Large Displacement Analysis of Thin Plates

Abstract

A finite element procedure for large deflection analysis of thin plates that exhibits monotonic convergence to results obtained using the von Karman plate equation is presented. A simplified method of solution is also developed that yields acceptable results with a significant reduction in computational effort. The Kirchoff thin plate assumptions are used, together with the appropriate nonlinear terms in the strain displacement equations to express the potential energy functional in terms of the displacement fields. The functional is discretized according to the usual finite element techniques and two sets of equations that essentially uncouple the in-plane and bending effects are obtained. Thus, the storage requirements of the computer program are based on a 3-degree-of-freedom per nodal point system although 5-degree-of-freedom are available to define the deformation of the idealized structure. This results in a significant reduction in storage requirements.