Shape optimization with topological changes and parametric control

Chen, Jiaqin; Shapiro, Vadim; Suresh, Krishnan; Tsukanov, Igor

doi:10.1002/nme.1943

Cited by 138 publications

(56 citation statements)

References 56 publications

(86 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chen et al [59] constructed the level set function using B-splines and parameterized primitives combined with R-functions, and shape and topology optimization with parametric control was performed for the minimum compliance problem. Wei and Wang [60] proposed a structural optimization method based on the piecewise constant level set method [61,62] where multi-phases are represented using a level set function.…”

mentioning

confidence: 99%

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

Yamasaki

Nishiwaki

Yamada

et al. 2010

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYStructural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton-Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method.

show abstract

mentioning

confidence: 99%

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

Yamasaki

Nishiwaki

Yamada

et al. 2010

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…16, the expression for the recovered data-set was modified by doubling the parameter values of the holes (middle image) or the main cylinder (rightmost image). Parameters of extracted expressions can be modified manually by a designer or automatically by some algorithms in order to satisfy some modeling criteria [18,14]. …”

Section: Applicationsmentioning

confidence: 99%

An evolutionary approach to the extraction of object construction trees from 3D point clouds

Fayolle

Pasko

2016

Computer-Aided Design

View full text Add to dashboard Cite

In order to extract a construction tree from a finite set of points sampled on the surface of an object, we present an evolutionary algorithm that evolves set-theoretic expressions made of primitives fitted to the input point-set and modeling operations. To keep relatively simple trees, we use a penalty term in the objective function optimized by the evolutionary algorithm. We show with experiments successes but also limitations of this approach.

show abstract

“…These methods are not considered as parameterized implicit function methods, which is the focus of this paper, because the parameterization is of discrete components or voids and therefore they do not directly parameterize an implicit function. Also, 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.…”

Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

View full text Add to dashboard Cite

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.

show abstract

Shape optimization with topological changes and parametric control

Cited by 138 publications

References 56 publications

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

An evolutionary approach to the extraction of object construction trees from 3D point clouds

Minimum length-scale constraints for parameterized implicit function based topology optimization

Contact Info

Product

Resources

About