Topological optimization of composite laminated structure with shape derivative and level set

The shape derivatives of the functional for domain integral and boundary integral were derived in details by employing the material distribution function of the level set. A theoretical model of the stiff continuum structure for the composite laminated structure was established. By the combination of the shape derivative and the augmented Lagrangian multipliers, a novel sensitivity analysis for the mean compliance with the composite laminated structure was presented. The evolution of the structural design boundary was controlled by the artificial velocity which makes the objective function descent. The level set surface of a higher-dimensional function can be moved up and down without changing its topology structure, and the optimization boundaries embedded on level set function can automatically modify the topology structure by the boundaries merging and breaking. The extensively studied 2D examples of the clamped beam were employed to demonstrate the validity of the present methodologies.