Separable stress interpolation scheme for stress-based topology optimization with multiple homogenous materials

This research develops a new interpolation scheme, a separable stress interpolation (SSI) which allows stress-based topology optimization with multiple materials (STOMM). In common material interpolation function such as extended solid isotropic material with penalization (SIMP) for multiple materials, Youngʹs modulus is interpolated from those of several solids to a smaller value with respect to design variables whose number is same as the number of considered materials. When the same interpolated Youngʹs modulus is used for stress evaluation, it is found that the calculated stress norm becomes a small value when ones are assigned to the design variables of each element causing physically unacceptable layouts. In order to resolve this ill-posed issue for STOMM, we present the SSI scheme which computes the stress constraints of stacked elements separately. For a stable topology optimization process, the computational issues of the p-norm stress measure, the number of stress evaluation points inside an element, and the correction parameter for the approximated stress measure are addressed for STOMM. Furthermore, we present a new regional constraint method based on the sorting algorithm. The applicability and limitations of the newly developed framework are discussed in the context of its application to several stress-based topology optimizations with multiple materials.