Topology Optimization For Localizing Design Problems: An Explorative Review

Topology Optimization For Localizing Design Problems: An Explorative Review

Reichard, C.A.

Langelaar, M. (mentor)

Mechanical, Maritime and Materials Engineering

Precision and Microsystems Engineering

2012-09-25

Topology optimization is a valuable tool that can assist engineers in the design of many complex problems. However optimization techniques often have difficulties dealing with problems that have a strong tendency to localize in the global design domain forming a sparse design. Typically an extremely fine mesh is needed to capture these results, with high computational costs. Examples are seen in spanning of large bridges, reinforcements of thin plates, and the branching effect of a heat conduction problem. The aim of this explorative review is to identify different possibilities to improve the computational efficiency. Next to reviewing current techniques, also two novel ideas were developed and evaluated. The first idea is inspired by techniques present in fields such as computer graphics. In this field 3D objects used in animation are represented by skeleton models to reduce the complexity of the problem. Similar techniques are investigated to determine if such an approach can be used within topology optimization to develop an optimum structure. The second idea employs an adaptive substructuring technique in a less traditional manner. The computational domain is split in a part that is changing and one that is static during the optimization process. The overall goal of both proposed approaches is to improve the solution process by reducing the number of variables needed to be solved to obtain the response of the design. From these investigations and research many ideas are presented which bring benefit to the sparse problem in optimization. The idea of skeleton modeling is a potential method but has several issues in developing the model and obtaining the temperature response. The sub-structuring approach is a promising development offering significant improvements with up to approximately 67% time savings in the finite elements were shown for a design problem using 1% of the orignal volume.

topology optimization
heat conduction
sub-structuring
skeleton modeling

http://resolver.tudelft.nl/uuid:8fc92925-5796-403b-8ac2-0a63002d77bc

Student theses

master thesis

(c) 2012 Reichard, C.A.