دانلود رایگان مقاله عبارت تحلیلی در ادغام شعاعی BEM برای محاسبه تنش با انواع ضرایب متغیر

Abstract

This paper presents a set of new analytical expressions for evaluating radial integrals appearing in the stress computation of several kinds of variable coefficient elastic problems using the radial integration boundary element method (RIBEM). The strong singularity involved in the stress integral equation is explicitly removed from the derivation of the analytical expressions. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. In addition, because it can solve many kinds of variable coefficient elastic problems, this approach has a very wide applicability. The fourth-order spline (Radial Basis Function) RBF is employed to approximate the unknowns appearing in domain integrals caused by the variation of the shear modulus. The radial integration method is utilized to convert domain integrals to the boundary, which results in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented formulations.

6. Conclusion

An efficient boundary element analysis approach is presented for solving elastic stress problems with several kinds of variable shear modulus. The radial integration method is used to transform the domain integrals appearing in the stress boundary-domain integral equations into boundary integrals. The radial integral in RIM with several kinds of variable shear modulus is analytically integrated for domain integrals based on the employment of the compactly supported fourth-order spline RBF. The strong singularity involved in the stress integral equation is explicitly removed for the derivation of the analytical expressions. The derived formulation can save computational time considerably in forming non-homogeneous integral coefficients. For the use of the RIBEM to solve other problems [8,16], the final radial integrals can be classified into the evaluation of line integral as shown in Eq. (23), and the integration results Eqs. (24)–(45) can be applied to solve a broad range of engineering problems, not just limited to elastic problems.