Stochastic processes and Markov chains in shape and material optimization problems of composite structures

Commonly shape and material optimization for complex structures having complicated boundary and loading conditions requires FE analysis in order to determine accurately enough (especially for composite structures) objective functions. The solutions of such class of problems become difficult as we use probabilistic algorithms. Therefore, a general method using the Markov chain and stochastic equations is proposed to reduce the total number of iterations (computations) that are necessary to obtain a global optimum (or a quasi-global). The proposed method can be applied both for isotropic and anisotropic (composite laminates) structures. The method is illustrated by a numerical example.