Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints

Abstract

Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed inplane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behaviour with respect to fiber orientation changes significantly, in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behaviour has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally, determining the fiber orientations. The finite element method, coupled with an optimisation routine, is employed in analysing and optimising the laminates. Numerical results are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads.