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Zbl 0817.73038
Schwab, Christoph
Boundary layer resolution in hierarchical models of laminated composites. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 28, No.5, 517-537 (1994). ISSN 0764-583X

Summary: The hierarchical modelling of a linear heat conduction problem in an orthotropic sandwich plate of thickness $2 d$ is analyzed and the asymptotic structure of the solution and the boundary layers are obtained. A family of lower dimensional, hierarchical models with increased model order in a $O(d\vert\ln d\vert)$ vicinity of the lateral edge is constructed by energy projection. It is shown that these models converge in the energy norm with optimal order as $d\to0$ to the exact solution regardless of the boundary layers.

MSC 2000:: *74E30 Composite and mixture properties
74K20 Plates
80A20 Heat and mass transfer

Keywords: convergence; linear heat conduction problem; orthotropic sandwich plate; asymptotic structure; energy norm

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