求弹性半平面问题基本解的一个直接方法
A Direct Method for Deriving Fundamental Solution of Half-Plane Problem
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摘要: 本文利用镜像法[2]和直接积分导出了弹性半平面问题的基本解.这个推导方法比Gladwell用镜像法和富氏变换要直观.这个基本解对于用边界元法分析半平面域具有任意外形孔洞的应力集中问题将起着十分重要的作用.Abstract: A fundamental solution for half-plane problems which will play a key role in calculation of the stress concentration around a hole embedded in half-plane is derived by a method combining images with direct integrations. It is wore intuitive than the Fourier transform method used by Gladwell[6]. In addition, the principle and procedure of boundary element method to solve the half-plane problems are also presented by means of Betti's reciprocal theorem in this paper.It is shown that the. computing procedure for half-plane problems is much more convenient using the fundamental solution presented here than the one adopted by C.A. Brebbia[1].
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[1] Brebbia,C.A,The Boundary Element Methods for Engineers,Pentech Press(1978),139-145. [2] Brebbia,C.A,Boundary Element Techniques in Engineering,Newnes-Butterworths(1980),102-110. [3] Rekach,V.G,Manual of the Theory of Elasticity,Mir Publishers,Moscow(1979),165-168. [4] Sneddon,I,N.,Fourier Transforms,上海交通书店影印(1951),416-419 [5] Telles,J.C.F.and C.A、Brebbia,Boundary element solution for half-plane problem,Int.J.Solids and Structures,12(1981). [6] Gladwell,G.M.L,Contact Problems in the Classical Theory of Elasticity Germantown,Sijthoff and Noordhoff(1980),230-235. -
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