Optimality criteria method for topology optimization under multiple constraints

The existing framework of optimality criteria method is limited to the optimization of a simple energy functional with a single constraint on material resource. The present work extends the optimality criteria method to the case of multiple constraints. The difficulty in updating the Lagrangian multipliers is treated by gradient-split Taylor series expansion. Applications of the method are illustrated by computing the optimal structures under multiple displacement constraints, and by designing the material cells under given macroscopic elastic tensors that correspond to both positive and negative Poissonʹs ratios.