混合夹杂问题的边界元法

该文提出了一种求解含固体、流体和孔隙等多类型夹杂的混合夹杂问题的边界元法。混合夹杂问题实质也是多连通域问题,但内边界的位移和面力都是未知量,导致该问题因定解条件不足而无法直接求解。根据不同类型夹杂的本构关系建立了各夹杂与基体界面面力与位移之间的关联矩阵,从而形成除给定边界条件以外的补充定解条件,使问题得以解决。以平面问题为例,分别对只含固体夹杂、流体夹杂以及同时含有孔隙、固体和流体夹杂的情况进行了计算,模拟了含100个随机分布夹杂的板材的弹性模量,验证了该方法的有效性、程序的正确性和可靠性。

BOUNDARY ELEMENT METHOD FOR PROBLEMS WITH MULTIPLE TYPES OF INCLUSIONS

A new boundary element method is presented for solving the problems of 2D solids with multiple types of inclusions such as elastic inclusions, fluid inclusions and pores. Essentially, this problem is also a multi-connected domain problem, but the displacements and tractions on the inner boundaries of the multi-connected domain are unknown quantities, which made the whole problem cannot be solved directly for the lack of adequate boundary conditions. According to the constitutive relations of the different types of inclusions, the so-called incidence matrices are established between the tractions and displacements on the inclusion-matrix interfaces, and they are just the complementary boundary conditions that we are trying to find, consequently the problem can be solved without any difficulty. To verify the validity of the presented method as well as the correctness and the reliability of the program, the examples of plane strain problems are illustrated, in which the solid matrix containing only one or all of the three types of inclusions respectively, and the effective elastic modulus are simulated for a sheet that contains up to 100 randomly distributed elastic inclusions.