Computational Physics Group

Karel Matous









Analysis and Optimization of Composite Materials and Structures

K. Matous

CTU, Fac. of Civil Eng., Dep. of Structural Mechanics
Thákurova, 166 29 Prague 6


The continuous development of composite materials, computer industry and the engineers' requirements for effective design in recent decades have led to searching for many different methods improving the design and overall performance of composite structures. In most applications, the aim has been of finding an optimum weight, strength, ply thicknesses or fibers orientation and prestress.

There are several useful theories developed and implemented in the presented thesis. The refined Mindlin Reissner theory is used to estimate an overall response of composite structures. It relies on Mindlin's kinematic assumptions with independent approximation of in-plane displacements within each layer. The continuity of in-plane displacements at ply interfaces is attained by imposing interfacial constraints. These constraints are added into the modified variational principle through Lagrange multipliers, which represent the out of plane shear stresses. Multilayered plate element is based on a special procedure for interpolating the transverse shear strains. In most engineering problems, however, we need a shell element for a correct discretization. Therefore, the multilayered shell element based on the same layered theory, is derived and tested.

A number of important issues are addressed. First, the elastic behavior of composite laminates is investigated. Then the effect of plastic flow developed in the matrix is explored. In particular the plastic response of ductile graphite-aluminum composite system for given load increments is determined using the Mises yield condition and the Phillips kinematic hardening rule. Fibers are assumed to remain elastic, but subjected to initial prestress in order to improve an overall response of the laminates. An optimal level of the initial fiber prestress is found with the help of a powerful optimization technique. This procedure generates an optimum distribution of the fiber prestress within each layer, which substantially increases the load bearing capacity of laminates as well as reduces their maximum deflection.

The micromechanical modeling is based on the Mori-Tanaka method in combination with Dvorak's transformation field analysis. This approach provides piecewise uniform approximations of the instantaneous local strain and stress fields in the phases and estimates of the overall instantaneous properties of a representative volume of the heterogeneous solid.

Crucial point of the presented work is the domain decomposition and the parallel solver for layered structures. Similarity between the systems of equations derived from the layered theory and those arisen from the Finite Element Tearing and Interconnecting method (FETI), suggests a strategy for implementation of a parallel environment. A preconditioning and an orthogonalization is added to reduce the number of iterations. A number of large systems of equations are solved and the scalability is tested. The FETI algorithm is compared with the direct solver, which proved its ability to solve large composite structures.

The thesis describes several problems of the analysis and optimization of composite materials and structures and gives a brief introduction and proofs.


Financial support for this work was provided by the GACR 103/00/0756 and CTU grant No. 3099K1322. Their financial assistance is gratefully acknowledged.
© 2006 UIUC and Dr. Karel Matous