bluuebunny/crossref_metadata_2025 huggingface dataset:
Large deflection inelastic pseudo‐transient analysis of laminated composite plates
Authors: Kant T. , Kommineni J. R.
Published: August 2005

A pseudo‐transient (static) linear, geometric, material and combined geometric and material non‐linear analyses of composite laminates are presented. A nine‐noded isoparametric quadrilateral finite element belonging to the Lagrangiar family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. Elasto‐plastic material behaviour is incorporated using the flow theory of plasticity. In particular, a modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for by assuming a constant transverse shear strain across the thickness of the laminate and the geometric non‐linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of plastic behaviour through the thickness. A wide range of numerical examples is presented to demonstrate the validity and efficiency of the present approach. The results for combined non‐linearity are also presented. The variety of results presented here, which are based on realistic material properties of often‐used advanced laminated composite plates, and especially those for combined non‐linear analysis, should serve as a reference for future investigations.
A variationally coupled FE–BE method for transient problems
Authors: Belytschko T. , Lu Y. Y.
Published: August 2005

A variationally coupled finite element–boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solutions.
An accelerated subspace iteration method
Authors: Rajendran S. , Narasimhan M. V.
Published: August 2005

The subspace iteration method is widely used for the computation of a few smallest eigenvalues and the corresponding eigenvectors of large eigenproblems. Under certain conditions, this method exhibits slow convergence. For improving the convergence of the method, a few acceleration techniques are already available in the literature. In this paper, yet another method is presented. The method has been applied for the computation of a few smallest eigenpairs of some typical eigenprobiems. The results indicate that the acceleration method is efficient for large eigenproblems. Simplicity, ease of computer implementation, absence of parameters whose values are to be chosen based on experience and effectiveness for large problems are the attractive features of the proposed method.
A new eight‐node quadrilateral shear‐bending plate finite element
Authors: Polit O. , Touratier M. , Lory P.
Published: August 2005

A new eight‐node quadrilateral shear‐bending Reissner–Mindlin plate finite element for the very thin and thick plates without locking and spurious zero‐energy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four‐ and eight‐node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight‐node quadrilateral shear‐bending plate finite element proposed has been found to be very efficient.
A forward gradient time integration procedure for an internal variable constitutive model of Sn–Pb solder
Authors: Busso E. P. , Kitano M. , Kumazawa T.
Published: August 2005

A self‐correcting forward gradient time integration procedure is formulated for the integration of a new unified visco‐plastic constitutive model for an eutectic solder alloy using a tensorial internal state variable. The procedure has been implemented numerically into a commercial FE code through a user‐material subroutine and is well suited to deal with numerically stiff constitutive equations. This is accomplished through an automatic subincrementation procedure controlled by a maximum allowed equivalent inelastic strain increment per time step.

For illustration purposes, two examples are discussed: (i) uniaxial test simulations to reveal the optimum combination of the user‐specified tolerance and the prescribed load step size to obtain a desired accuracy at a minimum cost, (ii) a large‐scale three‐dimensional analysis of an integrated circuit (IC) package's solder joint to show the capability of the proposed procedure to deal with thermomechanical loading.
A parallel finite element contact/impact algorithm for non‐linear explicit transient analysis: Part II—Parallel implementation
Authors: Malone James G. , Johnson Nancy L.
Published: August 2005

A parallel implementation of the contact algorithm discussed in Part I of this paper has been developed for a non‐linear dynamic explicit finite element program to analyse the response of three‐dimensional shell structures. The parallel contact algorithm takes advantage of the fact that in general only some parts of the structure will actually be in contact at any given time. Special interprocessor communication routines and a method which enables individual processors to dynamically build local contact domains during execution have been developed. The performance of the parallel contact algorithm has been studied by executing the program on 128 processors of a distributed‐memory multiprocessor computer.
On stability and convergence of finite element approximations of Biot's consolidation problem
Authors: Murad Márcio A. , Loula Abimael F. D.
Published: August 2005

Stability and convergence analysis of finite element approximations of Biot's equations governing quasistatic consolidation of saturated porous media are, discussed. A family of decay functions, parametrized by the number of time steps, is derived for the fully discrete backward Euler–Galerkin formulation, showing that the pore‐pressure oscillations, arising from an unstable approximation of the incompressibility constraint on the initial condition, decay in time. Error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented, and a post‐processing technique is employed to improve the pore‐pressure accuracy.
About the numerical simulation of the sheet metal stamping process
Authors: Gontier C.
Published: August 2005

The following is a summary of several years' research work devoted to the development of a sheet metal forming computer program. A few aspects of the membrane formulation are discussed, leading to the conclusion that instability problems cannot be avoided. Then a complete formulation including bending, based on the large‐displacement equations of plates, is developed. An expression for the tangent matrix is obtained. Elastic behaviour, yield equation and the plastic flow rule are reformulated in a suitable basis. A reliable method for stress projection on the yield surface, based on a ‘dichotomic’ algorithm, is presented. Many other features of the simulation problem are discussed: contact and frictional effects, thickness updating and geometry definitions. Finally, three illustrative test cases are presented.
Structural optimization based on preconditioned conjugate gradient analysis methods
Authors: Schmit Lucien A. , Lai Ye‐Chen
Published: August 2005

An efficient method for structural optimization is presented. Instead of classical direct decomposition methods, Preconditioned Conjugate Gradient (PCG) methods, in conjunction with two proposed starting‐vector generation schemes, are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems. These inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization. This technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints. The effectiveness of the PCG methods of analysis in structural optimization is demonstrated. Comparison among different preconditioners is made. The effect of the proposed starting‐vector generation schemes is shown. The comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis, when using PCG methods of analysis, are assessed. The parallel computation potential of PCG methods is discussed. Because of the iterative nature of PCG analysis methods and the prospects they offer for parallel computation, it is found that PCG analysis methods show promise in the context of structural optimization.
Boundary element discretization of plane elasticity and plate bending problems
Authors: Aristodemo M. , Turco E.
Published: August 2005

The paper deals with the discretization of the integral equations arising in the boundary formulation of plane elasticity and plate bending problems. Particular attention is paid to the efficiency of the interpolation used in approximating the boundary quantities and to the precision and computational convenience in evaluating the boundary integrals. The proposed discretization model is based on the use of a quadratic B‐spline approximation to represent the boundary variables and on the results from the analytical integration to compute the boundary coefficients. The advantages are those of accuracy and the saving of computer time. Some numerical results allow an analysis of the performance of the model.
Investigation of regularization parameters and error estimating in inverse elasticity problems
Authors: Maniatty Antoinette M. , Zabaras Nicholas J.
Published: August 2005

The method of Tarantola1 based on Bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in Schnur and Zabaras.2 It is shown that when normal Gaussian distributions are assumed and the error in the data is uncorrelated, the Bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in Schnur and Zabaras,2 As such, the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem. Examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution.
An algorithm for the optimization of directionally stretched triangulations
Authors: Zhang Hou , Trépanier Jean‐Yves
Published: August 2005

A procedure for the optimization of stretched triangular grids is described. The method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non‐linear spring system. The function is minimized using a gradient method based on the steepest descent. Examples are provided to show the applicability of the method to computational fluid dynamics problems.
Error estimators and enrichment procedures for the finite element analysis of thin sheet large deformation processes
Authors: Bonet Javier
Published: August 2005

An essentially geometric error measure capable of estimating the accuracy with which a faceted element mesh describes the continjous exact geometry of a deforming sheet is presented in this paper. This error is based on an estimated strain tensor between discrete and approximate geometries. Additionally, the paper describes the enrichment process which, at a reasonable computational cost, ensures that the error targets are met whilst generating as few elements as possible. In particular, the enrichment algorithm is based on a judicious combination of two simple operations, namely, side splitting and diagonal swapping. Finally, several applications relating to superplastic forming components are presented.
A new least‐squares finite element model for combined Navier–Stokes and Darcy flows in geometrically complicated domains with solid and porous boundaries
Authors: Nassehi V. , Petera J.
Published: August 2005

In this paper we present a novel method for linking Navier–Stokes and Darcy equations along a porous inner boundary in a flow regime which is governed by both types of these equations. The method is based on a least‐squares finite element technique and uses isoparametric C1 continuous Hermite elements for domain discretization. We show that our technique is superior to previously developed models for the combined Navier–Stokes/Darcy flows. The previous works use weighted residual finite element procedures in conjunction with C0 elements which are inherently incapable of linking Navier–Stokes and Darcy equations. The paper includes the application of our model to a geometrically complicated axisymmetric slurry filtration system.
Incompressibility and axisymmetry: A modified mixed and penalty formulation
Authors: Jinka Ashoka G. K. , Lewis Roland W.
Published: August 2005

This paper describes a modified penalty and two‐field mixed formulation for the analysis of incompressible axisymmetric field problems, A discussion of the existing difficulties with incompressibility and axisymmetric formulations is covered in detail. To facilitate the exact satisfaction of incompressibility in axisymmetric bodies during finite element modelling procedures, a modified shape function is used in the description of radial displacement. Further, the modification to the radial displacement interpolation function overcomes the lacunae of the existing mixed and penalty formulations by eliminating the bias of the isoparametric element behaviour in a divergence free continuum state. A six‐noded triangular element, with a central bubble function, is considered to amplify the issues connected with incompressibility in axisymmetric geometries. The bilinear displacements, along with three reduced/selective integration rules in the case of the modified penalty method and three discontinuous pressure nodes in the element for the case of the modified mixed method, are shown to be equivalent in the case of a numerical study of the incompressible cylinder expansion problem. The displacements, stresses and pressure values obtained from the modified methods will be shown to be in close agreement with exact solutions available from the literature. The numerical treatment proposed in the present study clearly demonstrates the performance and the need for modified methods in the analysis of incompressible axisymmetric engineering problems.
Non‐linear analysis of thin‐walled structures using plate elements
Authors: Chin C. K. , Al‐Bermani F. G. A. , Kitipornchai S.
Published: August 2005

This paper presents a simple and efficient rectangular thin plate element for elastic geometric non‐linear analysis of thin‐walled structures. Based on the updated Lagrangian formulation and small strain hypothesis, this element can accurately predict the non‐linear pre‐ and post‐buckling load–deflection paths of a plate structure. Using symbolic manipulation, the linear and geometric stiffness matrices for the rectangular thin plate element are derived explicitly, thereby eliminating the need for numerical integration. The element contains 30 degrees of freedom (d.o.f.): 14 d.o.f. for the in‐plane (membrane) action and 16 d.o.f, for the out‐of‐plane (bending) action. Several examples involving the large deflection behaviour of thin‐walled structures are presented to demonstrate the accuracy, efficiency and versatility of the method.
Plate buckling loads by the boundary element method
Authors: Syngellakis S. , Elzein A.
Published: August 2005

A boundary element solution of the plate buckling problem is extended and refined to accommodate any combination of loading and support conditions. It is complemented by a similar boundary element formulation yielding the prebuckling membrane state of stress for non‐uniform distributions of edge loads. Both continuous and discontinuous models of various orders of approximation for boundary as well as domain unknowns have been employed and their effect on the accuracy of the solution algorithm assessed. The computer code incorporates automatic mesh generation schemes for both the boundary and the domain through which a wide range of plate geometries can be discretized and analysed. Further, gains in both efficiency and accuracy are achieved by taking advantage of any support and loading symmetries and reducing the formulation to a standard eigenvalue problem. A large number of plate examples are solved to optimize the choice of various modelling parameters and to establish the reliability of the proposed analysis.
Robust boundary triangulation and delaunay triangulation of arbitrary planar domains
Authors: Subramanian G. , Raveendra V. V. S. , Kamath M. Gopalakrishna
Published: August 2005

A simple and robust boundary triangulation algorithm is proposed and, based on it, completely automatic Delaunay mesh generation procedures are developed. The algorithm is equally applicable to convex, non‐convex and multiply connected planar domains. In this approach, given the nodes, the number of triangles formed is precisely known and any desired control over mesh generation is possible.
Time‐space method for multidimensional melting and freezing problems
Authors: Saitoh T. S. , Nakamura M. , Gomi T.
Published: August 2005

In this paper, the time–space method (TSM) for multidimensional melting and solidification problems is proposed. In the proposed TSM, the timewise co‐ordinate is incorporated into one of the spatial co‐ordinates, thereby transforming the usual transient 2‐D (or 3‐D) problems into steady 3D (or 4‐D) boundary‐value problems.

Since time integration is not necessary, the TSM has a feature that eliminates the so‐called numerical instability which has been a great concern in the principal numerical methodologies in the past. That is, no error propagation in the timewise direction occurs in the TSM calculation.

The TSM is applicable to almost all transient heat transfer and flow problems. The computer running time will be reduced to only 1/100th–1/1000th of the existing schemes for 2‐D or 3‐D problems. The sample calculations are presented for a 2‐D melting problem in a square cavity and the validity of the present method is examined.
Self‐similar solutions for axisymmetric jets using two turbulence models
Authors: Ghazzawi N. A. , Rabadi N. J.
Published: August 2005

Similarity solutions for incompressible axisymmetric jets using a k–ϵ and a constant eddy diffusivity turbulence models are considered. For the k–ϵ model, the governing equations are very complex. Therefore, a transformation that simplifies these equations and makes them amenable to efficient numerical solution is used. Results for the velocity, turbulent kinetic energy and dissipation rate are obtained. Also, velocity decay rate, growth rate, entrainment and kinetic energy decay rate are determined. A comparison with experimental data and other works utilizing a parabolic marching asymptotic solution to the full partial differential equations is made. This comparison shows that similarity solutions are more accurate than solutions using numerical marching procedures.
Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints
Authors: Weatherill N. P. , Hassan O.
Published: August 2005

A method is described which constructs three‐dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.
On the non‐singular traction‐BIE in elasticity
Authors: Huang Q. , Cruse T. A.
Published: August 2005

The work reported herein develops a generalized traction‐BIE formulation which involves only weakly singular integrals (in the three‐dimensional problem) or totally regular integrals (in the two‐dimensional problem). The first step deals with the terms in the Somigliana displacement identity, and then the derivatives of these terms. The only conditions required for the existence of the traction‐BIE and the related Somigliana stress identity are weak continuity of the in‐plane derivatives of the surface displacements and of the surface tractions. It is shown that the Cauchy Principal Value (CPV) interpretations so commonly used in BIE developments are unnecessary. The formulation is established not only at a smooth boundary point, but also at a corner point. The extension of the non‐singular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements applicable to a generalized problem statement as well as the usual BEM implementations is also shown. In the demonstrated formulation, the source points are located directly at the boundary nodes and non‐conformal elements are not needed.
Thermal postbuckling analysis of cylindrically curved composite laminates with a hole
Authors: Madenci E. , Barut A.
Published: August 2005

A non‐linear finite element analysis including a new flat shell element has been developed to examine the response of laminated panels going through large deflections and rotations under uniform temperature change. The equilibrium path describing the relationship between temperature and deflection is sensitive to the material system, hole size, in‐plane boundary conditions and radius of curvature. Certain laminate configurations exhibit snap‐through and bifurcation along this path. The accuracy of the results for a cylindrically curved panel is established by considering numerous validation problems with known solutions. The method has been demonstrated to be highly effective for predicting the non‐linear response of thin composite shells subjected to uniform temperature change in the presence of large displacements and rotations and material anisotropy.
Reduced minimization theory in beam elements
Authors: Oak‐Key Min , Yong‐Woo Kim
Published: August 2005

By using the field‐consistency and least‐squares fit concepts, reduced minimization theory is proposed to show the effect of numerical integration on the behaviour of C0‐continuous beam elements when the Jacobian is constant within an element. The theory provides a unified viewpoint on the relationship between spurious constraint, the location of optimal sampling points and integration order. The conventional Uniformly Reduced Integration (URI) and Selective Reduced Integration (SRI) are redefined by using reduced minimization theory. We also present numerical reduced minimization theory, which explains the effects of more‐than‐two‐order‐lower reduced integration when Gaussian quadrature is employed.
Control of spurious mechanisms for 20‐node and transition sub‐integrated hexahedral elements
Authors: Sze K. Y.
Published: August 2005

In this paper, control of spurious mechanisms for sub‐integrated 20‐node and transition hexahedral elements is devised by an assumed stress approach. The higher‐order stress modes for stabilizing the sub‐integrated elements are identified by examining the spurious mechanisms. With an admissible simplification of the flexibility matrix, row vectors of the leverage matrix can be used as stabilization vectors. Numerical examples for the stabilized 20‐node element are presented. Accuracy of the derived element is far better than the fully integrated displacement elements. Meanwhile, the former also consumes marginally less CPU time than the latter.
Discrete shape sensitivity equations for aerodynamic problems
Authors: Hou Gene J.‐W. , Taylor Arthur C. , Korivi Vamshi M.
Published: August 2005

Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a pre‐elimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.
Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity
Authors: Michaleris Panagiotis , Tortorelli Daniel A. , Vidal Creto A.
Published: August 2005

Tangent operators and design sensitivities are derived for transient non‐linear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods. The derived formulations are suitable for finite element implementations. Analyses of systems, with materials that exhibit history dependent response, may be obtained directly by applying the analyses of transient non‐linear coupled systems. Rate‐independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes.
Two‐dimensional elastodynamic displacement discontinuity method
Authors: Siebrits E. , Crouch S. L.
Published: August 2005

A time‐domain elastodynamic displacement discontinuity method is presented for analysing two‐dimensional problems in solid mechanics. Linear, continuous in time and piecewise linear in space interpolation functions are assumed for the displacement discontinuities. Causal and analytical integrations are used throughout. The resulting numerical algorithms are time marching and implicit. The displacement discontinuity method can be used to model a class of traction boundary value problems, where the unknowns are the transient shear and normal discontinuities in displacement across the surface of a mathematical crack in an infinite, isotropic and homogeneous linear elastic medium.
Multiple quadrature underintegrated finite elements
Authors: Liu Wing Kam , Hu Yu‐Kan , Belytschko Ted
Published: August 2005

New multiple‐quadrature‐point underintegrated finite elements with hourglass control are developed. The elements are selectively underintegrated to avoid volumetric and shear locking and save computational time. An approach for hourglass control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural co‐ordinates so that the elements require no stabilization parameter. To improve accuracy over the traditional one‐point‐quadrature elements, several quadrature points are used to integrate the internal forces, especially for tracing the plastic fronts in the mesh during loading and unloading in elastic–plastic analysis. Two‐ and four‐point‐quadrature elements are proposed for use in the two‐ and three‐dimensional elements, respectively. Other multiple‐quadrature points can also be employed. Several numerical examples such as thin beam, plate and shell problems are presented to demonstrate the applicability of the proposed elements.
Finite volumes and finite elements: Two ‘good friends’
Authors: Idelsohn S. R. , Oñate E.
Published: August 2005

In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.
A Lagrangian approach to the non‐causal inverse dynamics of flexible multibody systems: The three‐dimensional case
Authors: Ledesma Ragnar , Bayo Eduardo
Published: August 2005

This paper addresses the problem of end‐point trajectory tracking in flexible multibody systems through the use of inverse dynamics. A global Lagrangian approach is employed in formulating the system equations of motion, and an iterative procedure is proposed to achieve end‐point trajectory tracking in three‐dimensional, flexible multibody systems. Each iteration involves firstly, a recursive inverse kinematics procedure wherein elastic displacements are determined in terms of the rigid body co‐ordinates and Lagrange multipliers, secondly, an explicit computation of the inverse dynamic joint actuation, and thirdly, a non‐recursive forward dynamic analysis wherein generalized co‐ordinates and Lagrange multipliers are determined in terms of the joint actuation and desired end‐point co‐ordinates. In contrast with the recursive methods previously proposed, this new method is the most general since it is suitable for both open‐chain and closed‐chain configurations of three‐dimensional multibody systems. The algorithm yields stable,non‐casualactuating joint torques and associated Lagrange multipliers that account for the constraint forces between flexible multibody components.
A temperature‐based formulation for finite element analysis of generalized phase‐change problems
Authors: Celentano Dsego , Oñate Eugenio , Oller Sergio
Published: August 2005

A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
A numerical method for introducing an arbitrary yield function into rigid–viscoplastic FEM programs
Authors: Zhou D. , Wagoner R. H.
Published: August 2005

Many standard yield functions (Hill, von Mises, etc,…) allow the derivation of simple equations relating the effective strain rate to principal strain rates explicitly. Such yield functions are easily implemented in rigid–viscoplastic finite element method programs. Other yield functions (Hosford, e.g.) do not allow for this simple approach. A numerical method was proposed in this paper to solve this problem which meets the requirement of rigid–viscoplastic finite elements and can generate the material stiffness terms (first and second derivatives of the effective strain rate with respect to principal strain rates) at any strain state. The numerical method was found to be numerically efficient, accurate and robust. As an example of the procedure, Hosford's yield function was introduced in a rigid–viscoplastic finite element program and results for the punch stretching simulation were compared with Hill‐type materials. The numerical efficiency of the method was also compared. Simulation of full dome formability test, plane strain and square punch stretching was performed by this numerical method with Hosford's yield function.
A space–time coupled p‐version least‐squares finite element formulation for unsteady fluid dynamics problems
Authors: Bell Brent C. , Surana Karan S.
Published: August 2005

This paper presents a p‐version least‐squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled. The dimensionless form of the differential equations describing the problem are first cast into a set of first‐order differential equations by introducing auxiliary variables. This permits the use of C° element approximation. The element properties are derived by utilizing p‐version approximation functions in both space and time and then minimizing the error functional given by the space–time integral of the sum of squares of the errors resulting from the set of first‐order differential equations. This results in a true space–time coupled least‐squares minimization procedure.

A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. The space–time coupled p‐version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space–time coupled approach. For non‐linear problems the non‐linear algebraic equations resulting from the least‐squares process are solved using Newton's method with a line search. This procedure results in a symmetric Hessian matrix. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance.

The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection–diffusion and Burgers equations. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space–time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements. The work presented in this paper provides the basis for the extension of the space–time coupled least‐squares minimization concept to two‐ and three‐dimensional unsteady fluid flow.
Inflation of hyperelastic cylindrical membranes as applied to blow moulding. Part I. Axisymmetric case
Authors: Khayat R. E. , Derdouri A.
Published: August 2005

The free and confined axisymmetric inflation of a cylindrical membrane is considered in this study. The problem is formulated to include single and multiple contacts between the cylinder and the surrounding solid boundary. The material is assumed to obey the Mooney–Rivlin constitutive equation. Unlike various finite element based discretization approaches, the present formulation is based on a set of ordinary differential equations governing the deformation field. The resulting two‐point‐boundary‐value problem is solved using the finite element method. Comparison between theory and experiment leads to good agreement. Stick condition upon contact is assumed. Examples of complex geometries including a blow‐moulded bottle are treated. An example of simultaneous stretch and inflation is also given.
A free‐formulation‐based flat shell element for non‐linear analysis of thin composite structures
Authors: Madenci E. , Barut A.
Published: August 2005

A flat shell element based on the free‐formulation finite element concept is developed for analysing geometrically non‐linear thin composite shells. A corotational form of the updated Lagrangian formulation is utilized. Numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element. These results are obtained by solving the incremental equilibrium equations through the cylindrical arc‐length method.
A parallel boundary element formulation for determining effective properties of heterogeneous media
Authors: Ingber Marc S. , Womble David E. , Mondy Lisa A.
Published: August 2005

This paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective properties of two heterogeneous physical systems. The first physical system is comprised of spheres sedimenting in a viscous fluid at low Reynolds numbers. The effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity. The second physical system is a short‐fibre reinforced composite. The effective property for this system is the composite modulus. The determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of heterogeneities to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus‐wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus‐wrap mapping can be shown to minimize communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.
Object oriented matrix classes for use in a finite element code using C++
Authors: Zeglinski Gordon W. , Han Ray P. S. , Aitchison Peter
Published: August 2005

This paper presents a new method of writing finite element programs using the programming approach known as object oriented programming (OOP). More specifically, the C++ language is used to illustrate the key OOP concepts. In addition to the OOP finite element examples, a detailed discussion of OOP techniques in the creation of a generalized matrix library is presented. The C++ language is used in this paper because it is more suited to numerical programs than a pure OOP language such as Smalltalk. The efficiency, flexibility and maintainability of the C++ program are shown to be superior to a comparable version written in a non‐OOP language, such as FORTRAN. The matrix library contains a number of matrix objects that are useful for specific types of matrix related problems. Different sparse storage schemes are implemented for each different type of matrix. A large number of functions are provided for each matrix type in order to implement many common matrix operations. In applications, the OOP paradigm allows the functions to be used in a very simple way that is common to all the matrix types. The sample finite element code included in this paper is primarily intended to illustrate the key concepts of OOP style. This paper explains how to set up a finite element hierarchy, material hierarchy and how to integrate this with the matrix hierarchy (library). Thus, a completely object oriented finite element program can be written.
The monomial method and asymptotic properties of algebraic systems
Authors: Burns Scott A.
Published: August 2005

The monomial method is a numerical method for solving systems of algebraic equations. It is related to Newton's method, but is based on an approximation that is monomial, rather than linear, in form. It has been shown previously that the monomial method has a number of properties not shared by Newton's method that are responsible for enhanced performance. This paper demonstrates that many of the performance characteristics of the monomial method can be explained in terms of asymptotic properties of algebraic systems, and the ability of the monomial method to exploit these properties. The monomial method recasts the algebraic system to have monomial asymptotes in all directions, so that the monomial approximation becomes asymptotically exact. This explains the very rapid movement toward a solution in the first iteration from distant starting points that has been observed with the monomial method. Problem types with ‘good asymptotics’ are found to be solved very effectively by the monomial method. Several specific engineering applications with good asymptotics are identified, and suggestions are made regarding other types of engineering applications that are likely to be handled effectively by the monomial method.
Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method
Authors: Kang Shinill , Zabaras Nicholas
Published: August 2005

The aim of this work is to calculate the optimum history of boundary cooling conditions that, in two‐dimensional conduction driven solidification processes, results in a desired history of the freezing interface location/motion. The freezing front velocity and heat flux on the solid side of the front, define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved.

The so‐called two‐dimensional inverse Stefan design problem is formulated as an infinite‐dimensional minimization problem. The adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem. The sensitivity and adjoint equations are derived in a moving domain. The gradient of the cost functional is obtained by solving the adjoint equations backward in time. The sensitivity equations are solved forward in time to compute the optimal step size for the gradient method. Two‐dimensional numerical examples are analysed to demonstrate the performance of the present method.
On the robustness and efficiency of the SAM algorithm for structural optimization
Authors: Stander Nielen , Snyman J. A. , Coster J. E.
Published: August 2005

A parameter study involving a feasibility factor, adaptive tolerance refinement and active set and move limits is conducted on the interior feasible direction method with successive approximations (SAM). The study involves the sizing design of five structural problems of which one is a large power transmission tower to be designed in adherence with a standard design code. It is concluded that a move limit is dispensable for this application while adaptive tolerance refinement makes the algorithm more efficient. Optimal ranges for the feasibility factor and active set limits are suggested. This study reaffirms and quantifies the exceptional stability and robustness of the SAM algorithm.
Sequential quadratic programming for non‐linear elastic contact problems
Authors: Björkman Gunnar , Klarbring Anders , Sjödin Björn , Larsson Torbjörn , Rönnqvist Mikael
Published: August 2005

The physical problem considered in this paper is that of a non‐linear elastic body being indented by a rigid punch. The treatment is based on finite element discretization and sequential quadratic programming (SQP). The finite element formulation is obtained through a variational formulation, which generalizes to frictionless contact a three‐field principle which involves deformation, volume strain and hydrostatic pressure as independent fields. We compare an incremental load method and a method where the indentation for the final load is sought directly. Crucial for the second method is the use of a line search with respect to a merit function which measures the infeasibility in the optimality criteria for the problem; this line search also includes a check of the orientation‐preserving condition of a positive determinant of the deformation gradient. Each iteration within an SQP method requires the solution of a quadratic programming (QP) subproblem, and four different methods for the solution of these subproblems are compared. The performance of the overall procedure is also compared to that of a commercially available system. Test examples ranging from 23 to 770 displacement degrees of freedom are treated. The computational results show that the proposed solution concept is feasible and efficient. Furthermore, it can be applied to general non‐linear elastic contact problems, since it does not include any ad hoc rules.
A unified set of resequencing algorithms
Authors: Souza Luiz T. , Murray David W.
Published: August 2005

A general algorithm for resequencing equations and finite element meshes is presented. This algorithm incorporates, in a unified form, the most successful resequencing schemes, namely: the Sloan, Gibbs–King (GK) and Gibbs–Poole–Stockmeyer (GPS) algorithms. As well it provides a context within which the development of new algorithms may take place with a minimum of change. It is easily programmed and has been shown to speed up the execution of the original GK algorithm.
Application of high‐order quadrature rules to time‐domain boundary element analysis of viscoelasticity
Authors: Lee Sang Soon , Westmann R. A.
Published: August 2005

This paper presents an accurate and efficient method for the treatment of time integrals in time‐domain boundary integral equations for viscoelastic problems. First, the integral equations in space and time are derived for linear viscoelastic and thermo‐viscoelastic problems. Then various quadrature rules are discussed for the computation of time integrals. A modified Simpson's rule is proposed as an effective integration scheme. The proposed procedure requires a small computational effort and it is applicable even in time‐domain boundary element analysis of many different problems. Numerical results of example problems show the accuracy and effectiveness of the proposed method.
Unified and mixed formulation of the 4‐node quadrilateral elements by assumed strain method: Application to thermomechanical problems
Authors: Zhu Y. Y. , Cescotto S.
Published: August 2005

In this paper, a class of ‘assumed strain’ mixed finite element methods based on the Hu–Washizu variational principle is presented. Special care is taken to avoid hourglass modes and shear locking as well as volumetric locking. An unified framework for the 4‐node quadrilateral solid and thermal as well as thermomechanical coupling elements with uniform reduced integration (URI) and selective numerical integration (SI) schemes is developed. The approach is simply implemented by a small change of the standard technique and is applicable to arbitrary non‐linear constitutive laws including isotropic and anisotropic material behaviours. The implementation of the proposed SI elements is straightforward, while the development of the proposed URI elements requires ‘anti‐hourglass stresses’ which are evaluated by classical constitutive equations. Several numerical examples are given to demonstrate the performance of the suggested formulation, including static/dynamic mechanical problems, heat conduction and thermomechanical problems.
Simulation of free surfaces in 3‐D with the arbitrary Lagrange–Euler method
Authors: Szabo Peter , Hassager Ole
Published: August 2005

The arbitrary Lagrange–Euler (ALE) kinematic description has been implemented in a 3‐D transient finite element program so as to simulate multiple fluid flows with surfaces and interfaces of general shapes.

The description of fluid interfaces includes continuity of velocity and a discontinuous tangential and normal stress appropriate for fluids of variable interfacial tension.

The formulation is particularly relevant to the description of low and intermediate Reynolds number flow dominated by interfacial tension.