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Computational Science, Engineering & Technology Series
ISSN 1759-3158 CSETS: 7
COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, Z. Bittnar
Chapter 10
A Mortar Approach for the Analysis and Optimization of Composite Laminated Plates C. Cinquini and P. Venini
Department of Structural Mechanics, University of Pavia, Italy Full Bibliographic Reference for this chapter
C. Cinquini, P. Venini, "A Mortar Approach for the Analysis and Optimization of Composite Laminated Plates", in B.H.V. Topping, Z. Bittnar, (Editors), "Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 10, pp 239-254, 2002. doi:10.4203/csets.7.10
Keywords: mortar method, composite plates, optimization.
Summary
A mortar method is introduced for the analysis of L-shaped
generally-orthotropic thin composite plates. The underlying
differential operator is a fourth-order one that calls for
interface conditions on the normal displacement as well as on
its normal derivative. We therefore move from the few existing
approaches for the bi-Laplacian operator and extend it to handle
the fourth-order laminated plate operator. However, we do not
resort to Lagrange polynomials and relevant quadrature points as
frequently done in the field of mortar methods but make use of
standard polynomials with exact (symbolic) integration. A few
numerical examples concerning the analysis and optimization of
laminated composite plates are presented to validate the proposed
approach.
The design of laminated composite plates and shells is an extremely challenging task mainly because of the large number of design variables, i.e. laminae thicknesses and ply angles. Furthermore, one may show that the design process is non-convex so that peculiar numerical schemes are to be developed that are able to escape local minima of the objective function in the design variable space. In fact, the huge variety of design alternatives often advice to cast the design problem as an optimal design one. Thousands of structural and sensitivity analysis are then to be performed for the optimal design to be achieved. The finite-element method, though far more general than spectral approaches as to the geometry of the structure, may however lead to very cumbersome if not prohibitive design sessions. Therefore, spectral methods may represent a sound alternative, at least in the case of rather regular design domains. In fact, standard spectral methods are basically limited to convex quadrilateral domains whereas domain decomposition approaches, [1], and mortar methods in paricular, [2], represent a recent powerful tool that, among others, present the following beneficial features:
References
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