Element stacking method for topology optimization with material-dependent boundary and loading conditions

A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite element models or topology optimization reformulation may be necessary.

The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have independent degrees of freedom. Some test problems are considered to check the effectiveness of the proposed stacking method.