Computational Physics Group

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

© 2006 UIUC and Dr. Karel Matous