弹性力学反平面剪切问题的半逆解法

Semi-Inverse Method for Anti-Plane Shear Problem of the Theory of Elasticity

半逆解法是求解弹性力学问题的重要解析方法,它通过假设部分或全部应力分量的函数形式,推导出满足相容方程的应力函数,再求出满足边界条件的应力分量,进而利用位移边界条件求出位移分量。弹性力学教学中一般只介绍半逆解法在弹性力学平面问题中的运用,文章通过实例介绍了弹性力学反平面剪切问题及其应力函数法,给出了半逆解法求解弹性力学反平面剪切问题的过程,发展了半逆解法在弹性力学问题中的应用。

The semi-inverse method is an important analytical method for solving the elasticity problems.It deduces the stress function satisfying the compatible equation by assuming the function form of some or all of the stress components,and then finds the stress components which satisfy the boundary conditions.The displacement components can be finally obtained by using the displacement constraint boundary conditions.In the teaching of the theory of elasticity,only the application of the semi-inverse method for the plane problems of the theory of elasticity is introduced.In this paper,the anti-plane shear problem of theory of elasticity and its stress function method are introduced by an analysis example,and the solving process of the anti-plane shear problem is given by using the semi-inverse method,which expands the application of the semi-inverse method in the problemof theory of elasticity.