Abstract
The discussion on solution procedures with stress components or stress functions is very few in comparison with the displacement method. In this paper some considerations of the stress function method in solving problems of elastostatics are given theoretically. A new stress function is introduced from the existing analogous relationship between stress function tensor and strain tensor through incompatibility tensor and compatibility equations in terms of strain components. Also, the relationship between this new stress function and the conventional stress function(Maxwell's stress function and Morera's stress function) is made clear. Fundamental equations which are indispensable in solving three-dimensional homogeneous isotropic elastic problems are derived in three case with use of each stress function. The effectiveness of our solution method with new stress function is shown in comparison with the expressions of displacement and stress components with the Galerkin vector. Finally, explicit forms on Fourier series solution of a simple supported thick plate subjected to a sinusoidal load are given.
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