Asymptotic Analysis of Periodic Structures
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This article is published in Journal of Applied Mechanics.The article was published on 1979-06-01 and is currently open access. It has received 5038 citations till now. The article focuses on the topics: Asymptotic analysis.read more
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Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
Journal ArticleDOI
Optimal shape design as a material distribution problem
TL;DR: In this article, various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable are described. But none of these methods can be used for shape optimization in a general setting.
MonographDOI
The Theory of Composites
TL;DR: Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli which govern the macroscopic behavior as mentioned in this paper.
Journal ArticleDOI
Homogenization and two-scale convergence
TL;DR: In this article, the authors define a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions, and prove that bounded sequences in $L^2 (Omega )$ are relatively compact with respect to this new type of convergence.
Journal ArticleDOI
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
Thomas Y. Hou,Xiao-Hui Wu +1 more
TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.
References
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Partial Differential Equations with Periodic Coefficients and Bloch Waves in Crystals
Farouk M. Odeh,Joseph B. Keller +1 more
TL;DR: In this paper, the existence and completeness of Bloch waves and Kohn-Luttinger waves in unbounded domains for a class of partial differential equations which includes the Schrodinger equation was proved.
Book ChapterDOI
Intégrales stochastiques par rapport aux martingales locales
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/conditions) of the agreement with the séminaire de probabilités (Strasbourg) are described.
Journal ArticleDOI
Random evolutions: A survey of results and problems
Journal ArticleDOI
On the uniqueness of solutions of stochastic differential equations II
Shinzo Watanabe,Toshio Yamada +1 more