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International Journal for Multiscale Computational Engineering
インパクトファクター: 1.016 5年インパクトファクター: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v5.i3-4.70
pages 249-260

Applications of the Gunther Problem in Multiscale Systems

Pavel Grinfeld
Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA

要約

Various problems of heterogeneous multiscale systems are analyzed from the variational point of view. Since many composite materials consist of different components, the optimal functions may experience discontinuities along internal interfaces. In many instances, the locations of the interfaces is not a priori known, but must instead be determined by the variation principle. One of the first attempts of analyzing such problems was presented by Gunther, which we advance in several directions. In the Gunther problem, the integrand q (x, w, Δw)depends on the spatial gradients of a scalar field w (x). For one of the simplest types of discontinuities sort, Gunther found the formula of the first variation and established the appropriate extension of the Weierstrass-Erdmann transversality conditions. We establish some explicit solutions of the boundary value problems associated with the Gunther problem and derive the expression for the second variation.


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