A novel mapping finite element method for stress analysis in two dimensions

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Abstract
A mapping finite element method has been proposed in this paper for the solution of elasto-static problems in two dimensions. In this method the physical problem domain is mapped into an ‘image’ domain using exponential-polar type mapping functions. Properties of finite elements in the image domain are also obtained in accordance with the transformation implemented; these elements are then used to solve the problem in the image domain, subject to the appropriately transformed boundary conditions. Results of examples considered show that the proposed method, which is, incidentally, no more difficult or cumbersome to implement than the standard FEM, gives significantly better accuracy than when the standard FEM is used to solve the problem in the physical domain, using the same number of equations. Furthermore, since physical space is logarithmically condensed into the image space, the method is capable of dealing with large aspect ratio problems more simply and economically than is possible with the standard FEM or the boundary element method.

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