Stress-based shape and topology optimization with cellular level set in B-splines

2020 ◽  
Vol 62 (5) ◽  
pp. 2391-2407
Author(s):  
Yelin Song ◽  
Qingping Ma ◽  
Yu He ◽  
Mingdong Zhou ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Cellular Level ◽  
Shape And Topology Optimization ◽  
B Splines ◽  
And Topology

scholarly journals Shape and topology optimization based on the convected level set method

2016 ◽  
Vol 54 (3) ◽  
pp. 659-672 ◽  
Author(s):  
Kentaro Yaji ◽  
Masaki Otomori ◽  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Shape And Topology Optimization ◽  
And Topology

scholarly journals A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

Level Set Based Robust Shape and Topology Optimization Under Random Field Uncertainties

2009 ◽  
Author(s):  
Shikui Chen ◽  
Sanghoon Lee ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Uncertainty Propagation ◽  
Level Set Methods ◽  
Random Variable ◽  
Shape And Topology Optimization ◽  
Extended Space ◽  
And Topology ◽  
Material Uncertainties ◽  
Gauss Type

A level-set-based method for robust shape and topology optimization (RSTO) is proposed in this work with consideration of uncertainties that can be represented by random variables or random fields. Uncertainty, such as those associated with loading and material, is introduced into shape and topology optimization as a new dimension in addition to space and time, and the optimal geometry is sought in this extended space. The level-set-based RSTO problem is mathematically formulated by expressing the statistical moments of a response as functionals of geometric shapes and loading/material uncertainties. Spectral methods are employed for reducing the dimensionality in uncertainty representation and the Gauss-type quadrature formulae is used for uncertainty propagation. The latter strategy also helps transform the RSTO problem into a weighted summation of a series of deterministic topology optimization subproblems. The above-mentioned techniques are seamlessly integrated with level set methods for solving RSTO problems. The method proposed in this paper is generic, which is not limited to problems with random variable uncertainties, as usually reported in other existing work, but is applicable to general RSTO problems considering uncertainties with field variabilities. This characteristic uniquely distinguishes the proposed method from other existing approaches. Preliminary 2D and 3D results show that RSTO can lead to designs with different shapes and topologies and superior robustness compared to their deterministic counterparts.

A Meshless Level Set Method for Shape and Topology Optimization

2011 ◽  
Vol 308-310 ◽  
pp. 1046-1049 ◽  
Author(s):  
Yu Wang ◽  
Zhen Luo
Keyword(s):  
Topology Optimization ◽  
Free Boundary ◽  
Level Set Method ◽  
Level Set ◽  
Level Set Methods ◽  
Discrete Level ◽  
Shape And Topology Optimization ◽  
Level Set Function ◽  
And Topology ◽  
Set Function

This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. To taking advantage of the implicit free boundary representation scheme, structural design boundary is represented through the introduction of a scalar level set function as its zero level set, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and also to construct the shape functions for mesh free function approximation. The meshless Galerkin global weak formulation is employed to implement the discretization of the state equations. This provides a pathway to simplify two numerical procedures involved in most conventional level set methods in propagating the discrete level set functions and in approximating the discrete equations, by unifying the two different stages at two sets of grids just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function by finding the design variables of the size optimization in time. One benchmark example is used to demonstrate the effectiveness of the proposed method. The numerical results showcase that this method has the ability to simplify numerical procedures and to avoid numerical difficulties happened in most conventional level set methods. It is straightforward to apply the present method to more advanced shape and topology optimization problems.

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