Generalized Three-Dimensional Theory of Elastic Body Stability. Part 2. Small Deformations

Equations of the three-dimensional stability theory for the case of small deformations are deduced from general equations of the generalized theory of stability of nonlinearly elastic bodies with finite deformations. It is shown that relationships of the stability theory for small deformations will be identical for different models of nonlinearly elastic media if an additional assumption on smallness of the strain tensor as compared to the rotation tensor is made. The variational statement of a three-dimensional problem of the stability theory is formulated. The relationships of the three-dimensional stability theory in components are presented including those in the orthogonal basis.

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