Subregion generalized variational principles for elastic thick plates

Abstract

In this paper, the subregion generalized variational principle for elastic thick plates is proposed. Its main points may be stated as follows:

• 1. Each subregion may be assigned arbitrarily as a potential region or complementary region. The subregion variational principles of potential energy, complementary energy and mixed energy represent three special forms of this principle.

• 2. The number of independent variational variables in each subregion may be assigned arbitrarily. Any one of the subregions may be assigned, as a one-variable-region, two-variable-region or three-variable-region.

• 3. The conjunction conditions of displacements and stresses on each interline of neighbouring subregions may be relaxed. On the basis of this principle the finite element analysis of non-conforming elements for thick plates can be formulated.

Different finite element models for thick plates can be obtained by different applications of this principle. In particular, the subregion mixed variational principle for thick plates may be applied to formulating the subregion mixed finite element method for thick plates.