Feasibility of Alternative Finite Element Formulations within Topology Optimization

Feasibility of Alternative Finite Element Formulations within Topology Optimization

Feitsma, J.W.

Aragon, A.M. (mentor)

Mechanical, Maritime and Materials Engineering

PME

Engineering Mechanics

2016-04-28

In this work, topology optimization is used to obtain optimal designs with minimal compliance as the objective. The checkerboard problem, refers to a resulting optimal topology where the material is distributed in regions of alternating solid and void elements. It has been shown that these regions emerge due to higher stiffness of the checkerboard patterns compared to the stiffness of uniformly distributed material. In this work a study is performed on the feasibility of non-traditional finite element formulations to deal with the checkerboard problem. Two alternative finite element formulations were studied in this work. The main focus is given to the p-version of the finite element method, also referred to as p-FEM. In addition, the mixed-enhanced formulation of Kasper and Taylor is discussed briefly. These finite element formulations will be compared to the formulation commonly used. In this thesis the main research question is: Can the use of alternative finite element formulations in topology optimization be used to solve the checkerboard-problem? In this thesis is is shown that the p-FEM does prevent checkerboards when elements with polynomial order p greater equal to 2 are used. When even higher-order elements are used the final designs do not change significantly compared to p=2. It was found that computational time increases significantly with the element order, without an increase in the design resolution. The mixed-enhanced formulation does not alleviate the checkerboard problem. Although small changes in design are found compared to standard Q4, checkerboards are still observed. Finally it has been shown that local p-refinement can be employed to locally alleviate checkerboards. Two strategies have been introduced, which based on the element densities, are able to locally change the element orders. Checkerboard-free designs are obtained using the minimum number of higher-order elements as possible. Although the concept of local p-refinement was proven, the presented methods are not yet optimal. An increase in computation time is observed and user specified tolerances were used. Hence, there is still room for improvement.

Topology optimization
checkerboards
p-FEM

http://resolver.tudelft.nl/uuid:73979d57-fdc4-4002-add5-b172344537fa

Student theses

master thesis

(c) 2016 Feitsma, J.W.