Chapter 10 - Analysis of Plates

Abstract

The analysis of plates is presented. If the plate is thin and deflections are small, the in-plane displacement components u and v (membrane displacements) are uncoupled from the transverse displacement component w (bending displacement). Linear and quadratic triangular membrane elements are presented. For the linear triangular element in the xy plane, a linear displacement model is used for u and v. The element has sixdegrees of freedom or unknowns (two at each corner node) and the resulting stiffness matrix, of order 6×6, and the consistent load vectors, of order 6×1, are derived. If the plate lies in the three-dimensional space (instead of in the xy plane), the global stiffness matrix of order 9×9 in the xyz-coordinate system is derived using a suitable coordinate transformation matrix. For the quadratic triangular membrane element, six nodes (corners and mid-side points), are considered. A rectangular membrane element is presented for in-plane forces with its stiffness matrix. For bending of plates, a three-node triangle element is developed. Several other triangular and rectangular plate elements, with different transverse displacement models (with different nodal degrees of freedom), are summarized.