Design of variable-stiffness composite panels for maximum buckling load

A generalized reciprocal approximation is presented for design of variable-stiffness laminated composite panels for maximum buckling load. The buckling load is expanded in terms of the inverse of the stiffness tensor. For discretized panels such an approximation has the important property of being separable, which allows the maximization to be carried out at each discrete node separate from the others. This makes the algorithm particularly suited to parallel computations. The sensitivity analysis is performed exactly using an adjoint method, requiring only one back substitution using the already factored inplane stiffness matrix with different right hand sides to compute the sensitivities for all design variables. A conforming CLPT finite element is used for the buckling analysis of rectangular plates and the proposed reciprocal approximation is used to update fiber orientation angles at each finite element node. Numerical results obtained for rectangular plates show that significant improvements can be gained in the buckling load by allowing the stiffness properties to vary spatially. The case of repeated eigenvalues is handled using a dual formulation.