On the stress function approach in three-dimensional elasticity. (English) Zbl 1117.74007

Summary: Stress function-based solution procedures in elasticity require the knowledge of those stress functions that give zero complementary strain energy. In the two-dimensional case, the structure of zero-energy first-order stress functions is as simple as that of the zero-energy displacements, and the number of zero-energy modes is three. This paper investigates the more complicated three-dimensional case and, considering a possible set of six independent first-order stress functions, derives zero-energy stress functions in polynomial form. It is pointed out that the number of zero-energy stress function modes in the three-dimensional case is infinite.


74B05 Classical linear elasticity
74A10 Stress
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