COMPATIBILITY CONDITIONS OF STRUCTURAL MECHANICS FOR FINITE-ELEMENT ANALYSIS

The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover with little effort that, historically, this facet of structural mechanics has not been adequately researched by the profession. Now the compatibility conditions have been researched and understood to a great extent. For finite element discretizations, the compatibility conditions are banded and can be divided into three distinct categories: 1) the interface compatibility conditions, 2) the cluster, or field, compatibility conditions, and 3) the external compatibility conditions. The generation of the compatibility conditions requires the separating of a local region, next writing the deformation displacement relation for the region, and finally eliminating the displacements from those relations. The procedure to generate all three types of compatibility conditions is presented and illustrated through examples of finite element models. The uniqueness of the compatibility conditions thus generated is shown. The utilization of the compatibility conditions has resulted in the novel integrated force method. The solution that is obtained by the integrated force method converges with a significantly fewer number of elements, compared to the stiffness and the hybrid methods.