Structural optimization has over the past decades qualified as an important tool in the design process. The method can be grouped into topology, size and shape optimization. The objective of the optimization can be to minimize the stresses weight or compliance for a given amount of material and boundary conditions. The method can be utilized to design engineering structures but it can also be used to tailor mircostructures.
The most widely used numerical scheme for topology optimization is the Solid Isotropic Material with Penalization (SIMP) scheme where the density is approximated as constant within each element. The objective of the optimization is in the present work to find a design that maximizes the stiffness for a given amount of material. The advantage of using the stiffness as the objective, or rather its complement the compliance, is that it is a global measure and thus can be represented by a scalar value. Moreover, the constraint on the volume is also particular simple since it is linear and monotone which in most cases gives rise to a robust numerical algorithm. The SIMP procedure is based on a sequence of convex approximations and the algorithm is simple to implement and at the same time numerically efficient. A distinct black/white solution is obtained by penalizing gray designs via a scaling of the elastic constitutive relation. This formulation has been shown to be ill-posed due to the length scale missing in the formulation. The remedy to this problem regularize the problem via e.g. a filter.
- Topology optimization of hyperelastic structures
- Stress constraint
- Transients and path-dependent problems
- Contact formulation
- Shape optimization
- Lawrence Livermore National Laboratory, USA
Technion - Israel Institute of technology
- Hanyang University, South Korea
- Dalian University of Technology, China