Fully adaptive isogeometric topology optimization using MMC based on truncated hierarchical B-splines

Xie, Xianda; Yang, Aodi; Wang, Yingjun; Jiang, Ning; Wang, Zhen

doi:10.1007/s00158-021-02850-1

Cited by 16 publications

(12 citation statements)

References 76 publications

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“…A uniform mesh with the size of 24 × 12 is used to discretize the design domain initially. Figure 12 illustrates the optimized designs of Michell structure by SGTHB-TOs with m = 2, 3, ATHB-TO, 69 THB-TO, 65 HITO-MMC, 64 and THITO-MMC, 70 where the edge blurring is observed in the boundaries of designs by SGTHB-TO with m = 3 and ATHB-TO as well as THB-TO. The ideal material layout of the Michell structure cannot be acquired by HITO-MMC and THITO-MMC optimized from 24 × 12 uniform computational mesh initially, as presented in Figure 12.…”

Section: Comparisons Between Different Hb/thb Based To Methodsmentioning

confidence: 99%

Section: F I G U R E 16mentioning

confidence: 99%

“… DOFs comparisons between SGTHB‐TOs and HB/THB based TO methods 64,65,69,70 as well as IGA based SIMP method performed on a dense mesh…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Chen et al 68 presented an adaptive T‐spline finite cell method to perform structural shape optimization. To make the full potential of THB, fully adaptive TO methods are presented in References 69,70 with respect to SIMP and MMC frameworks. However, edge blurring around boundaries of converged design occur in TO performed on a fully adaptive THB space, 69 termed as SGTHB‐TO without admissible restriction in this work, as illustrated in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…DOFs comparisons between SGTHB-TOs and HB/THB based TO methods64,65,69,70 as well as IGA based SIMP method performed on a dense mesh F I G U R E 17 Problem setting and initial design of L-shaped cantilever6.3 Compliant mechanismIn order to verify the versatility of SGTHB-TO in designing compliant mechanism, a 2D compliant mechanism is optimized by SGTHB-TO. The configuration associated with the problem is shown in Figure23(A) with the dimension size and boundary conditions as well as the upper limit of solid material volume.…”

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confidence: 99%

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Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening

Xie

Yang

Jiang

et al. 2021

Numerical Meth Engineering

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In the present work, we propose an adaptive topology optimization (TO) method under suitably graded truncated hierarchical B-spline refinement and coarsening (SGTHB-TO). A series of algorithms have been devised to implement admissible adaptivity of SGTHB-TO by resorting to the definitions of suitably graded isogeometric hierarchical meshes. We apply the proposed SGTHB-TO method to two-dimensional and three-dimensional TO problems of compliance and compliant mechanism. According to the numerical results, SGTHB-TOs with or without admissible restriction share similar optimization processes, except that numerical artifact, such as edge blurring and islanding gray regions occurring in SGTHB-TO without admissible restriction, can be eliminated by SGTHB-TO with admissible parameter equaling to 2. Besides, the convergence rate can be largely accelerated by imposing an admissible constraint on SGTHB-TO for TO problems with geometric nonlinearity existing in the design domain, which is attributed to the improved numerical accuracy by the admissible adaptive discretization scheme of isogeometric analysis (IGA). Therefore, the SGTHB-TO method with the admissible parameter equaling to 2 is a more effective adaptive TO method than SGTHB-TO without considering admissible restriction, in terms of both numerical stability and convergence rate.

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Section: Comparisons Between Different Hb/thb Based To Methodsmentioning

confidence: 99%

Section: F I G U R E 16mentioning

confidence: 99%

“… DOFs comparisons between SGTHB‐TOs and HB/THB based TO methods 64,65,69,70 as well as IGA based SIMP method performed on a dense mesh…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening

Xie

Yang

Jiang

et al. 2021

Numerical Meth Engineering

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IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Villalba,

Gonçalves,

Dias-de-Oliveira

et al. 2023

Struct Multidisc Optim

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Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems.

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Isogeometric analysis based mesh adaptation for time dependent problems

Bahari,

Habbal,

Ratnani

2024

Engineering with Computers

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Fully adaptive isogeometric topology optimization using MMC based on truncated hierarchical B-splines

Cited by 16 publications

References 76 publications

Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening

Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening

IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Isogeometric analysis based mesh adaptation for time dependent problems

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