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Indeterminacy of first order stress functions and the stress- and rotation-based formulation of linear elasticity. (English) Zbl 0809.73018

Summary: Following from the indeterminacy of the nonsymmetric tensor of first order stress functions, satisfaction of the linear three-dimensional translational equilibrium equations can be achieved by the use of only six non-zero first order stress functions instead of nine. Utilizing this fact, redundant variable approximations in assumed nonsymmetric stress- based procedures can be avoided on the one hand, and, on the other, independent Euler equations and natural boundary conditions of mixed variational principles using nonsymmetric stresses as independent variables can be obtained. In this paper, the independent governing equations of linear elasticity in terms of stresses and rotations are derived using Fraeijs de Veubeke’s complementary energy-based mixed variational principle [B. Fraeijs de Veubeke, Int. J. Engin. Sci. 10, 745-763 (1975; Zbl 0245.73031)].

MSC:

74B10 Linear elasticity with initial stresses
74B05 Classical linear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics

Citations:

Zbl 0245.73031
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References:

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