• Corpus ID: 231979193

Shape optimization of light structures and the vanishing mass conjecture

@inproceedings{Babadjian2021ShapeOO,
  title={Shape optimization of light structures and the vanishing mass conjecture},
  author={Jean-François Babadjian and Flaviana Iurlano and Filip Rindler},
  year={2021}
}
This work proves rigorous results about the vanishing-mass limit of the classical problem to find a shape with minimal elastic compliance. Contrary to all previous results in the mathematical literature, which utilize a soft mass constraint by introducing a Lagrange multiplier, we here consider the hard mass constraint. Our results are the first to establish the convergence of approximately optimal shapes of (exact) size ε ↓ 0 to a limit generalized shape represented by a (possibly diffuse… 
Nonlocal basis pursuit: Nonlocal optimal design of conductive domains in the vanishing material limit
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References

SHOWING 1-10 OF 50 REFERENCES
Optimization of light structures: the vanishing mass conjecture
We consider the shape optimization problem which consists in placing a given mass $m$ of elastic material in a design region so that the compliance is minimal. Having in mind optimal light
Structural Optimization of Thin Elastic Plates: The Three Dimensional Approach
The natural way to find the most compliant design of an elastic plate is to consider the three-dimensional elastic structures which minimize the work of the loading term, and pass to the limit when
Shape optimization by the homogenization method
Summary.In the context of shape optimization, we seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading. This problem is known not to be
Michell trusses in two dimensions as a $$\Gamma $$Γ-limit of optimal design problems in linear elasticity
We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as
Optimization of Structural Topology in the High-Porosity Regime
Optimal design and relaxation of variational problems, III
Abstract : This paper has attempted a synthesis of three subjects that have developed separately - optimal design, homogenization, and relaxation in the calculus of variations. The underlying theme
Symmetric Div-Quasiconvexity and the Relaxation of Static Problems
We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and
On the optimal constants in Korn's and geometric rigidity estimates, in bounded and unbounded domains, under Neumann boundary conditions
We are concerned with the optimal constants: in the Korn inequality under tangential boundary conditions on bounded sets $\Omega \subset \mathbb{R}^n$, and in the geometric rigidity estimate on the
Concentration versus Oscillation Effects in Brittle Damage
This work is concerned with an asymptotic analysis, in the sense of Γ‐convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is
Characterization of optimal shapes and masses through Monge-Kantorovich equation
Abstract.We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show
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