The method of solving axisymmetric problems in elastic space by complex function and some examples

Abstract

This paper proves Love's stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variates reasonably^[1], 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.