A rotation-free quadrature element formulation for free vibration analysis of thin sectorial plates with arbitrary boundary supports

Abstract

Due to corner stress singularities, free vibration analysis of thin sectorial plates with arbitrary boundary supports including a free vertex is a rather challenging problem. In this paper, a novel rotation-free quadrature element formulation based on Kirchhoff plate theory is presented to solve the problem. Different from all existing quadrature thin plate element formulations, rotational degrees of freedom are not used. Instead, a boundary point is modeled by two nodes separated by a very small distance and thus the C1 continuity is easily enforced. Explicit formulations with arbitrary number of nodes and nodes of any type are worked out to ease the p-refinement. Numerical results demonstrate that the proposed formulation is simple, straightforward and has excellent performance for solving thin sectorial plate with arbitrary combinations of boundary supports. Some tabulated data are believed new which may serve as a reference.