A multi-resolution method for 3D multi-material topology optimization

Park, Jaejong; Sutradhar, Alok

doi:10.1016/j.cma.2014.10.011

Cited by 89 publications

(42 citation statements)

References 62 publications

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“…The largest part of these costs is associated with finite element analysis (FEA) and the associated sensitivity analysis. By increasing the resolution of the design field relative to the analysis mesh, attempts have been made to reduce this cost [5][6][7][8][9]. In these works, the design field is characterized by the distribution of design variables in the domain.…”

Section: Introductionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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SUMMARYTopology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing nonuniqueness.

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Section: Introductionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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“…Computational complexity is the outstanding challenge in these approaches due to requiring a considerable number of expensive simulations to capture variations in parameter/stochastic space. Multiresolution and multifidelity finite element (FE) models have been used in a number of studies to enhance the computational efficiency of topology optimization . These multiresolution/multifidelity topology optimization approaches are explored within a deterministic framework, ie, when the focus is only on a limited number of deterministic simulations throughout different mesh resolutions.…”

Section: Introductionmentioning

confidence: 99%

Parametric topology optimization with multiresolution finite element models

Keshavarzzadeh

Kirby

Narayan

2019

Numerical Meth Engineering

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Summary We present a methodical procedure for topology optimization under uncertainty with multiresolution finite element (FE) models. We use our framework in a bifidelity setting where a coarse and a fine mesh corresponding to low‐ and high‐resolution models are available. The inexpensive low‐resolution model is used to explore the parameter space and approximate the parameterized high‐resolution model and its sensitivity, where parameters are considered in both structural load and stiffness. We provide error bounds for bifidelity FE approximations and their sensitivities and conduct numerical studies to verify these theoretical estimates. We demonstrate our approach on benchmark compliance minimization problems, where we show significant reduction in computational cost for expensive problems such as topology optimization under manufacturing variability, reliability‐based topology optimization, and three‐dimensional topology optimization while generating almost identical designs to those obtained with a single‐resolution mesh. We also compute the parametric von Mises stress for the generated designs via our bifidelity FE approximation and compare them with standard Monte Carlo simulations. The implementation of our algorithm, which extends the well‐known 88‐line topology optimization code in MATLAB, is provided.

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“…Several other material interpolation schemes for multi‐material topology optimization have also been proposed. These include peak function uniform multiphase materials interpolation , generalizations of SIMP and rational approximation of material properties schemes , and a family of discrete material optimization methods . For a rigorous comparative study on these interpolation schemes, we refer to .…”

Section: Introductionmentioning

confidence: 99%

An isogeometric approach to topology optimization of multi-material and functionally graded structures

Taheri

Suresh

2016

Int. J. Numer. Meth. Engng

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Summary A new isogeometric density‐based approach for the topology optimization of multi‐material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric non‐uniform rational B‐spline‐based parameterization leading to exact modeling of the geometry, removing numerical artifacts and full analytical computation of sensitivities in a cost‐effective manner. An extension of the perimeter control technique is introduced where restrictions are imposed on the perimeters of density fields of all phases. Consequently, not only can one control the complexity of the optimal design but also the minimal lengths scales of all material phases. This leads to optimal designs with significantly enhanced manufacturability and comparable performance. Unlike the common element‐wise or nodal‐based density representations, owing to higher order continuity of density fields in this method, their gradients required for perimeter control restrictions are calculated exactly without additional computational cost. The problem is formulated with constraints on either (1) volume fractions of different material phases or (2) the total mass of the structure. The proposed method is applied for the minimal compliance design of two‐dimensional structures consisting of multiple distinct materials as well as functionally graded ones. Copyright © 2016 John Wiley & Sons, Ltd.

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A multi-resolution method for 3D multi-material topology optimization

Cited by 89 publications

References 62 publications

Bounds for decoupled design and analysis discretizations in topology optimization

Bounds for decoupled design and analysis discretizations in topology optimization

Parametric topology optimization with multiresolution finite element models

An isogeometric approach to topology optimization of multi-material and functionally graded structures

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