The inner structure of sensitivities in nodal based shape optimisation

Abstract

The pseudo load matrix and the sensitivity matrix dominate design sensitivity analysis of shape optimisation problems. They describe how a structure reacts on an imposed design modification. We analyse these matrices for the model problem of nodal based shape optimisation by a singular value decomposition and show that they contain additional valuable information which is not yet used either in theory or computation of shape optimisation. The inner structure of the sensitivities is capable to formulate reduced quadratic sub-problems within the sequential quadratic programming approach. We also tackle the problem of indefinite Hessian matrices in nodal based shape optimisation. Furthermore, we avoid jagged boundaries and obtain meshindependent optimised structures applying density filtering technique to shape optimisation. Overall, we emphasise an enhanced analysis of sensitivities and point to unused substantial capabilities.

On structural shape optimization using an embedding domain discretization technique

“…There exist several approaches in the literature that aim to avoid such geometric distortion phenomena , where the common objective is to obtain from the steepest descent direction d in a more regular descent direction , which is then used to alter the domain boundary via within a numerical algorithm.…”

Variational sensitivity analysis of a nonlinear solid shell element

“…We obtain results that are comparable with and note that the more control points are used for geometry description, the more detailed structures can be gained. We additionally mark that sensitivity relations derived in this work can also be used to perform FE node‐based shape optimization (utilizing of some additional tools like filters and mesh control techniques, see and for details).…”

“…Some additional tools such as filters and mesh control techniques are necessary to perform shape optimization. Recent works on this topic are and . Geometry‐based shape optimization is the classical way to improve the properties of a structure.…”