Elastic Boundary Element Method Research Articles

A method for direct evaluation of singular integral in direct boundary element method

AbstractA new method is presented for evaluating the Cauchy principal value integral and the free term in the three‐dimensional elastic boundary element method. This method expresses the singular integral as the sum of a weakly singular integral and an integrable Cauchy principal value integral. The former can be computed by means of the usual standard Gaussian quadrature after a transformation suggested by Lachat and Watson,10 who correctly limited its use only to weakly singular integral. The latter can be calculated by direct integration in the Cauchy principal value sense. This paper also points out some limitations in the use of triangle polar co‐ordinate suggested by Li et al.11 and later extended by Zhang and Xu.16 The general expression of the free term for a boundary point with arbitrary characteristic surface is also presented. Simple numerical examples which verify the efficiency and accuracy of the present method are given.

The multiple Reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary

AbstractThis paper presents a new boundary element approach to transform domain integrals into equivalent boundary integrals. The technique, called the Multiple Reciprocity Method, is applied to 2‐D elasticity problems and operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces, as well as loadings due to linear and quadratic temperature distributions. Numerical examples are presented to demonstrate the accuracy and efficiency of the method.

A method identifying defects by inverse analysis using boundary element method.

In this paper, the defect with noncircular shape in a two-dimensional structural component is identified by using the complex method incorporated into the two-dimensional elastic boundary element method. The method for searching for the defect is that the norm of boundary displacement, defined as the sum of the square of the difference between experimental values and numerical solutions, becomes minimum when the assumed defect coincides with the real one. The complex method is used to find the defect shape and position with minimal norm by iteratingly modifying the fictitious defect boundary within some constraint conditions without calculating derivatives. The procedure of defect identification is discussed under several numerical examples, and it is shown that the present method is efficient and accurate in searching for the real defect.

Pseudo-body force boundary element method for thermoelastic problems

The Boundary Element Method (BEM) formulations for the elastic bodyforce problems can be extended to allow for the temperature changes. The temperature changes may be treated using two different ways of either the domain approach, or the boundary approach. In the domain approach, the integrals involving the thermal strains and body forces remain as domain integrals, whereas in the boundary approach or the so-called pseudo-body force approach, the temperature derivative can be assumed as a kind of bodyforce. The integrals due to pseudo-body force and the actual bodyforce can then be transferred over the boundary provided that the scalar potential due to the actual and pseudo-body force are harmonic in nature. Thus, in the boundary approach, the integrals due to temperature and body force are in the form of boundary integrals. In the numerical formulations, the basic features of the elastic BEM formulations still apply, only some modifications required which essentially concern the known vector of the resulted system of linear equations, and also the calculations of the stress and strain. The efficiency of the BEM pseudo-body force approach in handling thermoelastic and bodyforce problems is assured.

2軸応力下の空洞まわりの弾塑性応力解析

A new method for elasto-plastic stress analysis of underground rock cavern, under the condition of bi-axial initial stress, is presented by jointing two existing methods, a boundary element method for elasticity and a characteristics method for plasticity. An efficient scheme is presented and discussed, as well as its successful application to a circular opening. This coupling method is effective to analyze the extent of the plastic area which is of fundamental importance for the construction of rock cavern.In the present method, the analytical region is divided into two areas, the plastic area and the infinite elastic area. Then the wall of the opening is in general divided into the elastic range Gamma;1 and the plastic range Gamma;2. The plastic stress field around the opening can be independently analyzed by the characteristics method, where the boundary condition is given by the surface traction acting on the wall of the opening.The elastic stress field around the opening is firstly analyzed by the boundary element method of constant element, and the surface range where the elastic stress state exceeds the criterion of yielding is assumed as a virtual plastic range Gamma;2. And then the extent of the plastic area and the final shape of the boundary Gamma;3 between the two areas are analyzed by the iteration, in which the plastic area is gradually expanded until the elastic stress state at Gamma;3 satisfies the criterion of yielding. In this iteration, the boundary element method is used for the stress analysis of the infinite elastic area and the inner boundary condition on Gamma; =Gamma;1+Gamma;3 is given from the plastic stress field around the opening basing on the continuity of surface traction on Gamma;3. It is discussed that the present method is available for the partial yielding domain and the full yielding domain in the initial stress space in Fig. 10, since the tensile fracturing is not considered in the present scheme.The present method is successfully applied to a single circular opening. It is made clear that the maximum depth of plastic area is mainly depending upon the maximum principal stress of the initial stress, and the influence of the ratio of the principal stresses is small as shown in Fig. 11. Therefore, it is noted that the maximum depth of plastic area can be approximately estimated from the analytical solution under hydrostatic pressure.

The boundary element method in elasticity

This paper describes the application of the boundary element method in elasticity starting by discussing the basic weighted residual expressions. Boundary elements of different orders are presented and discussed, together with the numerical integration schemes. The relationships are presented for three dimensional elasticity and specialized to the two dimensional case. Results are presented and discussed, specially in relation to finite elements and other “domain” type techniques.