Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique

This paper presents a simple but effective additive hyperelasticity technique to circumvent numerical difficulties in solving the material density-based topology optimization of elastic structures undergoing large displacements. By adding a special hyperelastic material to the design domain, excessive distortion and numerical instability occurred in the low-density or intermediate-density elements are thus effectively alleviated during the optimization process. The properties of the additional hyperelastic material are established based on a new interpolation scheme, which allows the nonlinear mechanical behaviour of the remodelled structure to achieve an acceptable approximation to the original structure. In conjunction with the adjoint variable scheme for sensitivity analysis, the topology optimization problem is solved by a gradient-based mathematical programming algorithm. Numerical examples are given to demonstrate the effectiveness of the proposed method.