.
Published: August 2005

This paper investigates the performance of a class of methods based on the Preconditioned Conjugate Gradient (PCG) method for the solution of large and sparse systems of linear equations which arise from the p‐version of the adaptive finite element method. The hierarchical type of preconditioning used in the past is extended to the SSOR and incomplete factorization type preconditioning and applied with a global handling of the stiffness matrix. The paper also presents some new ideas on Domain Decomposition (DD) matrix‐handling techniques, whereby the explicit formulation of the resulting Schur complement is avoided by utilizing the PCG method with efficient preconditioners and by processing separately on the coarse and the fine mesh. The suitability of the methods to the p‐version of the adaptive finite element method is demonstrated through extensive numerical tests in two dimensions.
A new energy and momentum conserving algorithm for the non‐linear dynamics of shells
Authors: Simo J. C. , Tarnow N.
Published: August 2005

A numerical time‐integration scheme for the dynamics of non‐linear elastic shells is presented that simultaneously and independent of the time‐step size inherits exactly the conservation laws of total linear, total angular momentum as well as total energy. The proposed technique generalizes to non‐linear shells recent work of the authors on non‐linear elastodynamics and is ideally suited for long‐term/large‐scale simulations. The algorithm is second‐order accurate and can be immediately extended with no modification to a fourth‐order accurate scheme. The property of exact energy conservation induces a strong notion of non‐linear numerical stability which manifests itself in actual simulations. The superior performance of the proposed scheme method relative to conventional time‐integrators is demonstrated in numerical simulations exhibiting large strains coupled with a large overall rigid motion. These numerical experiments show that symplectic schemes often regarded as unconditionally stable, such as the mid‐point rule, can exhibit a dramatic blow‐up in finite time while the present method remains perfectly stable.
Dynamic stability of non‐linear shells of revolution under consideration of the fluid–soil–structure interaction
Authors: Wunderlich W. , Schäpertöns B. , Temme C.
Published: August 2005

The dynamic behaviour of liquid‐filled shells of revolution is investigated considering the soil–structure interaction and the fluid–structure interaction, respectively. In the circumferential direction the loads and variables are approximated by Fourier series. The shell is modelled through shell ring elements including non‐linear behaviour, coupled with isoparametric continuum ring elements and special infinite elements for the soil and isoparametric pressure ring elements for the fluid. Transient loadings like earthquake excitation and the non‐linearities of the shell and the soil require an analysis in the time domain. To reduce the size of the problem, linear parts of the system are condensed by the substructure technique. The soil region is divided into two parts, a near field permitting non‐linearities like plastification or uplifting of the shell, and a far field for the treatment of radiation of energy.

The boundary conditions for the shell footing have a strong influence on the distribution of the axial membrane forces and, hence, on the stability limit, which is mostly governed by plastic collapse and caused by the dynamically activated pressure acting on the tank wall. It is shown how the soil properties influence the dynamic stability of the shell under harmonic excitation and under realistic earthquake motion.
Numerical methods for optimal control of impressed cathodic protection systems
Authors: Hou L. Steven , Sun W.
Published: August 2005

Some optimal control problems arising from impressed cathodic protection systems are considered. Our objective is to find the location of anodes and the current density on the anodes that yield an optimal potential distribution on the cathode. We present a simple formula for the linear model and a gradient algorithm for the non‐linear model. Boundary element methods are employed for the numerical calculation.
A new concept in two‐dimensional auto‐adaptative mesh generation
Authors: Remondini L. , Trompette P. , Leon J. C. , Noel F.
Published: August 2005

The new method presented here is capable of building finite element meshes and managing their adaptation simultaneously to the object load case and geometry before any calculations, i.e. an a priori mesh adaptation is conducted. The principle relies on an analogy between a finite element mesh and the equilibrium position of a network of branches. Each branch is adequately sized by setting force–length ratios, called force densities. Starting from these data, the nodal co‐ordinates are obtained through the solution of a linear system which describes the equilibrium state of the net. This method seems very attractive since the only given data are: a connectivity table, the number of boundary and interior nodes and a geometrical description of the boundaries.

It is also demonstrated how to obtain the equilibrium nodal positions when boundary nodes are allowed to slide and evolution laws of force densities cope with punctual forces and geometric singularities. A comparison of results is conducted between meshes issued by the new technique and those obtained with standard FE codes.
A Lanczos‐based method for structural dynamic reanalysis problems
Authors: Carey Cheryl M. M. , Golub Gene H. , Law Kincho H.
Published: August 2005

In this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original system Ax = λx, procedures are developed for the modified standard eigenvalue Problem (A + ΔA)x̄ = λx̄, where

ΔA = ΣjBSjBT, where Sj = S ∈ ℛp × p, p ≪ n and B ∈ ℛn × p is constant for all the perturbations Sj.

ΔA = ΣiΣj BiSjBiT, where Bi ∈ ℛn × p may vary with the pertubations Sj.

The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate the applications of the method.
Elastoacoustic analysis of submerged fluid‐filled thin shells
Authors: Jeans R. A. , Mathews I. C.
Published: August 2005

The analysis of fluid‐filled thin shells is discussed in this paper. It is well known that a boundary element formulation of the exterior acoustic problem becomes ill‐conditioned at certain critical frequencies. For a coupled boundary‐element/finite element formulation of the coupled elasioacoustic problem the formulation suffers from the same numerical ill‐conditioning. However, for fluid‐filled thin shell problems the resulting coupled formulation is unique at all frequencies. In this paper the condition numbers of the coupled and uncoupled formulations are calculated and the uniqueness of the coupled formulation is demonstrated for submerged fluid‐filled thin shells.
Studies of domain‐based formulations for computing exterior problems of acoustics
Authors: Harari Isaac , Hughes Thomas J. R.
Published: August 2005

The propagation and decay of acoustic waves in exterior domains in an essential ingredient in the study of fluid–structure interaction. A strategy must be devised to compute solutions over domains which are unbounded. Exact impedance conditions at an artificial external boundary are specified by the DtN method, yielding an equivalent problem that is suitable for domain‐based computation. The DtN boundary condition is non‐reflective, giving rise to exact (and thereby unique) solutions. The truncated DtN operator, which is employed in practice, fails to inhibit the reflection of higher modes, so that non‐unique solutions may occur at their harmonics. Simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number. There are three characteristic length scales in the computational problem: the radius of the artificial boundary, the geometry of the body (represented by the internal boundary) and the mesh size. Numerical studies examine the dependence of the conditioning of finite element coefficient matrices on the number of terms in the truncated DtN operator vs. the wave number non‐dimensionalized by each of the length scales. Analytic results regarding the number of terms sufficient for unique solutions are confirmed. As long as this criterion is respected, no upper limit on the allowable wave number is detected. A local approximation of the boundary conditions restores uniqueness for all wave numbers.
The interaction of a submerged axisymmetric shell and three‐dimensional internal systems
Authors: Ettouney Mohammed M. , Daddazio Raymond P. , Abboud Najib N.
Published: August 2005

The problem of axisymmetric shells submerged in an infinite fluid subjected to an arbitrary loading is usually solved by reducing the system to a set of two‐dimensional problems. This is accomplished by using Fourier series, thereby uncoupling the circumferential harmonics of the axisymmetric system. Thus, a computationally expensive three‐dimensional solution is replaced by a computationally efficient set of two‐dimensional solutions without any loss of accuracy. However, with the addition of arbitrary three‐dimensional subsystems internal to the submerged axisymmetric shell, the circumferential harmonics become coupled. In this case, the computational advantage attributable to the circumferential Fourier decomposition compared to a fully three‐dimensional solution is greatly reduced.

This paper introduces a novel method to solve such three‐dimensional systems while keeping the circumferential harmonics of the axisymmetric shell uncoupled. This is accomplished by relating the admittance matrix of the three‐dimensional substructure, expressed in terms of its connection degrees of freedom, and the response of the empty system to solve for the interaction forces between the axisymmetric shell and the internal system. Using these interaction forces, the response of the full system can be obtained, Thus, the efficiency of the two‐dimensional solution is maintained while solving an arbitrary three‐dimensional problem. Sample problems illustrating the performance of this approach will be solved.
The Cartesian collapsed‐dimension method for use in numerical 2‐D radiation calculations in absorbing–emitting media
Authors: Blank David A.
Published: August 2005

A new numerical approach has been devised for performing accurate absorbing–emitting non‐scattering radiation calculations for Cartesian co‐ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of ‘effective intensity rays’ which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very thin case.
Hyperbolic paraboloid shell analysis via mixed finite element formulation
Authors: Omurtag M. H. , Aköz A. Y.
Published: August 2005

An isoparametric rectangular mixed finite element is developed for the analysis of hypars. The theory of shallow thin hyperbolic paraboloid shells is based on Kirchhoff–Love's hypothesis and a new functional is obtained using the Gâteaux differential. This functional is written in operator form and is shown to be a potential. Proper dynamic and geometric boundary conditions are obtained. Applying variational methods to this functional, the HYP9 finite element matrix is obtained in an explicit form. Since only first‐order derivatives occur in the functional, linear shape functions are used and a C0 conforming shell element is presented. Variation of the thickness is also included into the formulation without spoiling the simplicity. The formulation is applicable to any boundary and loading condition. The HYP9 element has four nodes with nine Degrees Of Freedom (DOF) per node—three displacements, three inplane forces and two bending, one torsional moment (4 × 9). The performance of this simple, and elegant shell element, is verified by applying it to some test problems existing in the literature. Since the element matrix is obtained explicitly, there is an important save of computer time.
Safeguarded use of the implicit restarted lanczos technique for solving non‐linear structural eigensystems
Authors: Abdel‐Aziz Mohammedi R.
Published: August 2005

This paper presents a new algorithm for evaluating the eigenvalues and their corresponding eigenvectors for large‐scale non‐linear eigensystems in structural dynamics. The algorithm is based on solving a sequence of algebraic eigenproblems and updating the parameter λ. The implicitly restarted Lanczos method had been determined to be well suited for solving the linear eigenproblems that arise in this context. A zero‐finder approach that uses rational interpolation to approximate the generalized eigenvalues has been developed to update λ.

The methodology of the new algorithm developed here is designed to evaluate a subset of the parametrized non‐linear eigencurves at specific values of λ. Numerical experiments show that the new eigensolution technique is superior to existing approaches for large‐scale problems and competitive for small‐size problems. The main emphasis of this contribution is the derivation and analysis of this scheme for non‐linear structural eigensystems.
Model reduction and process control of thermomechanical behaviour of non‐linear material deformation
Authors: Grandhi Ramana V. , Thiagarajan Ramesh
Published: August 2005

This paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non‐linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off‐line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case studies.
A new family of explicit time integration methods for linear and non‐linear structural dynamics
Authors: Chung Jintai , Lee Jang Moo
Published: August 2005

A new family of explicit single‐step time integration methods with controllable high‐frequency dissipation is presented for linear and non‐linear structural dynamic analyses. The proposed methods are second‐order accurate and completely explicit with a diagonal mass matrix, even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non‐linear structural dynamics. Stability and accuracy of the new explicit methods are analysed for the linear undamped/damped cases. Furthermore, the new methods are compared with other explicit methods.
Bandwidth reduction by simulated annealing
Authors: Dubuc Eduardo J.
Published: August 2005

The method of Simulated Annealing (SA) is investigated in the concrete problem of bandwidth reductio. We develop a very efficient way to compute the transitions, and this allows long annealing sessions (Monte Carlo runs) in reasonable time, enabling meaningful experimenting. It is demonstrated (empirically) that the neighbourhood relation in the space of states of the system greatly influences the convergence of the annealing. A pure SA algorithm is developed and used to obtain new lower bounds for the bandwidth in the 30 Everstine problems used as a benchmark for testing bandwidth reduction algorithms. An hybrid algorithm is also developed to be used in practice. It consists of an annealing session (without previous melting) run in cascade after the Cuthill‐McKee algorithm. The running times are of the same order as those of the deterministic algorithms now in use, and improvements of (typically) 20 per cent are obtained on the 30 Everstine problems.
Second‐order sensitivity analysis in vibration and buckling problems
Authors: Godoy Luis A. , Taroco Edgardo O. , Feuoo Raul A.
Published: August 2005

A perturbation approach for the first‐ and second‐order sensitivity analysis of eigenvalue problems, as they arise in buckling and vibration of structural systems, is presented. A particular feature introduced in the formulation is the dependence of all matrices that model the problem not only on the design parameter, but also on a pre‐critical state. Thus, the sensitivity of the response of the fundamental path in buckling problems, or a pre‐stressed state, in vibration problems, are introduced in the analysis. Two techniques are considered in this work: the direct and the adjoint methods. First‐ and second‐order sensitivity equations for eigenvalues and eigenvectors are obtained, and it is shown that second‐order sensitivity of an eigenvalue can be accomplished by using only one adjoint problem.
Finite element hydrodynamic friction model for metal forming
Authors: Liu Wing Kam , Hu Yu‐Kan
Published: August 2005

The complex contact conditions on the three‐dimensional (3‐D) tooling‐workpiece interface, such as non‐penetrations, slip–stick phenomena and friction forces due to the relative motion of contacting surfaces, are of vital importance in metal forming operations. Usually, a lubricant is provided as an interface medium between the tool and the workpiece to avoid strain localization, wear and surface damage. Hence, a simple friction law such as Coulomb friction, involving only a constant friction coefficient, cannot model the contact phenomena accurately. In this research, a realistic friction model, which accounts for the tribological behaviour, and most importantly, the effect of surface roughness on the lubricated contact, is developed. This model has been implemented in a 3‐D arbitrary Lagrangian Fulerian finite element code for metal forming analysis. The applicability of the proposed model is demonstrated by the simulation of fluid‐lubricated thrust bearing and sheet metal stretch forming.
Successive conjugate gradient methods for structural analysis with multiple load cases
Authors: Suarjana Made , Law Kincho H.
Published: August 2005

This paper discusses the use of conjugate gradient method for structural engineering analysis with multiple load cases. Specifically, we introduce a modified conjugate gradient method for the solution of a system of linear equations with multiple right‐hand sides. We show how this method can be used to improve the performance of block conjugate gradient method. Numerical results are presented to illustrate the effectiveness of the numerical schemes developed in this study.
Numerical solution of Bernoulli‐type free boundary value problems by variable domain method
Authors: Mejak George
Published: August 2005

The variable domain method for a free surface problem is considered as a weighted residual method. This considerably simplifies discretization of the problem and at the same time allows implementation of any standard discretization technique. Discretization of the problem results in a non‐linear system of equations for discrete values of a field variable and co‐ordinates of the nodes on the free boundary. Variables corresponding to a field variable are eliminated and the resulting non‐linear system is of considerable smaller size. Some new update strategies of the Jacobian together with discussion of the cost‐effectiveness and covergence rate are introduced and compared to Broyden's method. Numerical results which confirm validity of the presented discussion are given for three potential free surface problems, (i) two‐dimensional free jet impingement against an infinite wall, (ii) axisymmetric free jet impingement subjected to gravity and surface tension forces, and (iii) computation of critical flow over a weir. In case (i) comparison with known analytical results is given, while in case (iii) a good agreement with previously published results is established.
From the individual element test to finite element templates: Evolution of the patch test
Authors: Felippa Carlos A. , Haugen Bjørn , Militello Carmelo
Published: August 2005

This paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high‐performance elements and element‐level error estimators for those elements. The approach takes off from our previous work in high‐performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single‐element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher‐order parts. The application of this decomposition to the “sanitization” of the non‐convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element‐level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element‐level error estimators, respectively.
Refined nine‐parameter triangular thin plate bending element by using refined direct stiffness method
Authors: Cheung Y. K. , Wanji Chen
Published: August 2005

Based on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non‐conforming elements is proposed. The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured. The well‐known BCIZ nine‐parameter triangular thin plate bending element is refined by the RDSM to yield a new nine‐parameter thin plate bending element RT9. Numerical examples are presented to show that the present model passes the patch test and possesses high accuracy.
Optimal design of material properties and material distribution for multiple loading conditions
Authors: Bendsøe Martin P. , Díaz Alejandro R. , Lipton Robert , Taylor John E.
Published: August 2005

An extension of recent work1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented. Material properties are represented in the most general form possible, namely, as elements of the unrestricted set of positive‐semi‐definite constitutive tensors of a linearly elastic continuum. Existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2‐norm or the trace of the constitutive tensors is included. The optimized material properties can be derived analytically. The optimization of the layout of the material leads to a sizing problem of structural optimization involving a non‐linear, non‐smooth elasticity analysis. The computational solution of this problem is discussed and illustrated with examples.
A finite element method for stability problems in finite elasticity
Authors: Reese S. , Wriggers P.
Published: August 2005

In this paper a finite element method is developed to treat stability problems in finite elasticity. For this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches. These results can then be used to derive an efficient numerical scheme for the computation of singular points.
New finite element model for analysis of Kirchhoff plate
Authors: Zhao Zhenfeng , Chen Wanji
Published: August 2005

A new kind of approach to formulate an isotropic thin plate bending element is presented. The strain energy of the element is decomposed into two parts: an integral concerning the first strain invariant and a line integral around the elemental boundary. The former can be discretized by quasi‐conforming technique1 and the latter can be directly calculated using the interpolation of the deflection and its normal slope along the element boundary. By this method, an assumed first strain invariant quadrilateral element (AFSIQ) is derived. The procedure of formulating the element and the numerical examples show that the new kind of element not only simplifies the formulation considerably but also has excellent accuracy.
Improved finite difference method for equilibrium problems based on differentiation of the partial differential equations and the boundary conditions
Authors: Arad M. , Segev R. , Ben‐Dor G.
Published: August 2005

A numerical algorithm for producing high‐order solutions for equilibrium problems is presented. The approximated solutions are improved by differentiating both the governing partial differential equations and their boundary conditions.

The advantages of the proposed method over standard finite difference methods are: the possibility of using arbitrary meshes; the possibility of using simultaneously approximations with different (distinct) orders of accuracy at different locations in the problem domain; an improvement in approximating the boundary conditions; the elimination of the need for ‘fictitious’ or ‘external’ nodal points in treating the boundary conditions.

Furthermore, the proposed method is capable of reaching approximate solutions which are more accurate than other finite difference methods, when the same number of nodal points participate in the local scheme.

A computer program was written for solving two‐dimensional problems in elasticity. The solutions of a few examples clearly illustrate these advantages.
Heat conduction effects on strain localization in plane‐strain tension
Authors: Tuǧcu P.
Published: August 2005

The deformation behaviour of a rectangular block under tension is investigated for a rate‐ and temperature‐dependent solid using the finite element method. Isotropic behaviour is assumed and the effect of deformation‐induced heat generation is studied in conjunction with heat conduction. Localization into diffuse necking is examined by applying the instability criterion defined for the particular rate‐dependent behaviour. The influence of different thermal boundary conditions on the deformation mode considered, is demonstrated by means of parametric studies.
Reduced minimization in Lagrangian Mindlin plate element with arbitrary orientation under uniform isoparametric mapping
Authors: Yong‐Woo Kim , Oak‐Key Min
Published: August 2005

For the displacement‐based Lagrangian Mindlin plate elements oriented arbitrarily under uniform isoparametric mapping without internal distortion, a theoretical interpretation on the conventional shear‐reduced integration is presented by introducing the concept of reduced minimization. It reveals that the conventional shear‐reduced integration such as URI and SRI prevents the unmatched coefficients of shear strains from becoming spurious constraints. Thus, the shear‐reduced integration eliminates spurious constraints and prevents locking.
Coarse division transform based preconditioner for boundary element problems
Authors: Bulgakov V. E. , Białecki R. A. , Kuhn G.
Published: August 2005

This paper is devoted to the development of efficient preconditioners for an iterative solution of equation sets arising in the Boundary Element Method (BEM). A standard collocation system of equations is transformed to a new basis associated with an auxiliary coarse division model for boundary unknowns and solved in this basis. New systems have rapidly decreasing coefficients and by neglecting a large number of them it is possible to construct readily invertible, sparse preconditioners for iterative procedures. The specific features of the transformed matrix can be attributed to the analytical properties of integral equations. Although the transformation is based on an auxiliary coarse division model, it does not require any additional operations with boundary elements. All manipulations necessary to construct the mapping are performed on the level of algebraic equations. Numerical experiments included in the paper confirm a high rate of convergence of the developed iterative scheme.
On the incompressible constraint of the 4‐node quadrilateral element
Authors: Hueck Ulrich , Schreyer Howard L. , Wriggers Peter
Published: August 2005

The standard plane 4‐node element is written as the summation of a constant gradient matrix, usually obtained from underintegration, and a stabilization matrix. The split is based on a Taylor series expansion of element basis functions. In the incompressible limit, the ‘locking’‐effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher‐order term in the Taylor series.

The incompressibility condition is formulated in a weak sense so that the element displacement field is divergence‐free when integrated over the element volume. The resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first‐order terms of the Taylor series. The corresponding eigenvalue enforces incompressibility implicitly by means of a penalty‐constraint. Analytical expressions for that constant‐dilatation eigenpair are derived for arbitrary element geometries. It is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner.

For several classical and recent elements, the eigensystems are analysed numerically. It is shown that most of the formulations reflect the incompressible constraint identically. In the incompressible limit, the numerical accuracies of the elements are compared.
CLP(ℛ) as a general finite element model definition language
Authors: Strooper P. A. , Stylianou M. , Tabarrok B.
Published: August 2005

There are today as many finite element input languages as there are finite element programs. These input languages were developed to serve one purpose: to provide the analyst with the means to convey the necessary analysis and design criteria to specific finite element programs. They were not developed as general finite element model‐definition languages, and as a result their syntax and semantics are often unnatural and contrived. In this work we do not invent a new input language. Instead, we propose and evaluate the Contraint Logic Programming language CLP(ℛ) as a general finite element model‐definition and input language.
Merits and limitations of optimality criteria method for structural optimization
Authors: Patnaik Surya N. , Guptill James D. , Berke Laszlo
Published: August 2005

The merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.
A new approach to free‐form surface mesh control in a CAD environment
Authors: Noel F. , Leon J. C. , Trompette P.
Published: August 2005

An adaptive process controlling the position of nodes on a surface mesh is presented. The control can depend on one (or more) criterion(ria) about element quality. The mesh is attached, through the concept of classification, to a geometric model issued by a computer aided design software. Thus, the surface domain is described by entities currently available in such systems, i.e. any free‐form patches like Non‐Uniform Rational B‐Spline or Bézier patches can be used, even if they are restricted. Multi‐connected surface domains can be treated using the same geometrical definition. The method described allows nodes to slide on a patch or jump from a patch onto another one. Such movements greatly improve the mesh quality with regard to a chosen criterion. Problems occurring with patch‐by‐patch meshing techniques when surfaces patches exhibit significant size differences are then overcome. The adaptation technique can be made independent of CAD data structures and meshing techniques, hence it constitutes the basis of a mesh management module.
Conformal grid generation for high aspect ratio simply and doubly connected regions
Authors: Baty Roy S. , Morris Philip J.
Published: August 2005

Conformal co‐ordinate transformations are used to map rectangular computational domains onto arbitrary simply and doubly connected regions with smooth boundaries. The efficient numerical schemes of Wegmann involving the solution of the inverse boundary correspondence function problems associated with the mapping of the unit disc or circular annulus onto simply or doubly connected domains, respectively, are employed. The numerical implementation of these schemes is emphasized. Examples are generated for regions with elliptic inner and outer boundaries. Additional examples are used to demonstrate the accuracy and convergence of the schemes and their practical limitations. The techniques are found to converge well if holomorphic functions are used to describe the boundaries. The use of preconditioning maps is also discussed.
A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems
Authors: Farhat Charbel , Chen Po‐Shu , Mandel Jan
Published: August 2005

We present a new efficient and scalable domain decomposition method for solving implicitly linear and non‐linear time‐dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time‐independent problems. Computational results confirm that the optimal convergence properties of the time‐independent FETI method are preserved in the time‐dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large‐scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time‐dependent problems, including the fictitious domain decomposition method.
Adaptive two‐step methods for semidiscretized wave equations
Authors: Franco J. M. , Petriz F.
Published: August 2005

Adaptive two‐step direct integration methods are constructed for the integration of second‐order semidiscrete evolution equations possessing oscillatory solutions. The methods are based on a class of adaptive multistep methods for a semilinear test model whose frequency is known. They are constructed following the notion of diagonally implicit RK‐methods by using efficient rational approximations to cos v, v ≥ 0. Our interest is centered on the dispersion (or phase errors) of the dominant components in the numerical oscillations when these methods are applied to a linear homogeneous test model. Two‐step methods which have high order of dispersion (up to 12), whereas the algebraic order is relatively low (2 or 4), are derived. Applications of these methods to linear as well as non‐linear test models and to semidiscretized hyperbolic equations reveal a good behaviour with regard to error propagation when they are compared with other conventional methods.