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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.

MSC:

74B05 Classical linear elasticity
74A10 Stress
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References:

[1] Fraeijs de Veubeke, B. M.: Stress function approach. Proc. of the World Congress on Finite Element Methods in Structural Mechanics, pp. J.1–J.51. Bournemouth, UK 1975.
[2] Fraeijs de Veubeke, B. M.: Diffusive equilibrium models. Lecture Notes for the International Research Seminar on ‘The theory and application of finite element methods’. University of Calgary, Alberta, Canada 1973. · Zbl 0281.73049
[3] Geradin, M. (ed.): B. M. Fraeijs de Veubeke memorial volume of selected papers. Alphen aan den Rijn: Sijthoff & Noordhoff 1980. · Zbl 0443.01020
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