Optimal layout of multiple bi-modulus materials

A modified solid isotropic material with penalization (SIMP) method is proposed for solving layout optimization problems of multiple bi-modulus materials in a continuum. In the present algorithm, each bi-modulus material is replaced by two distinct isotropic materials to avoid structural reanalysis for each update of the design domains. To reduce the error in local stiffness due to the material replacement, the modification factor of each finite element is calculated according to the local stress state and the moduli used in the previous structural analysis. Three numerical examples are considered to demonstrate the validity and applicability of the present approach. Numerical results show that the final layout of materials is determined by factors that include the moduli difference of each bi-modulus material and the difference among material moduli