This paper presents a new inverse analysis approach for identifying material properties and unknown geometries for multi-region problems using the Boundary Element Method (BEM). In this approach, the material properties and coordinates of an unknown region boundary are taken as the optimization variables, and the sensitivity coefficients are computed by the Complex-Variable-Differentiation Method (CVDM). Due to the use of CVDM, the sensitivity coefficients can be accurately determined in a way that is as simple to use as the Finite Difference Method (FDM) and an inverse analysis for a complex composite structure can be easily performed through a similar procedure to the direct computation. Although basic integral equations are presented for heat conduction problems, the application of the proposed algorithm to other problems, such as elastic problems, is straightforward. Two numerical examples are given to demonstrate the potential of the proposed approach.

This paper describes a robust and efficient elasto-plastic boundary element method (BEM) intended for complex problems in geomechanics. Some novel techniques are employed to evaluate the singular integral equations accurately and efficiently. In particular, the strong singularities arising in the domain integrals of the stress integral equations are removed by transforming them from domain integrals to (cell) boundary integrals. Adaptive integration schemes are used throughout to optimize the integration process. The system equations are condensed by recasting them in terms of the plastic multiplier, and a novel Newton–Raphson algorithm delivers greatly improved solution times. Some examples demonstrate the scope and power of the method.

In this paper, a set of internal stress integral equations is derived for solving thermoelastic problems.A jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations. The strongly singular domain integral is then regularizedusing a semi-analytical technique. To avoid the requirement of discretizing the domain into internal cells,domain integrals included in both displacement and internal stress integral equations are transformedinto equivalent boundary integrals using the radial integration method (RIM). Two numerical examples for 2D and 3D, respectively, are presented to verify the derived formulations.

In this paper, a new and simple boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals. The strong singularities appearing in internal stress integral equations are removed by transforming the domain integrals to the boundary. Other weakly singular domain integrals are transformed to the boundary by approximating the initial stresses with radial basis functions combined with polynomials in global coordinates. Three numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

A novel set of auxiliary equations, which supplement the fundamental boundary integral equations, for the treatment of corners and edges arising in discontinuous traction problems and at zonal intersections is derived. Based on these equations, an efficient linear 3D multi-region BEM algorithm is presented which can deal with arbitrarily many regions. Numerical examples demonstrate the effectiveness of this algorithm.