两相材料空间问题基本解的显式张量表示*
An Explicit Tensor Expression for the Fundamental Solutions of a Bimaterial Space Problem
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摘要: 本文应用张量运算将文献中的三维两相无限体的集中力基本解表示为张量形式,从而使其能够直接用于边界积分方程和边界元方法,以分析两相材料空间弹性力学问题.本文结果包括了Mindlin问题、Lorentz问题和均质体空间问题的基本解.Abstract: In this paper, by using the method of tensor operation, the fundamental solutions,given in the references listed, for a concentrated force in a three-dimensional biphaseinfinite solid were expressed in the tensor form, which enables them to be directly appliedto the boundary integral equation and the boundary element method for solving elasticmechanics problems of the bimaterial space. The fundamental solutions for Mindlin'sproblem, Lorentz's problem and homogeneous space problem ore involved in the present results.
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[1] L.Rongved,Force interior to one of two joined semi-infinite solids,Proc.2nd Midwestern Conf Solid Mech.(1955),1～13. [2] J.Dundurs and M.Hetenyi,Transmission of force between two send-infinite solids,J Appl.Mech.,32(1965),671～674. [3] 黄克服、王敏中,两相材料构成空间的弹性力学基本解,中国科学,A(1991), 40-46. [4] 乐金朝,三维复合材料断裂力学问题的超奇异积分方程解法,上海交通大学博士学位论文(1994). [5] Y.C.Fung, Foundations of Solid Mechanics,Prentice-Hall,NJ(1965). [6] 木须·结城·浦,三次元境界要素解析における Mindlinの解の有用性,机论,A(1987),1864-1869 [7] N.Pban-Thien,On the image system for the Kelvin-state,J Elasticity,13(1983),231～235. -
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