Finite-Element Bending Analysis for Plates

A general approximate solution method applicable to the bending analysis of structural plates is presented. The plates may have variable thicknesses and arbitrary shapes. Additionally, the plates may possess variable material properties. Arbitrary normal, thermal and boundary loading conditions have been included. The analysis has been so formulated that it may be easily adapted to the analysis of folded plate and shell structures. The analysis is developed by expressing the plate bending equations, written as functions of the transverse deflection, and the bending moments, by means of a variational theorem. The plate to be analyzed is represented by a series of finite elements. Forms of the primary dependent variables (transverse deflection and moments) are assumed within each element and are related to moment and displacement unknowns at the element nodes. The approximate solution is obtained by taking the variational of the function with respect to the node values of the unknowns, thus generating a set of linear algebraic equations which define these nodal values. The application and accuracy of the procedure is illustrated by an example.