Abstract
A general solution of plane elastic problems using the complex variable has been developed by Muschelisvili. His solution, for simply connected areas, requires the determination of two analytic functions, given by two integral equations, in which the loaded area in the z-plane is transformed to a unit circle in the ζ-plane. The integrations involved have been carried out only for cases in which the mapping function is rational. In this paper a method of solution is derived when the Taylor's series for the mapping function is known. This leads to solving an infinite set of simultaneous equations in which the unknowns are the coefficients in the Taylor's expansion of the analytic functions defined by Muschelisvili. These equations are readily solved by an iterative process, giving results of any required degree of accuracy. To illustrate the application of the method, the problem of a square with equal and opposite tensions directed along a diagonal, and applied at the extremities of that diagonal, is given.
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