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The subject of this paper is the calculation of charge distribution on the surfaces of thin conducting nanotubes in electrostatic problems, by the boundary element method (BEM). A line model of a nanotube is proposed here. This model overcomes the problem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples. Copyright © 2006 John Wiley & Sons, Ltd.

This paper presents a formulation for shape optimization in thermoelasticity using a meshless method, namely the element-free Galerkin method. Two examples are treated in detail and comparisons with previously published finite element analysis results demonstrate the excellent opportunities the EFG offers for solving these types of problems. Smoother stresses, no remeshing, and better accuracy than finite element solutions, permit answers to shape optimization problems in thermoelasticity that are practically unattainable with the classical FEM without remeshing. For the thermal fin example, the EFG finds finger shapes that are missed by the FEM analysis, and the objective value is greatly improved compared to the FEM solution. A study of the influence of the number of design parameters is performed and it is observed that the EFG can give better results with a smaller number of design parameters than is possible with traditional methods. Copyright © 2001 John Wiley & Sons, Ltd.

The standard (singular) boundary node method (BNM) and the novel hypersingular boundary node method (HBNM) are employed for the usual and adaptive solutions of three-dimensional potential and elasticity problems. These methods couple boundary integral equations with moving least-squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter. The ‘hypersingular residuals’, developed for error estimation in the mesh-based collocation boundary element method (BEM) and symmetric Galerkin BEM by Paulino et al., are extended to the meshless BNM setting. A simple ‘a posteriori’ error estimation and an effective adaptive refinement procedure are presented. The implementation of all the techniques involved in this work are discussed, which includes aspects regarding parallel implementation of the BNM and HBNM codes. Several numerical examples are given and discussed in detail. Conclusions are inferred and relevant extensions of the methodology introduced in this work are provided. Copyright © 2001 John Wiley & Sons, Ltd.

The Boundary Node Method (BNM) is developed in this paper for solving three-dimensional problems in linear elasticity. The BNM represents a coupling between Boundary Integral Equations (BIE) and Moving Least-Squares (MLS) interpolants. The main idea is to retain the dimensionality advantage of the former and the meshless attribute of the later. This results in decoupling of the ‘mesh’ and the interpolation procedure.For problems in linear elasticity, free rigid-body modes in traction prescribed problems are typically eliminated by suitably restraining the body. However, an alternative approach developed recently for the Boundary Element Method (BEM) is extended in this work to the BNM. This approach is based on ideas from linear algebra to complete the rank of the singular stiffness matrix. Also, the BNM has been extended in the present work to solve problems with material discontinuities and a new procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body. Copyright © 1999 John Wiley & Sons, Ltd.

The Element-Free Galerkin (EFG) method allows one to use a nodal data structure (usually with an underlying cell structure) within the domain of a body of arbitrary shape. The usual EFG combines Moving Least-Squares (MLS) interpolants with a variational principle (weak form) and has been used to solve two-dimensional (2-D) boundary value problems in mechanics such as in potential theory, elasticity and fracture. This paper proposes a combination of MLS interpolants with Boundary Integral Equations (BIE) in order to retain both the meshless attribute of the former and the dimensionality advantage of the latter! This new method, called the Boundary Node Method (BNM), only requires a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself. An underlying cell structure is again used for numerical integration. In principle, the BNM, for 3-D problems, should be extremely powerful since one would only need to put nodes (points) on the surface of a solid model for an object. Numerical results are presented in this paper for the solution of Laplace's equation in 2-D. Dirichlet, Neumann and mixed problems have been solved, some on bodies with piecewise straight and others with curved boundaries. Results from these numerical examples are extremely encouraging. © 1997 by John Wiley & Sons, Ltd.

Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non-linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green–Naghdi rate, are considered here within the same setting with only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material constitutive laws, including a hypoelastic model and a unified isotropic viscoplastic model, for these two objective rates. The numerical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.

A Finite Element Graph (FEG) is defined here as a nodal graph (G), a dual graph (G*), or a communication graph (G˙) associated with a generic finite element mesh. The Laplacian matrix (L(G),L(G*) or L(G˙)), used for the study of spectral properties of an FEG, is constructed from usual vertex and edge connectivities of a graph. An automatic algorithm, based on spectral properties of an FEG (G, G* or G˙), is proposed to reorder the nodes and/or elements of the associated finite element mesh. The new algorithm is called Spectral PEG Resequencing (SFR). This algorithm uses global information in the graph, it does not depend on a pseudoperipheral vertex in the resequencing process, and it does not use any kind of level structure of the graph. Moreover, the SFR algorithm is of special advantage in computing environments with vector and parallel processing capabilities. Nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh. If G is used, then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix. If either G* or G˙ is used, then the elements in the mesh are suitably reordered for a finite element frontai solver, A unified approach involving FEGs and finite element concepts is presented. Conclusions are inferred and possible extensions of this research are pointed out. In Part II of this work,1 the computational implementation of the SFR algorithm is described and several numerical examples are presented. The examples emphasize important theoretical, numerical and practical aspects of the new resequencing method.

In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G˙ associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.

The focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems, and the use of these sensitivities to carry out optimal design. Direct differentiations of the boundary integral formulation of Poisson's equation for charge conservation and of the non-linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities. Methods for solving the sensitivity equations are discussed. A numerical implementation of the methods is validated through several examples. It is demonstrated that the Design Sensitivity Coefficients (DSCs) of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these DSCs.

The purpose of this short paper is to describe an experience at converting a scalar-serial elastic axisymmetric BEM code to a vector-parallel environment on an IBM . This is a single zone BEM computer program.

This paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells. The formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields. To facilitate extension to materially non-linear analysis, the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation. When desired, the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions. The element geometry is based on a nine-noded quadrilateral with biquadratic interpolation of the displacement field. The strain field is based on a bilinear interpolation with additional non-linear terms, chosen on the basis of eigenvalue analysis. The element passes the required patch tests, does not display either membrane or shear locking effects, and is free of communicable spurious modes. Numerical results are presented for elastic analyses of several standard plate and shell test problems.

Efficient solution of boundary-value problems for time-dependent inelastic deformation in metallic structures are generally solved by finite element methods and separate descriptions for time-independent plasticity and time-dependent creep are normally used. The boundary-integral equation method was recently applied for the first time to such problems. A very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler type time-integration scheme with automatic time-step control for time integration is presented. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor--corrector scheme for time-integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time-histories of loadings. The numerical results presented in the paper are for certain illustrative problems.

The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time-dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time-dependent Green's functions and convolution integrals. The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing. The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two-dimensional problems. Comparison with existing semi-analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.

A finite element formulation for elastoviscoplasticity problems in the presence of large strains and deformations is presented in this paper. The formulation is capable of using any of a class of combined creep-plasticity constitutive models with state variables for the description of material behaviour. The specific problem considered is plane strain extrusion using the constitutive model originally proposed by Hart. Numerical results are presented for sample problems and the important effects of extrusion speed and friction (at the die–workpiece interface) on the residual stresses in an extruded sample are investigated. The computer program developed here is quite general and can be modified to solve problems for other manufacturing processes like rolling, sheet forming, etc.

The efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper. This comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods.

A finite element formulation for the solution of time-dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep-plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above-mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi-steady or the unsteady diffusion equation for the determination of the temperature field, are carried out.

The accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time-dependent inelastic torsion of prismatic shafts. Several cross-sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic-time hardening creep constitutive model.