Topology optimization of hyperelastic structures with frictionless contact supports

Hyperelastic structures usually undergo large deformations and thus may be subject to deformation-dependent contact supports. This paper presents an effective topology optimization methodology for the compliance-minimization design of hyperelastic structures with frictionless contact supports. In the optimization model, the strain-energy function of hyperelastic material is represented by an artificial penalization model, and the contact boundary conditions are modeled with hypothetical nonlinear springs. The additive hyperelasticity technique is employed for circumventing the local buckling instability exhibited by low-density elements. In conjunction with the adjoint variable sensitivity analysis, the nonlinear topology optimization problem is solved by a gradient-based mathematical programming algorithm. Numerical examples are given to show the importance of considering contact supports and to demonstrate the applicability of the proposed method.