Analytic and finite element solutions for bending and buckling of orthotropic rectangular plates

Abstract

This paper presents a critical review of analytic solutions for bending and buckling of flat, rectangular, orthotropic thin plates. Considered are plates with all edges simply supported, two edges simply supported and two edges clamped, and all edges clamped. An orthotropy resealing technique is employed to simplify the analysis. The material orthotropy is characterized by two non-dimensional parameters, λ = (D22/D11 and η = (D12 + 2D26)/√D11D22. When η ≈ 1, many solutions for orthotropic plates can be obtained directly from the corresponding isotropic results. Systematic comparisons with finite element solutions are made for the critical buckling load of a plate under in-plane compression, and for deflection and stresses in a plate under out-of-plane uniform pressure. It is found that for plates with all edges clamped, the analytic solution for critical buckling load is neither accurate nor conservative; a better solution needs to be developed for design purposes. The validity of the thin plate theory solutions over a range of plate thicknesses is also examined.