An engineer's approach to optimal material distribution and shape finding

“…The procedure followed in this paper, inspired by works by Mlejnek and Schirrmacher [25] or more recent similar works by Andreassen and Andreasen [3], is adapted to the particular framework.…”

Section: Homogenizationmentioning

confidence: 99%

Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Noël

Duysinx

2016

Struct Multidisc Optim

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The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element method (XFEM) combined with a level set representation of the geometry, to deal with complex microstructures and handle large shape modifications while working on fixed meshes. The homogenization theory, allowing extracting the behavior of periodic materials built from the repetition of a representative volume element (RVE), is applied to impose macroscopic strain fields and periodic boundary conditions to the RVE. Classical numerical homogenization techniques are adapted to the selected XFEM-level set framework. Following previous works on analytical sensitivity analysis [31], the scope of the developed approach is extended to tackle the problem of stress objective or constraint functions. Finally, the method is illustrated by revisiting 2D classical shape optimization examples: finding the optimal shapes of single or multiple inclusions in a microstructure while minimizing its local stress field.

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“…The key concept of this method is how to treat the material composition in order to estimate the objective function, and thus to obtain the final shape of the device. There are two methods to treat the material composition, the homogenization method [5]- [7] and the density method [8].…”

Section: Topology Optimizationmentioning

confidence: 99%

Optimal Shape Design of Dielectric Micro Lens Using FDTD and Topology Optimization

Chung¹,

Lee²,

Kim³

2009

Journal of the Optical Society of Korea

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In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.

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An engineer's approach to optimal material distribution and shape finding

Cited by 235 publications

References 2 publications

A genetic algorithm for combined topology and shape optimisations

A genetic algorithm for combined topology and shape optimisations

Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Optimal Shape Design of Dielectric Micro Lens Using FDTD and Topology Optimization

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