bluuebunny/crossref_metadata_2025 huggingface dataset:
Combined effect of shear and large deformation on stress intensity factors
Authors: Alwar R. S. , Thiagarajan S.
Published: August 2005

An attempt has been made to study the influence of large deformation on the stress intensity factor in a cracked plate subjected to bending including shear deformation. It is assumed that singular terms for stress resultants and strains in the case of large deformation have the same angular distribution and order of singularity as in the case of a linear problem. With this in view the small deformation singular element has been used at the crack tip region surrounded by large deformation plate bending elements. The finite element analysis, based on total Lagrangian formulation combined with the modified Newton–Raphson technique, has been used to get numerical results. Several examples connected with large deformation of cracked plates subjected to bending are studied. Using the above technique stress intensity factors for linear and non‐linear cases have been compared.
Analysis of difference diagrams stability approximating a class of one‐ and two‐dimensional non‐linear–parabolic field equations
Authors: Wiak Slawomir
Published: August 2005

This paper describes the stability conditions for difference diagrams applied to the approximation of one‐ and two‐dimensional non‐linear field equations. The one‐dimensional electromagnetic field is described by vector B and vector E, and the two‐dimensional field by magnetic vector potential A.

It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered diagrams.
Multi‐domain general axisymmetric stress analysis by BEM
Authors: Wang Hui‐Ching , Banerjee Prasanta K.
Published: August 2005

It is well known that there are many benefits in solving axisymmetric solids subjected to non‐axisymmetric loading by using Fourier series expansion of field variables. Although many researchers have utilized this technique to solve problems of cooling towers and rocket nozzles, etc. by the Finite Element Method, the BEM formulation and implementation of such a method have been available only recently, mainly due to the efforts of Rizzo and Shippy3 and Mayr et al.4 In this paper these early developments have been generalized further by including more expansion terms, an efficient decomposition of kernels into symmetric and antisymmetric forms, improved evaluation of matrix coefficients and developing more general computer implementation to include surface stress calculations, effects of body forces and extensive substructuring facilities to analyse multi‐zone problems.
Eigenproperties of large‐scale structures by finite element partitioning and homotopy continuation
Authors: Zhang Yan , Harichandran Ronald S.
Published: August 2005

Finite element partitioning (or substructuring) is employed to estimate the eigenproperties of large‐scale structural systems. A homotopy equation is constructed and its solutions are characterized by a number of curves which connect the eigensolutions of the partitions with those of the complete system. A step‐by‐step tracing procedure is developed to follow these curves. At each step, prediction and correction are performed. The Rayleigh–Ritz procedure and the conjugate gradient method are used as predictor and corrector, respectively. Compared with the sole use of either the Rayleigh–Ritz or gradient methods, the proposed method is more reliable and more efficient for large‐scale problems. Numerical implementation is well suited for supercomputers.
A finite element model for composite beams undergoing large deflection with arbitrary cross‐sectional warping
Authors: Stemple Alan D. , Lee Sung W.
Published: August 2005

A finite element formulation has been developed to take into account the warping effect of composite beams undergoing large deflection or finite rotation. This formulation is to be used to model combined bending, torsional and extensional behaviour of composite helicopter rotor blades. The new approach can model thin to moderately thick walled composite beams with complicated cross‐sections, tapers and arbitrary planforms. The warping effects are incorporated by assuming warping displacements superimposed over cross‐sections normal to the beam axis in the deformed configuration of a shear flexible beam. The strain is assumed to vary linearly through the wall thickness. The fixed or total Lagrangian description is adopted in the present formulation and the Newton–Raphson method is used to solve the non‐linear equilibrium equation resulting from the finite element approximation. Numerical tests of example problems demonstrate the validity and effectiveness of the present approach.
A C0 finite element formulation for thin‐walled beams
Authors: Chen Hong , Blandford George E.
Published: August 2005

Timoshenko's and Vlasov's beam theories are combined to produce a C0 finite element formulation for arbitrary cross section thin‐walled beams. Section properties are generated using a curvilinear co‐ordinate system to describe the cross section dimensions. The element includes both shear and warping deformations caused by the bending moments and the bimoment. A Gauss quadrature order is employed which exactly integrates the bending and warping stiffness matrices and provides a reduced integration order for the shear stiffness matrices. Numerical results are presented for a channel section cantilever beam. The influence of shear deformation is investigated and the calculated results are shown to be in excellent agreement with the classical solutions.
Three‐dimensional crack analysis using singular boundary elements
Authors: Jia Z. H. , Shippy D. J. , Rizzo F. J.
Published: August 2005

A multi‐domain method of solving three‐dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The displacement and traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack‐front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny‐shaped crack.
An implicit integration algorithm with a projection method for viscoplastic constitutive equations
Authors: Hornberger K. , Stamm H.
Published: August 2005

Robinson's viscoplastic model, a representative of the so‐called overstress models, is integrated by use of the generalized midpoint rule. The solution of the non‐linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with Newton's method. Consistent tangent moduli are calculated and the quadratic convergence of the global Newton equilibrium iteration is shown. The time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration. Various numerical examples are considered to demonstrate the efficiency of the methods.
Automatic mesh generation from solid models based on recursive spatial decompositions
Authors: Perucchio Renato , Saxena Mukul , Kela Ajay
Published: August 2005

This paper introduces a two‐stage algorithm for the automatic conversion of solid models into finite element meshes. In Stage 1 the solid is approximated by a collection of variably sized cells generated by recursive spatial decomposition and stored in a logical tree. In Stage 2 the approximating cell structure, which includes cells that are wholly inside the solid (IN) as well as cells that are neither inside nor outside (NIO), is transformed into a finite element model. IN cells are directly mapped into finite elements while NIO cells are decomposed according to their topologically complexity through either template mapping or recursive element extraction. Although specifically designed for adaptive remeshing, the algorithm is of general use and can be implemented in any Solid Modelling System that supports Boolean operations on solids and maintains a complete boundary representation. Core algorithms for Stages i and 2 are rigorously developed to insure their applicability within a genuinely automatic procedure. Specific issues related to boundary evaluation and decomposition procedures are identified and discussed. The implementation of the algorithm into an experimental system based on the PADL‐2 solid modeller is described. The paper concludes with a comparative study of existing meshing algorithms based on recursive spatial decompositions.
Static non‐linear three‐dimensional analysis of a riser bundle by a substructuring and incremental finite element algorithm
Authors: Bernitsas Michael M. , Vlahopoulos Nickolas
Published: August 2005

The problem of static, non‐linear, large three‐dimensional deformation of riser bundles used in offshore oil and gas production is studied within the limits of small strain theory. The mathematical model consists of the models of component‐risers and connectors which hold risers together. Each riser is modelled as a thin walled, slender, extensible or inextensible tubular beam‐column. It is subject to non‐linear three‐dimensional deformation dependent hydrodynamic loads, torsion and distributed moments, varying axial tension, and internal and external fluid forces. The problem is solved numerically by developing an algorithm which features substructuring, condensation and non‐linear incremental finite elements. Substructuring is used to decompose the riser bundle problem into those of individual component‐risers and equilibria of connectors. Condensation is used along with the connector equilibrium equations to produce connector forces and moments. Strong non‐linearities present in the model are handled by an incremental finite element approach. Accuracy of the computer code is verified by solving simple three‐dimensional cases. Two three‐dimensional applications are solved for a bundle with seven component‐risers and up to a total of 1267 degrees of freedom. Finally, a comparison is made with numerical results of a two‐dimensional analysis code. The influence of problem size on total CPU time is discussed.
Treatment of corners in BIE analysis of potential problems
Authors: Walker S. P. , Fenner R. T.
Published: August 2005

At corners or edges in the boundary of the domain of a potential problem the local normal gradient of potential is double‐valued. When Dirichlet boundary conditions are specified there are thus two unknowns at a single nodal point, and the sets of equations resulting from the usual BIE discretization are rendered indeterminate. We discuss here earlier approaches to the resolving of this problem, and describe a further approach which appears to offer some advantages. Both normal gradients can be approximated directly from local potential boundary conditions, showing the problem indeed to be formally overdetermined. This ability is discarded, in favour of yielding a robust and well‐conditioned relationship between the two gradients. This, in conjunction with the BIE analysis, permits solutions of considerable accuracy to be found, including the gradients at such corner nodes. Illustrative calculations are presented for rectilinear and curvilinear domains. These show that, even with as few elements as there are corners, and thus one and a half times as many unknowns as there are nodal points, good approximations to the gradients can be obtained. The need for progressively finer discretization as a corner is approached is thus much reduced.
Static and dynamic analysis of space frames with non‐linear flexible connections
Authors: Shi G. , Atluri S. N.
Published: August 2005

This paper deals with the effect of non‐linearly flexible hysteritic joints on the static and dynamic response of space frames. It is shown that a complementary energy approach based on a weak form of the compatibility condition as a whole of a frame member, and of the joint equilibrium conditions for the frame, is best suited for the analysis of flexibly jointed frames. The present methodology represents an extension of the authors' earlier work14 on rigidly connected frames. In the present case also, an explicit expression for the tangent stiffness matrix is given when (i) each frame member, along with the flexible connections at its ends, is represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations and only moderate relative rotations and (iii) the non‐linear bending–stretching coupling is accounted for in each member. Several examples, with both quasi‐static and dynamic loading, are included, to illustrate the accuracy and efficiency of the developed methodology.
A new implementation of the Lanczos method in linear problems
Authors: Papadrakakis M. , Smerou S.
Published: August 2005

The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right‐hand sides. The versions of the method proposed in the past treat the right‐hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
Application of the complex variable boundary element method to solving potential problems in doubly connected domains
Authors: Kassab A. J. , Hsieh C. K.
Published: August 2005

The complex variable boundary element method (CVBEM) developed by Hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains. A cut is made in the doubly connected domain, and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations. Cauchy–Riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when Neumann and Robin conditions are imposed on the boundaries. The resulting nodal equations are expressed in matrix form, and coding rules and methods for checking the matrix elements are developed. Three solution methods (implicit, explicit and hybrid) are described, and by means of examples, the efficacy of these methods is discussed and compared.
Effects of material non‐linearity on the residual stresses in a dendritic silicon crystal ribbon
Authors: Ray Sujit K. , Utku Senol
Published: August 2005

Thermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermo‐elasto‐plastic behaviour of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with non‐zero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress responses.
A boundary‐integral formulation for complex three‐dimensional geometries
Authors: Rezayat Mohsen , Burton Thomas E.
Published: August 2005

A new boundary‐integral formulation is proposed to analyse the heat transfer in complex three‐dimensional geometries. One example of such geometry is the die sets in the injection moulding process. Networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. The derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi‐analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula. Although the techniques introduced here are applied to a particular problem in heat transfer, their potential application is much broader.
Hybrid method for transient response of circular pins
Authors: Chen Han‐Taw
Published: August 2005

The combined application of the Laplace transform and the finite element method is used to analyse the transient response of circular pins. The present method removes the time‐dependence terms from the governing differential equations and boundary conditions using the Laplace transform and then the eigenfunction expansion method is applied to reduce the two‐dimensional boundary value problem to that of one dimension. Accordingly, the final transformed equation can easily be solved by the finite element method. The transformed temperature is inverted to the physical quantity numerically. The present results agree well with analytical solutions. In addition, it is seen that the results of axisymmetric transient heat conduction problems with the central node at r = 0 can accurately be obtained using the present method.
The effect of temperature and total gas pressure on the moisture content in a capillary porous body
Authors: Lewis R. W. , Ferguson W. J.
Published: August 2005

The finite element method is used for the solution of two dimensional heat, mass and pressure transfer problems in capillary porous bodies. This paper demonstrates a practical solution to Luikov's three degree of freedom system of partial differential equations where, previously, only an analytical solution in one dimension was feasible.
Adaptivity in hybrid‐Trefftz finite element formulation
Authors: Jirousek J. , Venkatesh A.
Published: August 2005

With the advent of computer aided design (CAD), the development of fully or semi‐automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement.

The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p‐method associated with the so‐called hybrid‐Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.
Importance and use of rigid body mode in boundary element method
Authors: Vable Madhukar
Published: August 2005

The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
Non‐linear optimization technique for partial solution of generalized eigenvalue problems
Authors: Marcos B. , Béliveau J. G.
Published: August 2005

This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non‐linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
Formulation of implicit finite element methods for multiplicative finite deformation plasticity
Authors: Moran B. , Ortiz M. , Shih C. F.
Published: August 2005

Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non‐symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near‐incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
Magnetostatic field computations in terms of two‐component vector potentials
Authors: Albanese R. , Rubinacci G.
Published: August 2005

In this paper the magnetostatic problem is stated in terms of two‐component electric and magnetic vector potentials. An associated numerical method, based on the adoption of edge elements, is proposed. This procedure overcomes the cancellation problems and the complexity of the interface conditions encountered by similar approaches in the presence of magnetic inhomogeneities and discontinuities of currents and magnetic fields.
Computer simulation of turbulent swirling flows
Authors: Riahi A. , Salcudean M. , Hill P. G.
Published: August 2005

Simulation of turbulent swirling flows has been carried out to provide insight on streamline curvature effects. Numerical calculations were based on the control‐volume method. Turbulence effects were represented by two‐equation turbulence models. The analysis of steady flow between two concentric rotating cylinders showed that the most promising model which incorporates curvature effects is that based on mixing energy developed by Wilcox and Chambers, as opposed to the ad hoc modification to the standard k–ϵ model. This model has also been used to simulate the decay of turbulent swirling flow in a short cylinder. A comparison between calculations and experimental results for such flow fields has been presented.
A dynamic contact buckling analysis by the penalty finite element method
Authors: Kanto Y. , Yagawa G.
Published: August 2005

The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial‐and‐error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
Explicit integration for three‐dimensional degenerated shell finite elements
Authors: Vlachoutsis Stefanos
Published: August 2005

Explicit integration across the thickness for three‐dimensional degenerated shell finite elements is analysed. For this purpose a modifed formulation is proposed. The Jacobian matrix of the physical–parameter spaces transformation is decomposed into a product of ‘in‐middle‐surface’ and ‘out‐of‐middle‐surface’ terms. This enables an expansion to be carried out of the strain–displacement matrix into power series of the thickness variable. Explicit integration is then performed and the corresponding formulae of the stiffness and mass matrices are given. The possibility of ‘locking’ for thin structures is explained. The analysis is applied to homogeneous and multilayered structures. Numerical applications for linear problems are given in the last part of the paper.
A semi‐analytical method for time‐domain analyses of dam–reservoir interactions
Authors: Tsai Chong‐Shien , Lee George C. , Ketter Robert L.
Published: August 2005

Non‐linear responses of dam–reservoir systems are not well understood, because of the lack of an exact time‐domain solution for the far field (extending to infinity) of the fluid. This paper presents a procedure for efficient time‐domain analyses. It is based on a semi‐analytical solution and is suitable for the determination of the interactive behaviour of dam–reservoir systems.

In this formulation, the fluid domain is divided into a near (to the dam) field, which is finite, and a far field extending to infinity. Arbitrary shapes of the upstream face of the dam, and of the bottom of the reservoir floor in the near field, are presumed. Furthermore, the far field is assumed to have a constant depth. The irregular near field is modelled by using the finite element method. A time‐domain semi‐analytical solution is obtained for the far field. For a vertical dam subjected to earthquake and ramp loadings, numerical solutions obtained compared well with the piecewise exact form of the analytical solution.
Advanced development of time‐domain BEM for two‐dimensional scalar wave propagation
Authors: Israil A. S. M. , Banerjee P. K.
Published: August 2005

An improved formulation for solving 2D transient scalar wave propagation problems by the Boundary Element Method (BEM) is presented. The kernels presented are simpler and better behaved than those that have appeared in the published literature. An appropriate set of temporal shape functions for linear variation is used. For spatial variations isoparametric quadratic elements are used. All of these represent significant improvements over the present level of sophistication in the analysis of 2D transient scalar problems. The algorithm is implemented in a general purpose boundary element code known as GPBEST.
Application of the boundary element method to non‐linear diffusion with reaction problems
Authors: Ramachandran P. A.
Published: August 2005

An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non‐linear reaction in one dimension. The non‐linearity is handled by a process of quasi‐linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
Finite element analysis of multiconductor printed‐circuit transmission‐line systems
Authors: Castillo Steven , Pantic Zorica , Mittra Raj
Published: August 2005

In this paper the finite element method (FEM) is used to analyse general, multiconductor transmission‐line systems of arbitrary cross‐section. The per‐unit‐length matrices of capacitance, inductance, conductance and resistance, which characterize a multiconductor transmission line, are obtained from the FEM analysis. Numerical results are presented and compared both with experimental results and other available data.
A truncated Newton–Lanczos method for overcoming limit and bifurcation points
Authors: Papadrakakis M.
Published: August 2005

In this study procedures for overcoming limit and bifurcation points in large‐scale structural analysis problems are described and evaluated. The methods are based on Newton's method for the outer iterations, while for the linearized problem in each iteration the preconditioned truncated Lanczos method is employed. Special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method. The proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.
Flow through fissured porous media with deformable matrix
Authors: Valliappan S. , Khalili‐Naghadeh N.
Published: August 2005

An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non‐linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non‐linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.
Two‐level domain decomposition preconditioning for the p‐version finite element method in three dimensions
Authors: Mandel Jan
Published: August 2005

This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p‐version finite element method for three‐dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds.
Validation of structural computation codes in elastoviscoplasticity
Authors: Benallal A. , Chabrand P. , Ghazouane M. , Chaudonneret M. , Culié J. P. , Contesti E. , Gamha H. , Golinval J. C. , Turbat A.
Published: August 2005

This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples.
An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems
Authors: Bonet Javier , Peraire Jaime
Published: August 2005

A searching algorithm is presented for determining which members of a set of n points in an N dimensional space lie inside a prescribed space subregion. The algorithm is then extended to handle finite size objects as well as points. In this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object. The suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method.
Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum
Authors: Simo J. C. , Wong K. K.
Published: August 2005

We show that, for rigid body dynamics, the mid‐point rule formulated in body co‐ordinates exactly conserves energy and the norm of the angular momentum for incremental force‐free motions, but fails to conserve the direction of the angular momentum vector. Further, we show that the mid‐point rule formulated in the spatial representation is, in general, physically and geometrically meaningless. An alternative algorithm is developed which exactly preserves energy, and the total spatial angular momentum in incremental force‐free motions. The implicit version of this algorithm is unconditionally stable and second order accurate. The explicit version conserves exactly angular momentum in incremental force‐free motions. Numerical simulations are presented which illustrate the excellent performance of the proposed procedure, even for incremental rotations over 65 degrees. The procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells.
A general methodological analysis for optimum design
Authors: Navarrina Fermin , Casteleiro Manuel
Published: August 2005

Generalized applications of modern numerical analysis methods—while digital computers experienced a fast development—produced a first revolution in design techniques, allowing one to perform computations considered unapproachable until that time. Introduction of Computer Aided Design (CAD) techniques—while high‐performance graphic peripherals experience a fast development—is actually producing a second revolution, by making easy and fast most routine design tasks. However, the introduction of Computer Aided OPTIMUM Design techniques has not yet produced the expected third revolution, in spite of the big amount of research and the interest of its potential applications. The authors think that this fact is due mainly to the dispersion of the optimum design research, and to the lack of a well established doctrine.

In this paper we approach the design process from a general methodological perspective, suitable to be applied to a wide range of problems. The design process is organized in several related levels. This approach leads naturally to the concept of optimum design and to the statement of a general mathematical programming problem. The practical application of this methodology to any particular problem takes an efficient and modular form. First and second order sensitivity analysis techniques are introduced from the general formulation, and alternative techniques (adjoint state) of the direct differentiation method are discussed.

DAO2, a powerful and versatile computer aided optimum design system by the Finite Element Method, has been developed by the authors1 according to this general methodology. The system can solve efficiently 2D and 3D structural fixed‐geometry and shape optimization problems. The power and viability of this methodology is illustrated by the solution to a structural optimization problem. The shape of the central section of an arch dam is optimized. A linear elastic structural FEM analysis is simultaneously performed for plane stress and for radial symmetry—while constraints are imposed for several load cases—taking into account the construction and loading stages. It should be emphasized that the same optimum design is reached in a small number of iterations starting from two significantly different initial designs.
A Treatment of wall boundaries for turbulent flows by the use of a transmission finite element method
Authors: Manouzi H. , Fortin M.
Published: August 2005

A method to connect momentum Navier‐Stokes equations with the universal law of the wall using the finite element method is developed for turbulent wall flows. This method is based on a domain decomposition of the fluid into subdomains near a solid boundary where the law of the wall is valid. A transmission formulation is introduced to match these regions and a new class of boundary finite element is used. This finite element takes into account the near‐wall profile of the velocity and the transmission conditions. Computational results are presented for Poiseuille flow and flow over a backward‐facing step.
An investigation of a finite rotation four node assumed strain shell element
Authors: Parisch H.
Published: August 2005

The paper presents a shell formulation based on the ‘degenerated solid approach’. The theory employs covariant strains and performs explicit integration through the shell thickness. The rigid body motion is exactly represented. The consistent tangent stiffness matrix is evaluated for the four node quadrilateral. It is shown, in the final part, that this type of element, which distinguishes itself by a very simple and easily understandable theory, gives good answers for linear as well as non‐linear applications.
Non‐linear B‐stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity
Authors: Simo J. C. , Govindjee S.
Published: August 2005

A class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward‐Euler return maps as a particular case. More importantly, it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary Helmholz free energy function (B‐stability). Since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm, the requirement of B‐stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity. The analysis that follows depends critically on the assumption of convexity. In particular, the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation. The proposed algorithms obey the discrete counterpart of this classical principle.
Convergence of the Newton‐Raphson algorithm in elastic‐plastic incremental analysis
Authors: Caddemi S. , Martin J. B.
Published: August 2005

A spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method. This assumption permits the incremental problem to be formulated as a convex non‐linear programming problem. The classical Newton‐Raphson algorithm can be adopted to provide an iterative solution of the non‐linear programming problem. It is shown that if an elastic or secant predictor modulus is used, the algorithm converges monotonically. However, if a tangent predictor is used, a line search algorithm must be included to ensure convergence.
Mesh relaxation: A new technique for improving triangulations
Authors: Frey William H. , Field David A.
Published: August 2005

Given a list of points defining a domain boundary, a three‐stage process is often used to triangulate a domain. First, an appropriate distribution of interior points is generated. Next the points are connected to form triangles. And, finally, the connectivity data are used to reposition the interior points using the Laplacian smoothing technique, thereby usually improving the shapes of the shapes of the triangles. This paper describes a new techniques for mesh improvement—adjusting the connection structure during the second stage of this process. The new scheme, which we call mesh relaxation, consists of a procedure for iteratively making the mesh topology more regular by edge swapping. For each interior edge, a relaxation index is computed that depends on the degrees of its end points and adjacent points. Any edge for which this index exceed a prescribed threshold will be swapped, i.e. replaced by a new edge connecting the adjacent points of the original edge. After all edge swaps are completed, Laplacian smoothing is applied to the mesh. Example show that, when the mesh point density varies smoothly and due care is taken in the vicinity of the boundary, mesh relaxation can dramatically increase the regularity of the mesh and produce improve triangle shapes.
Material geometry optimization of involute structures using sensitivity derivatives with respect to global design variables
Authors: Hart Jonathan K. , Stanton Edward L. , Schmit Lucien A.
Published: August 2005

A behaviour sensitivity analysis and optimization capability for involute structures has been developed and implemented via a test version of the P/COMPOSITE Module (which includes the CPATCHES finite element code for the analysis of 3‐D composites) in PATRAN. The user may obtain the sensitivity of the structural response with respect to a set of up to eight global material geometry variables that span the space of useful designs. The integrands of the sensitivity integrals are calculated in closed form and the same volume integration utilities that are employed throughout CPATCHES are used. This capability is restricted to problems in linear statics and a Cholesky equation solver is used. The behaviour sensitivity derivatives are validated by finite difference testing and through their successful application in severai involute optimization problems.
Thermal aspects of shear localization in microporous viscoplastic solids
Authors: Zavaliangos A. , Anand L.
Published: August 2005

A set of phenomenological state variable constitutive equations for large deformations of isotropic, thermo‐elasto‐viscoplastic, porous materials is considered, and a new semi‐implicit, incrementally objective time‐integration procedure for these constitutive equations is developed. The constitutive equations and the time‐integration procedure are implemented in a finite element program, and used to study the shear band formation and ductile fracture initiation triggered by flow softening due to the combined effects of void growth and deformation heating, in a plane strain tension test.
Field‐consistency rules for a three‐noded shear flexible beam element under non‐uniform isoparametric mapping
Authors: Prathap G. , Naganarayana B. P.
Published: August 2005

Most studies on the three‐noded quadratic Timoshenko beam element have been based on a 2‐point Gaussian integration rule for the shear energy or on the use of a smoothed substitute shape function or assumed shear strain field to improve its performance. However, if the mid‐node of the element is slightly displaced from the mid‐point position, the consistency requirements for the constrained shear strain field are more complex. This paper investigates this problem and the findings throw more light on consistency procedures demanded for distorted quadrilateral plate and shell elements. The optimal element which emerges from this study has bending and shear strain fields which have a linear variation over the element under non‐uniform mapping.
A thick–thin triangular plate element
Authors: Zhongnian Xu
Published: August 2005

A simple and efficient triangular finite element is introduced for plate bending applications. The element is a three‐node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick‐thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.
Transient dynamic and damping analysis of laminated anisotropic plates using a refined plate theory
Authors: Pervez Tasneem , Zabaras Nicholas
Published: August 2005

A refined model is presented for the linear transient dynamic and damping analysis of laminated anisotropic composite plates. Experimental measurements of specific damping capacity of unidirectional composite beams are used to predict the specific damping capacity of laminated composite plates in various modes of vibration. A finite element idealization is adopted, and the quadratic Lagrangian element is used together with selective/reduced integration. A viscous damping approximation is then employed to calculate the damped transient response of laminated plates. The effects of transverse shear deformation, symmetry condition, boundary conditions, anisotropy, aspect ratio, fibre orientation and the lamination scheme on specific damping capacity and damped transient response are investigated. Realistic examples illustrate the importance of these parameters. The present results agree very closely with experimental results available in the literature and can serve as a benchmark for future comparison by other investigators.