Topology optimization with closed B-splines and Boolean operations

Zhang, Weihong; Zhao, Linying; Gao, Tong; Cai, Shaobin

doi:10.1016/j.cma.2016.11.015

Cited by 75 publications

(22 citation statements)

References 41 publications

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“…A generalized shape optimization method combining level set method and finite cell method [53] for structural designs using IGA can be found in Refs. [54,55]. More information of IGA-based design optimization can be found in a recent review in Ref.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

2020

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In structural design optimization involving transient responses, time integration scheme plays a crucial role in sensitivity analysis because it affects the accuracy and stability of transient analysis. In this work, the influence of time integration scheme is studied numerically for the adjoint shape sensitivity analysis of two benchmark transient heat conduction problems within the framework of isogeometric analysis. It is found that (i) the explicit approach (β = 0) and semi-implicit approach with β < 0.5 impose a strict stability condition of the transient analysis;(ii) the implicit approach (β = 1) and semi-implicit approach with β > 0.5 are generally preferred for their unconditional stability; and (iii) Crank-Nicolson type approach (β = 0.5) may induce a large error for large time-step sizes due to the oscillatory solutions. The numerical results also show that the time-step size does not have to be chosen to satisfy the critical conditions for all of the eigen-frequencies. It is recommended to use β % 0:75 for unconditional stability, such that the oscillation condition is much less critical than the Crank-Nicolson scheme, and the accuracy is higher than a fully implicit approach.

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Section: Introductionmentioning

confidence: 99%

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

2020

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“…1 Many topology optimization methods have been proposed, such as the homogenization method, 2 the Solid Isotropic Material with Penalization (SIMP) method, 3,4 the Evolutionary Structural Optimization (ESO) method, 5 the Level-Set Method (LSM), [6][7][8] and the Moving Morphable Components (MMC), 9,10 with a wide range of applications, including the frequency responses, [11][12][13] material microstructures, [14][15][16] and multiscale design, [17][18][19][20][21][22][23][24] as well as stress problems, 25,26 etc. 27 Material description models (MDMs) have been widely adopted to describe the structural topology due to its easiness. [2][3][4][5] SIMP can be regarded as a powerful variant of the homogenization method, which has received much popularity due to its conceptual simplicity.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric topology optimization for continuum structures using density distribution function

Gao

Luo

et al. 2019

Numerical Meth Engineering

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Summary This paper will propose a more effective and efficient topology optimization method based on isogeometric analysis, termed as isogeometric topology optimization (ITO), for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF involves two steps. (1) Smoothness: the Shepard function is firstly utilized to improve the overall smoothness of nodal densities. Each nodal density is assigned to a control point of the geometry. (2) Continuity: the high‐order NURBS basis functions are linearly combined with the smoothed nodal densities to construct the DDF for the design domain. The nonnegativity, partition of unity, and restricted bounds [0, 1] of both the Shepard function and NURBS basis functions can guarantee the physical meaning of material densities in the design. A topology optimization formulation to minimize the structural mean compliance is developed based on the DDF and isogeometric analysis to solve structural responses. An integration of the geometry parameterization and numerical analysis can offer the unique benefits for the optimization. Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.

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“…In recent years, great interest arises in a more efficient feature‐driven topology optimization method using implicit features and FE model with fixed mesh. Until now, superellipses, curved skeletons, bars with circular ends, engineering features constructed by means of Boolean operations, and closed B‐spline (CBS) curves have been developed for the definitions of solid and void features. This type of method is a promising approach that reflects the feature design intent of engineers and can easily be implemented in the computer‐aided design (CAD) framework.…”

Section: Introductionmentioning

confidence: 99%

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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Topology optimization with closed B-splines and Boolean operations

Cited by 75 publications

References 41 publications

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

Isogeometric topology optimization for continuum structures using density distribution function

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

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