Solving Laminated Plates by Domain Decomposition
J. Kruis, K. Matous and Z. Dostal
CTU, Fac. of Civil Eng., Dep. of Structural Mechanics
Thákurova, 166 29 Prague 6
Abstract
The refined Mindlin Reissner theory is used to estimate
the overall response of composite plates. The difficulties
with the solution of a system of algebraic equations,
which emerged in analysis of composite materials, are
studied and a special version of decomposition is
proposed. Similarity between the system of equations
derived from the layered theory and from the Finite
Element Tearing and Interconnecting method (FETI) suggests
a strategy for implementation of the parallel environment.
Several applications are investigated and a number of
numerical results are presented.
Conclusion
We have presented a model of composite laminated plates
and its discretization. The process combines a natural
layer by layer discretization approach with the parallel
technique that solves the problem in the similar way. New
modification of the basic FETI method with the
orthonormalization of constraints was used for the
solution of the resulting system of equations. The results
of the numerical experiments presented in this paper
indicate that there are problems of practical interest
that may be solved using this method. The work in the
progress extends this approach to enhance the
decomposition of each layer, the more general boundary
conditions and the preconditioning by the natural coarse
grid. Such generalization of the approach has been
developed and analyzed in (Farhat et. al). The results
obtained for both examples indicate a nice numerical
scalability and efficiency of the proposed numerical model
and solver to large areas of laminated composite materials
and structures.
Acknowledgment
Financial support for this work was provided by the
grant GACR 103/01/0400 and the Ministry of education of
Czech Republic J04/98:210000003. Their financial
assistance is gratefully acknowledged.
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