According to the nonlinear Karman equations, buckling and postbuckling behaviors of laminated shear deformable square and rectangular plates with four edges simply supported are studied by using a deflection type perturbation technique.

An asymptotic series solution is constructed by the perturbation technique of deflection type for postbuckling behavior of the plates with four simply supported edges in biaxial .

Techniques from probabilistic perturbation method and Hooke-Jeeves direct search method were employed to present the practical and effective method for the reliability multi- objective optimization design for caliper disc brake under the conditions of known probabilistic characteristics of basic random variables.

Following the trained NN,the probabilistic perturbation method is chosen to obtain the reliability-based robust design information.

Based on the interval mathematics, the sensitivity analysis theory and the Kronecker algebra, applying the Tayler series expand method and the probabilistic perturbation technique, the non-probabilistic interval analysis method is presented in this article to solve the eigenvalue problem of uncertain parameter structure system.