The Effect of Different Weighting Ratios, Length, and Thickness on Weighted Sum of the First Natural Frequency and Critical Buckling Load for a Laminated Composite Circular Cylindrical Shell

Abstract

In this study, a weighted sum, consisting two non-dimensionalized quantities critical buckling force and natural frequency, is employed to maximize the objective function for a laminated composite circular cylindrical shell. The function is considered to find the optimum solutions as the goal. Orientation angels of fibers are mentioned in a well-known configuration as candidate design, and critical buckling force and natural frequency values are derived with the first order shear deformation theory. The composite shell is considered with 8 layers, also the boundary conditions are assumed to be fully simply support and to satisfy boundary conditions displacement and slope components are defined in form of double Fourier series. After combination of differential operators and Fourier series, eventually the matrix L is found and Galerkin method gains function values. For this purpose, a program based on MATLAB is employed for the process. Validations of numerical results show that the used method is moderately satisfactory and acceptable in predicting the critical buckling force and the natural frequency of the shell in comparison with other works. As the conclusion, the effect of different weighting ratios, shell length-to-radius ratios, and shell thickness-to-radius ratios on the optimal designs are investigated and the results are compared.

Keywords

• weighted sum
• natural frequency
• buckling load
• laminated composite
• circular cylindrical shell