Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function

Zhang, Weihong; Zhao, Linying; Cai, Shaobin

doi:10.1016/j.cma.2015.06.012

Cited by 27 publications

(12 citation statements)

References 38 publications

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“…Implicit functions of closed form including KS function and R-function [16,17] are also applied by means of Boolean operations of basic geometric primitives. In this sense, the number of design variables, sensitivity analysis scheme and grey region control scheme are different between the density-based approach and the continuous LSM.…”

Section: Introductionmentioning

confidence: 99%

Feature-driven topology optimization method with signed distance function

Zhou

Zhang

Zhu

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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141

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Section: Introductionmentioning

confidence: 99%

Feature-driven topology optimization method with signed distance function

Zhou

Zhang

Zhu

et al. 2016

Computer Methods in Applied Mechanics and Engineering

Self Cite

141

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“…C refers to the elastic matrix of solid material and

\overset{M}{true}

is the weighted shape function matrix defined in Equation . In this work, the quadtree refinement is employed in each boundary cell to enrich the integral points on both boundaries Γ N and Γ T . “Ersatz material” is used to replace void materials in order to prevent the ill‐conditioning of stiffness matrix.…”

Section: Structural Computing and Sensitivity Analysismentioning

confidence: 99%

“…Meanwhile, shape and topology variations of the structure are interpreted as Boolean operations in terms of LSFs. The weighted B‐spline finite cell method (FCM) is applied for structural analysis . As the fixed mesh is used, the pressure load related to Neumann boundary is numerically discretized onto the control nodes of FCM.…”

Section: Introductionmentioning

confidence: 99%

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Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Zhou

Zhang

Zhu

2019

Numerical Meth Engineering

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Summary This work develops a concurrent shape and topology optimization method to solve the design problems of which the pressure loads are applied on designable boundaries. Implicit B‐spline curves including open B‐spline and closed B‐spline are introduced in the form of level‐set functions to act as common design primitives for the description of both moving pressure boundary and inner topology boundaries of a structure. Boolean operations are applied to describe mathematically the shape and topology variations. An artificial nondesignable offset domain of small bandwidth is introduced along the moving pressure boundary to ensure reasonably the imposition of pressure loads on solid materials. The pressure loads are numerically discretized onto the control nodes of finite cell method used for structural analysis with fixed mesh. Sensitivities of design‐dependent pressure loads with respect to both shape and topology design variables are explicitly derived. Numerical problems are finally solved to illustrate the presented method.

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“…Several failure cases of the centrifuge have been caused by the basket [4,7]; therefore, one of the major tasks of the geotechnical centrifuge design is make the basket as light as possible while satisfying the requirement of its strength. Shape optimization is important in seeking to improve mechanical properties and reduce weight [8][9][10][11][12][13]. In engineering practice, the shape optimization design of the basket is mostly based on the traditional finite element method (FEM), which makes the optimization design process timeconsuming and complicated.…”

Section: Introductionmentioning

confidence: 99%

Shape Optimization Design for a Centrifuge Structure with Multi Topological Configurations Based on the B-Spline FCM and GCMMA

2020

Applied Sciences

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The geotechnical centrifuge applied in various geotechnical engineering fields provides physical data for investigating mechanisms of deformation and failure and for validating analytical and numerical methods by simulating and studying the geotechnical problems. The basket, as one of the important components used to place the inspection model of centrifugal test, is designed to withstand complex loads. This paper presents an optimization design method for the basket based on the weighted B-Spline Finite Cell Method (FCM) and the globally-convergent method of moving asymptotes (GCMMA). In order to obtain a superior design solution, four topological configurations, i.e., original single web, porous dual web, open deep groove dual web, and connected closed dual web, are investigated and optimized. The mass is selected as the optimization objective, while key shape parameters and stress are regarded as design variables and the constraint, respectively. By optimization, the final masses of the four configurations are reduced greatly compared with the initial configurations, where the greatest weight loss, in case 4, is 10.6%. This indicates that the weighted B-Spline FCM and GCMMA can be well applied for shape optimization of structure in engineering design. In contrast to the final single web adopted in the traditional basket design in case 1, the final configuration in case 4, i.e., connected closed dual web, has the least mass. The final mass is reduced by 133.38 kg when the centrifuge strength requirement is met. Therefore, the final configuration in case 4, where the maximum von-Mises stress is 398.72MPa and mass is 781.82 kg, is superior to the three other configurations.

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Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function

Cited by 27 publications

References 38 publications

Feature-driven topology optimization method with signed distance function

Feature-driven topology optimization method with signed distance function

Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Shape Optimization Design for a Centrifuge Structure with Multi Topological Configurations Based on the B-Spline FCM and GCMMA

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