用复变函数法求解弹性力学空间轴对称问题的方法及解例

本文证明了空间轴对称问题的Love应力函数可用两个适当选择的复变量广义解析函数1]表示,并导出了应力分量、位移分量及边界条件的复变函数表达式.为了表明文中所述方法的可行性以及检验所得公式的正确性,本文用幂级数法求解了含有球形空腔的圆柱体在周围受压及两端受拉时的解答,与用其他方法得到的该问题的解答完全一致.最后本文还求解了一个锥体在侧面受均匀剪力时的解答,同时通过把常体力化为表面力以后还求解了锥体在重力作用下的解答.

The Method of Solving Axisymmetric Problems in Elastic Space by Complex Function and Some Examples

This paper proves Love's stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variates reasonably1], and deduces the expressions of the components of stress displacements and boundary conditions in complex function. To present the feasibility of the method here and examining the truth of the formulae founded in this paper, the problem of circular shaft with globular cavity pressed on the side and pulled at the ends is solved by using power series and the result is the same as that solved by other methods. In the end, the problem of a cone sheared by uniform shear stress on the sideface is solved, and the solution of a cone acted on by gravity is given by converting constant body forces into surface forces.