正交各向异性半平面内作用集中载荷的弹性解及边界元法常单元基本公式
The Elastic Solution of Concentrated Force Acting in Orthogonal Anisotropic Half-Plane and Constant Element Fundamental Formulae of Boundary Element Method
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摘要: 本文采用镜相法,推导出了正交各向异性半平面作用集中载荷的理论解,给出了常单元系数矩阵表达式,为采用边界元法求解半平面问题提供了必要的公式.特解表达形式简洁,对边界元间接法常单元和高次单元各积分均可求出其原函数,可避免计算程序中的定积分数值计算过程.Abstract: In this paper,the elastic solutions of concentrated force acting in orthogonal anisotropic half-plane are derived by imaginal method and the formulae of coefficient matrix for constant element are put forward.To solve half-plane problems numerically by BEM,this paper provides the necessary formulae.Because the expressions of fundamental solutions are very simple,the object functions could be obtained for every integral of constant element and higher order element of indirect BEM.Thus,the procedure of integration could be avoided in calculation program
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Key words:
- orthotropic /
- concentrated laod /
- elastic solution /
- boundary element method
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[1] 云天锉,集中力作用于剪切模量沿深度线性变化的半空间公式,应用数学和力学.6(1)(1985). [2] 尹雷方,弹性半平面问题的边界积分方程一边界元法,上海力学,(1)(1984). [3] 文王华,各向异性体平面问题边界元法,计算结构力学及其应用.(1)(1988). [4] 列赫尼茨基,Г.C.,《各向异性板》,科学出版社(1964). -
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