On interpolation methods for modeling low-density elements in topology optimization of geometrically nonlinear structures

Resumo

Modeling void regions is one of the main challenges in topology optimization of geometrically nonlinear
structures due to the excessive distortions of low-density elements. Several solutions to this problem have been

suggested in the literature, including interpolation methods such as the Energy Interpolation scheme and the Addi-
tive Hyperelasticity technique. These methods consist in interpolating each element’s model between the original

material for solid elements and a less stiff model for the low-density ones. In this work, we introduce the gen-
eral framework for topology optimization that handles several hyperelastic materials. Both interpolation methods

are explored in the solution of classic compliance-minimization problems under the assumption of plane strain
conditions with numerical results for two benchmark topology optimization problems being provided.