Shape and topology optimization based on the convected level set method

Yaji, Kentaro; Otomori, Masaki; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji; Pironneau, Olivier

doi:10.1007/s00158-016-1444-z

Cited by 24 publications

(8 citation statements)

References 45 publications

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“…the necessity of using high dense meshes in the design domain involving millions of elements and the application to new topological design problems (e.g. multiscale topological design [14,19,26,37], immersed boundary methods combined with XFEM techniques [41], convected methods [52], etc.). This is an issue to be explored in a subsequent research.…”

Section: Discussionmentioning

confidence: 99%

Variational approach to relaxed topological optimization: Closed form solutions for structural problems in a sequential pseudo-time framework

Oliver

Yago

Cante

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closedform solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the work.

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Section: Discussionmentioning

confidence: 99%

Variational approach to relaxed topological optimization: Closed form solutions for structural problems in a sequential pseudo-time framework

Oliver

Yago

Cante

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…It is evident that if we set d = r − R i to be the standard distance function from the interface [5,6] we can solve numerically for d in Equations (33)- (37) and verify that d is oscillating hence implying that the interface is oscillating back and forth in the radial direction. In addition I have compared to [16] for verification of a tan hyperbolic representation near the interface which is used there in a numerical approach. The solution given by Equation (33) can also be written in the form 1 −…”

Section: Resultsmentioning

confidence: 99%

A New Analytical Procedure to Solve Two Phase Flow in Tubes

Moschandreou

2018

MCA

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Abstract:A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves whereas when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

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“…In both cases, the reference state equation is represented by the linear elasticity problem, suitably incorporating information about the material distribution through an auxiliary function. The level set approach relies on a function χ governed by a time-dependent equation which makes an initial contour propagating towards the optimized final layout [20,21,30,31,32,33]. Density-based methods modify the elasticity equation by weighting the Lamé coefficients via a density function, ρ, which identifies the allocation of the material in the structure.…”

Section: The Topology Optimization Techniquementioning

confidence: 99%

POD-assisted strategies for structural topology optimization

Ferro

Micheletti

Perotto

2019

Computers & Mathematics with Applications

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We propose a new numerical tool for structural optimization design. To cut down the computational burden typical of the Solid Isotropic Material with Penalization method, we apply Proper Orthogonal Decomposition on SIMP snapshots computed on a fixed grid to construct a rough structure (predictor) which becomes the input of a SIMP procedure performed on an anisotropic adapted mesh (corrector). The benefit of the proposed design tool is to deliver smooth and sharp layouts which require a contained computational effort before moving to the 3D printing production phase.

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Shape and topology optimization based on the convected level set method

Cited by 24 publications

References 45 publications

Variational approach to relaxed topological optimization: Closed form solutions for structural problems in a sequential pseudo-time framework

Variational approach to relaxed topological optimization: Closed form solutions for structural problems in a sequential pseudo-time framework

A New Analytical Procedure to Solve Two Phase Flow in Tubes

POD-assisted strategies for structural topology optimization

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