Novel thin plate element theory based on a continuity re-relaxed technique

Abstract

Thin plate problem has been receiving much interest due to its wide application in engineering. In this paper, a novel thin plate element theory is proposed based on a continuity re-relaxed technique to avoid the high continuity requirement for thin plate formulation which needs the high computation cost. The problem is first discretized into a set of background cells with field nodes, and only deflection field is treated as the field variable. On top of the background cells, the integration domains are further formed. The curvatures over integration domains are restructured through the divergence theorem, and the continuity requirement of the trial deflection function for thin plate problems can be re-relaxed. The Galerkin weak form is then used to create the discretized system equations. The curvatures in the integration domains are constant, and the stiffness matrix of the system can be computed directly without numerical integration. The rotational essential boundary conditions are imposed in the process of curvature field construction. Some numerical examples are computed using the RPIM approximation function. The excellent results demonstrate the efficiency of the proposed method.