弹性力学问题解唯一的边界积分方程

Boundary Integral Equations of Unique Solutions in Elasticity

从积分方程式出发,应用基本解的特性分析,说明在力边值问题中,位移边界积分方程和面力边界积分方程的位移解不唯一· 提出了位移解唯一的条件,建立了唯一解的位移边界积分方程和面力边界积分方程· 实例计算结果表明唯一解的边界积分方程是有效的·

The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non_unique displacement solutions in a traction boundary value problem. The condition for the existence of unique displacement solutions is proposed for the traction boundary value problem. The degrees of freedom of the displacement solution are removed by the condition to obtain the boundary integral equations of unique solutions for the traction boundary value problems. Numerical example is presented to demonstrate the accuracy and efficiency of the present equations.