Abstract
This paper introduces explicit minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization methods. Length-scale control in topology optimization has many potential benefits, such as removing numerical artifacts, mesh independent solutions, avoiding thin, or single node hinges in compliant mechanism design and meeting manufacturing constraints. Several methods have been developed to control length-scale when using density-based or signed-distance-based level-set methods. In this paper a method is introduced to control length-scale for parameterized implicit function based topology optimization. Explicit constraint functions to control the minimum length in the structure and void regions are proposed and implementation issues explored in detail. Several examples are presented to show the efficacy of the proposed method. The examples demonstrate that the method can simultaneously control minimum structure and void length-scale, design hinge free compliant mechanisms and control minimum length-scale for three dimensional structures.
Highlights
Length-scale control in topology optimization has been a topic of interest since the early days of its development, almost 30 years ago (Bendsøe and Kikuchi 1988)
Numerical testing shows that the first strategy is not suitable, as the length-scale constraints can quickly trap the design in a local minima close to the initial design
This paper introduces minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization
Summary
Length-scale control in topology optimization has been a topic of interest since the early days of its development, almost 30 years ago (Bendsøe and Kikuchi 1988). An alternative to utilizing the signed-distance function is to add a fictitious quadratic energy functional to the objective function in order to control features in the level-set method (Luo et al 2008b; Chen et al 2008) This approach cannot satisfy the minimum structural size to an exact value. Chen et al (2007) proposed a method that combines components and void features with a spline-based parameterized implicit function to perform parametric shape and topology optimization This method has some control over lengthscale, as the maximum and minimum size of primitive features can be explicitly defined through geometric constraints. This paper introduces a new method that can control the minimum length-scale, in both solid and void regions, for parameterized implicit function based topology optimization. The parameterization scheme used in this paper is briefly reviewed in Section 4, followed by examples in Section 5 and conclusions
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