Structural Optimisation
Division of Solid Mechanics
Structural Optimisation has over the past decades qualified as an important tool in the design process. The method can be grouped into topology, size and shape optimisation. The objective of the optimisation can be to minimise the stresses weight or compliance for a given amount of material and boundary conditions. The method can be utilised to design engineering structures but it can also be used to tailor microstructures.
The most widely used numerical scheme for topology optimisation is the Solid Isotropic Material with Penalisation (SIMP) scheme where the density is approximated as constant within each element. The objective of the optimisation is in the present work to find a design that maximises 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 penalising 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 regularise the problem via e.g. a filter.
Current Projects
- Topology optimisation of hyperelastic structures
- Stress constraint
- Transients and path-dependent problems
- Contact formulation
- Shape optimisation
Current collaborators
- Lawrence Livermore National Laboratory, USA
- Technion - Israel Institute of technology
- Hanyang University, South Korea
- Dalian University of Technology, China
Contact
Mathias Wallin
Professor
mathias [dot] wallin [at] solid [dot] lth [dot] se (mathias[dot]wallin[at]solid[dot]lth[dot]se)
Profile in Lund University's Research portal
Matti Ristinmaa
Professor
matti [dot] ristinmaa [at] solid [dot] lth [dot] se (matti[dot]ristinmaa[at]solid[dot]lth[dot]se)