The Representation of Three-Dimensional Elastic Displacement Fields with the Aid of Complex Valued Functions for Several Curvilinear Coordinates

In the previous papers /1,2,3/ a complex representation of three-dimensional elastic stress and displacement fields has been given in such a way that the complex formulas of Muskhelishvili /4/ for plane strain are included as special cases. The complex representation involves six arbitrary complex functions which ensure the satisfaction of the equilibrium equations. Choosing appropriate complex functions one can obtain systematically infinite series of solution functions for curvilinear coordinates. For the treatment of boundary conditions the complex formulation can offer advantages. The purpose of this paper is to present a collection of formulas and results for a variety of coordinate systems so as to permit the convenient application of the complex-function method in elasticity. A detailed derivation of the complex represen­tation of displacements can be found in /1/. Applications of the method are given in /1,2,9/.