Multi-objective design for vibration and buckling of laminated plates by statistical treatment

A design approach is presented for dealing with multiple (six or even more) object functions in the optimal design problem of laminated composite plates. The proposed approach is divided into some steps. First, the design variables are discretized with a certain increment that depends on the required accuracy, and all the values of physical parameters (used as object functions) are calculated for the discrete values of design variables. The second step is based on statistical treatment of the data. The calculated values of each physical parameter for discrete design variables are normalized and modified to be the deviated values on the assumption that the values are subjected to the Gaussian distribution with the prescribed standard deviation and average. At the last step, the best design in global sense is determined by considering the weighted sum of the deviated object functions and also graphical presentations. In the application, a three-layered rectangular plate with angle-ply stacking sequence [θ/−θ/θ] is considered where a representative fiber orientation angle θ is a single design variable. The object functions are taken to be six physical parameters of vibration and various buckling problems.