Consistent formulation in isogeometric topology optimization for structural applications

Consistent formulation in isogeometric topology optimization for structural applications

Salden, P.H.W.

Turteltaub, S.R. (mentor)

Aerospace Engineering

Aerospace Structures and Materials

2016-09-26

Topology optimization is an automated design approach for structural applications that is gaining popularity in industry, including the aerospace sector. Resulting designs can be made suitable for traditional manufacturing techniques, although it is a technique that is particularly useful for non-conventional approaches such as additive manufacturing. The procedure allows for choosing a design objective, such as minimum compliance or maximum heat conduction. Given one or more constraints, the optimal distribution of material within a domain is computed. A popular topology optimization method is the so-called Solid Isotropic Material with Penalization (SIMP). It is traditionally implemented using piecewise constant density values, specified per element. One technical difficulty with this approach is the formation of “checkerboard-like” patterns where the material is assigned to one element while the adjacent elements contain no material. This issue has been circumvented through the application of filters that explicitly prevent the formation of checkerboards. However, as a result of the filtering process, the designs display structural members with relatively high thicknesses and, at the same time, the structural detail level is relatively low. Several authors in the scientific literature argue that this effect is beneficial from a manufacturing viewpoint. However, recent progress in manufacturing techniques, such as additive manufacturing (also known as 3D-printing), allows to manufacture components with an increased level of detail and complexity. From this point of view, it is relevant to study optimization procedures that preserve the level of detail displayed by unfiltered designs. In this project, SIMP is implemented using Isogeometric Analysis (IGA). In IGA, Non-Uniform Rational B-Splines (NURBS) replace the Lagrange polynomials classically used in Finite Element Analysis (FEA). Through the use of Bézier extraction, implementation changes are confined to the “shape routine”. Rather than working with piecewise constant density values, density is consistently approximated using NURBS. A consistent gradient formulation is derived as well. The effects on checkerboard formation are studied. Instead of filtering, separate meshes are used for density and displacement definition. A displacement mesh is obtained by further refining the density mesh, such that the displacement representation is more accurate. Adequate procedures for Gaussian integration are determined. The treatment is limited to two dimensional minimum compliance problems. It is found that a consistent density representation using NURBS does not prevent checkerboard formation. However, the use of separate meshes for density and displacement diminishes checkerboards. It also generates more detailed designs than those produced by filters. Obtained compliance values are lower as well. Through the use of IGA, arc-like geometries may be studied. At the same time, non-classical checkerboard patterns are observed.

topology optimization
isogeometric analysis
SIMP
Bézier extraction

http://resolver.tudelft.nl/uuid:257dc92a-d8df-4b2d-8715-6a69b4aa3ddd

Student theses

master thesis

(c) 2016 Salden, P.H.W.