Adaptive finite element based shape optimization in laminated composite plates

• ZZ type discretization error estimator for composite laminates.
• Shape optimization.
• Effect of discretization error control on final shape and weight minimization.
• First-ply failure as a constraint.

In this study a reliable shape optimization for laminated plate structures has been attempted. For a fixed higher order plate model, a simple a-posteriori strain recovery algorithm, following ZZ type patch recovery technique, has been developed. The recovery is seen to be accurate. The effect of higher approximation order and mesh refinement on the quality of the obtained solution quantities like stress components and displacements, is studied in detail. The shape of the cutout is optimized with weight minimization as the objective function and the first-ply failure criterion as the constraint. It is observed that control of the discretization error (via adaptive mesh refinements) leads to vastly different final designs, as compared to those obtained using reasonably refined meshes, but without adaptivity. It is seen that without adaptivity, the design obtained is unsafe, as either more material removal is predicted or failure is predicted at higher loads, as compared to that obtained using adaptivity.