Regularity of minimizers of quasi perimeters with a volume constraint

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

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Analytical validation of the Young–Dupré law for epitaxially-strained thin films

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202519500441 ◽

2019 ◽

Vol 29 (12) ◽

pp. 2183-2223 ◽

Cited By ~ 2

Author(s):

Elisa Davoli ◽

Paolo Piovano

Keyword(s):

Thin Films ◽

Contact Point ◽

Variational Model ◽

Analytical Validation ◽

Regularity Of Minimizers ◽

Transmission Problems ◽

Thin Film Model ◽

New Ideas ◽

Film Substrate ◽

Regularity Results

We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e. the angle formed at the contact point of films with the substrate. In particular, the Young–Dupré law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.

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Traceless Maps as the Singular Minimizers in the Multi-dimensional Calculus of Variations

Canadian Mathematical Bulletin ◽

10.4153/cmb-2016-094-5 ◽

2017 ◽

Vol 60 (3) ◽

pp. 631-640

Author(s):

M. S. Shahrokhi-Dehkordi

Keyword(s):

Convex Function ◽

Energy Functional ◽

Uniformly Convex ◽

Lagrange Equations ◽

Regularity Of Minimizers ◽

Uniformly Convex Function ◽

Bounded Lipschitz Domain ◽

Second Derivatives ◽

Image Position ◽

Singular Minimizers

AbstractLet Ω ⊂ ℝn be a bounded Lipschitz domain and consider the energy functionalover the space of W1,2(Ω, ℝm) where the integrand is a smooth uniformly convex function with bounded second derivatives. In this paper we address the question of regularity for solutions of the corresponding system of Euler–Lagrange equations. In particular, we introduce a class of singularmaps referred to as traceless and examine themas a new counterexample to the regularity of minimizers of the energy functional ℱ[ ·, Ω] using a method based on null Lagrangians.

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Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2020.105366 ◽

2020 ◽

Vol 90 ◽

pp. 105366 ◽

Cited By ~ 3

Author(s):

Bingquan Ji ◽

Hong-lin Liao ◽

Yuezheng Gong ◽

Luming Zhang

Keyword(s):

Second Order ◽

Volume Constraint ◽

Cahn Equation ◽

Order Energy ◽

Energy Stable Schemes ◽

Energy Stable

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Reliability of dose volume constraint inference from clinical data

Physics in Medicine and Biology ◽

10.1088/1361-6560/aa63d4 ◽

2017 ◽

Vol 62 (8) ◽

pp. 3250-3262 ◽

Cited By ~ 1

Author(s):

C M Lutz ◽

D S Møller ◽

L Hoffmann ◽

M M Knap ◽

M Alber

Keyword(s):

Clinical Data ◽

Volume Constraint ◽

Dose Volume

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