A new contact searching algorithm for general contact systems is proposed in this paper. Due to that the smooth and accurate geometry description is crucial to the contact stress analysis, we have worked out a free-formed-surface (FFS) algorithm specialized to model the contacting surface with the C1 boundary continuity and the exact boundary condition definition. Moreover, the geometrical description using the FFS produces those data required for determining the actual contact direction and calculating the exact contact penetration. Numerical simulation results demonstrate that our contact searching algorithm is robust and capable to simulate three-dimensional contact problems accurately. Copyright.

In order to improve the accuracy of the mixed element for irregular meshes, a penalty-equilibrating 3D-mixed element based on the Hu-Washizu variational principle has been proposed in this paper. The key idea in this work is to introduce a penalty term into the Hu-Washizu three-field functional, which can enforce the stress components to satisfy the equilibrium equations in a weak form. Compared with the classical hybrid and mixed elements, this technique can efficiently reduce the sensitivity of the element to mesh distortion. The reason for the better results of this penalty technique has been investigated by considering a simple 2D problem. From this investigation, it has been found that the penalty parameter here plays the role of a scaling factor to reduce the influence of the parasitic strain or stress, which is similar to the devised selective scaling factor proposed by Sze. Furthermore, compared with the hybrid stress element, the proposed element based on the three-field variational principle is more suitable for material non-linear analysis. Numerical examples have demonstrated the improved performance of the present element, especially in stress computation when FEM meshes are irregular.

In this paper, Voronoi cell finite element method (VCFEM), introduced by Ghosh and coworkers (1993), is applied to describe the matrix-inclusion interfacial debonding for particulate reinforced composites. In proposed VCFEM, the damage initiation is simulated by partly debonding of the interface under the assumption of the critical normal stress law, and gradual matrix-inclusion separations are simulated with an interface remeshing method that a critical interfacial node at the crack tip is replaced by a node pairs along the debonded matrixinclusion interface and a more pair of nodes are needed to be added on the crack interface near the crack tip in order to better facilitate the free-traction boundary condition and the jumps of solution. The comparison of the results of proposed VCFEM and commercial finite element packages MARC and ABAQUS. Examples have been given for a single inclusion of gradually interfacial debonding and for a complex structure with 20 inclusions to describe the interfacial damage under plane stress conditions. Good agreements are obtained between the VCFEM and the general finite element method. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials.

The Regular Hybrid Boundary Node Method (RHBNM) is developed in this paper for solving three-dimensional linear elasticity problems. Coupling modified functional with the Moving Least Squares (MLS) approximation, the RHBNM only requires discrete nodes constructed on the surface of a domain. Formulations and a general computer code of the RHBNM for 3D linear elasticity problems and the MLS interpolation on a generic surface have been developed. The RHBNM is formulated in terms of the domain and boundary variables. The domain variables are interpolated by classical fundamental solutions with the source points located outside the domain; and the boundary variables are interpolated by MLS approximation. The main idea is to retain the dimensionality advantages of the BNM, and localize the integration domain to a regular sub-domain, as in the MLBIE, such that no mesh is needed for integration. All integrals can be easily evaluated over regular shaped domains (in general, semi-sphere in the 3D problem) and their boundaries. Numerical examples for the solution of 3D elastostatic problems show that the high convergence rates with mesh refinement and the high accuracy with a small node number are achievable. The treatment of singularities and further integrations required for the computation of the unknown domain variables, as in the conventional BEM and BNM, can be avoided.

A new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented here. The formulation is expressed in terms of domain and boundary variables, and the domain variables are interpolated by classical fundamental solution; while the boundary variables are interpolated by moving least squares (MLS). The main idea is to retain the dimensionality advantages of the BNM, and get a truly meshless method, which does not require a 'boundary element mesh', either for the purpose of interpolation of the solution variables, or for the integration of the 'energy'. All integrals can be easily evaluated over regular shaped domains (in general, semi-sphere in the 3-Dproblem) and their boundaries. Numerical examples presented in this paper for the solution of Laplace's equation in 2-D show that high rates of convergence with mesh refinement are achievable, and the computational results for unknown variable are most accurate. No further integrations are required to compute the unknown variables inside the domain as in the conventional BEM and BNM. Copyright

An inverse approach based on the inherent strain method [ASME J. Engng Mater. Technol. 111 (1989) 1; Determination of residual stress based on the estimation of eigenstrain, PhD Thesis, 1996] using BEM has been proposed for constructing the residual stress existing in structures. Considering the stability of the inverse problem, the inherent strain field is approximately expressed as a series of some smooth basis functions, and the corresponding domain integral is transformed into boundary integral by means of the dual reciprocity boundary element method. In this way the advantage of the BE approach can be preserved. Numerical examples show the applicability of the presented scheme.

This paper presents the recent progress achieved by the authors' group on the simulation of 2D elastic solids containing a large number of randomly distributed inclusions using BEM. A new scheme of repeated similar sub-domain BEM is proposed in this paper. The randomly distributed inclusions investigated include identical circular inclusions, elliptical inclusions with identical size and shape but different orientation, and also inclusions with different shape, size and different material properties. The number of inclusions is approximately 100 by conventional BEM, and it can be more than 1000 by the fast multipole BEM on only one PC. The interface between the matrix and inclusion can be at the ideal interface as well as at the interface with interphase layers. The numerical results show that for such investigations, the BEM is more suitable compared to FEM and other numerical methods. The simulated effective elastic modulus are presented and compared with different theoretical results. Future investigations should be extended to simulation of 3D models and simulation on brittle failure process.

This paper presents simulation of 3D composite materials containing a large number of particles using a new version of adaptive fast multipole boundary element method (BEM). A scheme of similar sub-domain approach is also applied for the case of identical sphere particles. Generalized Minimum Residual Method (GMRES) is selected as an iterative solver for the equation systems implicitly arising from fast multipole BEM. The number of particles reaches 100 by the combination of above algorithms on an personal computer. Numerical results show that fast multipole BEM is applicable for large scale simulation of certain composite materials.

In this paper, fast multipole boundary element method is applied for largescale simulation of 2D crack problems. The scheme of parallel computation for fast multipole boundary element method is also presented and applied for 2D elasticity. GMRES is used as an iterative solver. Numerical results show high efficiency of this fast algorithm and scalability of its parallelization.