Structural optimization of shape and topology using an embedding domain discretization technique

(Own Funds)

Overall project:
Project leader: Paul Steinmann
Project members: Stefan Riehl
Start date: 1. January 2013
End date: 31. December 2018
Acronym:
Funding source:
URL:

Abstract

This project targets the formulation and implementation of a method for structural shape and topology optimization within an embedding domain setting. Thereby, the main consideration is to embed the evolving structural component into a uniform finite element mesh which is then used for the structural analyses throughout the course of the optimization. A boundary tracking procedure based on adaptive (or hierarchical) mesh refinement is used to identify interior and exterior elements, as well as such elements that are intersected by the physical domain boundary of the structural component. By this mechanism, we avoid the need to provide an updated finite element mesh that conforms to the boundary of the structural component for every single design iteration. Further, when considering domain variations of the structural component, its material points are not attached to finite element nodal points but rather move through the stationary finite element mesh of the embedding domain such that no mesh distortion is observed. Hence, one circumvents the incorporation of time consuming mesh smoothing operations within the domain update procedure. In order to account for the geometric mismatch between the boundary of the structural component and its non-conforming finite element representation within the embedding domain setting, a selective domain integration procedure is employed for all elements that are intersected by the physical domain boundary. This is to distinguish the respective element area fractions interior and exterior to the structural component. We rely on an explicit geometry description for the structural component, and an adjoint formulation is used for the derivation of the design sensitivities in the continuous setting.

Publications

Riehl S., Friederich J., Scherer M., Meske R., Steinmann P.:
On the discrete variant of the traction method in parameter-free shape optimization
In: Computer Methods in Applied Mechanics and Engineering 278 (2014), p. 119-144
ISSN: 0045-7825
DOI: 10.1016/j.cma.2014.05.009
Riehl S., Steinmann P.:
A staggered approach to shape and topology optimization using the traction method and an evolutionary-type advancing front algorithm
In: Computer Methods in Applied Mechanics and Engineering 287 (2015), p. 1-30
ISSN: 0045-7825
DOI: 10.1016/j.cma.2015.01.007
Riehl S., Steinmann P.:
On structural shape optimization using an embedding domain discretization technique
In: International Journal for Numerical Methods in Engineering 109 (2017), p. 1315 - 1343
ISSN: 0029-5981
DOI: 10.1002/nme.5326
Riehl S., Steinmann P.:
An integrated approach to shape optimization and mesh adaptivity based on material residual forces
In: Computer Methods in Applied Mechanics and Engineering 278 (2014), p. 640-663
ISSN: 0045-7825
DOI: 10.1016/j.cma.2014.06.010