Density-based shape optimization of 3D structures with mean curvature constraints

2021 ◽  
Vol 65 (1) ◽  
Author(s):  
Ronald Bartz ◽  
Thilo Franke ◽  
Sierk Fiebig ◽  
Thomas Vietor
Keyword(s):  
Shape Optimization ◽  
Mean Curvature ◽  
3D Structures

scholarly journals Existence of optimal shapes under a uniform ball condition for geometric functionals involving boundary value problems

2020 ◽  
Vol 26 ◽  
pp. 108
Author(s):  
Jérémy Dalphin
Keyword(s):  
Shape Optimization ◽  
Mean Curvature ◽  
Obstacle Problem ◽  
Optimization Problems ◽  
Existence Results ◽  
Quadratic Growth ◽  
Normal Vector ◽  
Boundary Values ◽  
Optimal Shapes ◽  
Fluid Membranes

In this article, we are interested in shape optimization problems where the functional is defined on the boundary of the domain, involving the geometry of the associated hypersurface (normal vector n, scalar mean curvature H) and the boundary values of the solution uΩ related to the Laplacian posed on the inner domain Ω enclosed by the shape. For this purpose, given ε > 0 and a large hold-all B ⊂ ℝn, n ≥ 2, we consider the class Oε(B) of admissible shapes Ω ⊂ B satisfying an ε-ball condition. The main contribution of this paper is to prove the existence of a minimizer in this class for problems of the form infΩ∈Oε(B) ∫ ∂Ωj[uΩ(x),∇uΩ(x),x,n(x),H(x)]dA(x). We assume the continuity of j in the set of variables, convexity in the last variable, and quadratic growth for the first two variables. Then, we give various applications such as existence results for the configuration of fluid membranes or vesicles, the optimization of wing profiles, and the inverse obstacle problem.

Shape Optimization of Combo Sensor using Quartz Crystal Resonator for Liquid Analysis

2016 ◽  
Vol 136 (8) ◽  
pp. 343-347 ◽  
Author(s):  
Ryo Sakai ◽  
Hiroaki Imai ◽  
Masayuki Sohgawa ◽  
Takashi Abe
Keyword(s):  
Shape Optimization ◽  
Quartz Crystal ◽  
Quartz Crystal Resonator ◽  
Crystal Resonator

Response surface techniques for diffuser shape optimization

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1512-1518 ◽  
Author(s):  
Jens I. Madsen ◽  
Wei Shyy ◽  
Raphael T. Haftka
Keyword(s):  
Shape Optimization ◽  
Response Surface
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