Material distribution and sizing optimization of functionally graded plate-shell structures

A high order shear deformation theory is used to develop a discrete model for the structural and sensitivity analyses allowing for the material distribution and sizing optimization of functionally graded material (FGM) structures. The finite element formulation for general FGM plate-shell type structures is presented, and a non-conforming triangular flat plate/shell element with 24° of freedom for the generalized displacements is used. The formulation accounts for geometric and material nonlinear behaviour, free vibrations and linear buckling analyses, and their analytical gradient based sensitivities. The p-index of the power-law material distribution and the thickness are the design variables. Mass, displacement, fundamental frequency and critical load are the objective functions or constraints. The optimization solutions, obtained by a Feasible Arc Interior Point gradient-based algorithm, for some plate-shell examples are presented for benchmarking purposes.