دانلود رایگان مقاله روش برای محاسبه تنش رابط hyper-singular در IIBEM برای حل مسایل کشش چند رسانه

Abstract

In this paper, a single stress integral equation is presented for solving multi-medium elasticity problems, and by using a newly proposed method for treating arbitrarily high order of singular boundary integrals, a new method is developed for computing the stresses on the interfaces of multi-media. Comparing to conventional multi-domain boundary element methods, the presented Interface Integral BEM (IIBEM) is more efficient in computational time, data preparing, and program coding. However, a big issue is encountered in IIBEM when computing the stresses on interfaces since the commonly used traction-recovery method in computing outer boundary stresses cannot be applied on the interfaces. Therefore, a direct method for handling a hyper-singular stress interface integral equation has to be used to obtain the interface stresses. In the direct method used in the paper, singularities are analytically removed by expressing the non-singular part of the integration kernel as a power series in a local distance defined on a projection line/plane, and the stresses on the interfaces can be evaluated precisely. Numerical examples are given to verify the correctness of the derived boundary-interface integral equations.

6. Concluding discussions

In this paper, a new boundary element method (BEM) is developed for computing 2D and 3D multi-medium interface stresses. The main feature of the method is that a single integral equation is used to solve multiple-medium problems. Comparing to the commonly used conventional multi-domain boundary element method, it has the advantages of less labor effort in preparing the input data, fast evaluation of interface integrals, and no need to assemble the system of equations from individual medium’s contributions. By using the lately proposed method treating hyper-singular boundary integrals, the hyper-singular integrals appearing in the stress boundary integral equations can be evaluated precisely. Numerical examples have demonstrated the correctness of the developed method.