Topology optimization with precise evolving boundaries based on IGA and untrimming techniques

Shakour, Emad

doi:10.1016/j.cma.2020.113564

Cited by 14 publications

(3 citation statements)

References 69 publications

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“…Besides simple consistency rules such as the Euler relation, the analysis of evolving surfaces, or model deformations, requires guaranteeing the consistency of the mesh with the model during the whole simulation process. This implies sampling a model consistently [CDRR04]; identifying small defects, holes, and handles [SH97, ACK13b]; removing the topological noise [WHDS04]; and even topologically replicating the boundaries during optimization [SA21].…”

Section: Mesh Indicatorsmentioning

confidence: 99%

A Survey of Indicators for Mesh Quality Assessment

Sorgente

Biasotti

Manzini

et al. 2023

Computer Graphics Forum

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We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two‐ and three‐dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality‐driven mesh optimization.

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Section: Mesh Indicatorsmentioning

confidence: 99%

A Survey of Indicators for Mesh Quality Assessment

Sorgente

Biasotti

Manzini

et al. 2023

Computer Graphics Forum

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“…Xu et al 30 maximized fundamental eigenfrequency by using level set based isogeometric topology optimization. An auxetic metamaterial is designed by employing IGA and three dimensional level set topology optimization by Nguyen et al 31 Also, Shakour et al, 32 recently, proposed an IGA based level set topology optimization with precise evolving boundaries by using untrimming techniques. It is also noted that studies on isogeometric topology optimization has not been restricted to the level set method and several topology optimization approaches have been introduced in literature.…”

Section: Introductionmentioning

confidence: 99%

A parameter space approach for isogeometrical level set topology optimization

Aminzadeh

Tavakkoli

2022

Numerical Meth Engineering

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In this article, a new isogeometrical level set topology optimization is introduced. In previous studies, the level set function is approximated by b-splines basis functions and the control net is updated during the optimization process. Since control points are not basically on the level set surface, a discrepancy between zero level of function that represents boundaries of the structure, and zero level of its control netis appeared. In this article, the idea is solving level set equation (LSE) over the parameter space of b-splines basis functions defined in the IGA model. Afterwards, the updated level set function is mapped into the physical space. The level set function is approximated over a grid defined in parameter space which is constantly a unit square. By doing so, control net of the IGA model and the grid for solving LSE are separated. Two well-known radial basis functions (RBF) and reaction-diffusion (RD) based methods are employed to solve the LSE. The proposed method is applied to minimize the mean compliance when certain amount of material is used and also for weight minimization subject to local stress constraints. Several numerical examples are presented to demonstrate performance and accuracy of the proposed method.

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“…IGA was already successfully used to discretize a Cahn–Hilliard type phase‐field approach for topology optimization by Dedè et al [19] employing an adaptive time‐stepping scheme. Recently, Shakour and Amir [34] propose a topology optimization procedure where a level‐set function is parametrized by means of B‐spline surfaces. However, an adaptive spatial mesh refinement/coarsening scheme has not been already implemented in the framework of IGA together with phase‐field topology optimization.…”

Section: Introductionmentioning

confidence: 99%

Additive manufacturing applications of phase‐field‐based topology optimization using adaptive isogeometric analysis

et al. 2021

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In this contribution, we apply adaptive isogeometric analysis to a diffuse interface model for topology optimization. First, the influence of refinement and coarsening parameters on the optimization procedure are evaluated and discussed on a two-dimensional problem and a possible workflow to convert smooth isogeometric solutions into 3D printed products is described. Second, to assess the required numerical accuracy of the proposed simulation framework, numerical results obtained adopting different stopping criteria are experimentally evaluated for a three-dimensional benchmark problem.

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Topology optimization with precise evolving boundaries based on IGA and untrimming techniques

Cited by 14 publications

References 69 publications

A Survey of Indicators for Mesh Quality Assessment

A Survey of Indicators for Mesh Quality Assessment

A parameter space approach for isogeometrical level set topology optimization

Additive manufacturing applications of phase‐field‐based topology optimization using adaptive isogeometric analysis

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