Frequency Optimization of Conical Shells under Mass Equality Constraint

As a major structural dynamic criterion in designing thin shells, the fundamental frequency is maximized for a specified total structural mass. The general optimization problem of metallic conical shell structures with clamped / free ends has been treated formally among all other types of boundary conditions. Both stiffened and unstiffened constructions are examined with the effective design variables selected to be the shell thickness distribution and the number, locations and size of the attached ring stiffeners. Structural analysis is based upon Donnell-Mushtari shell theory and an analytical approach based on Rayleigh-Ritz method has been implemented for calculating the natural vibration characteristics of the different shell types. The final optimization problem is formulated as a nonlinear mathematical programming problem solved by invoking the Matlab optimization toolbox routines, which implement the interior penalty function technique and interact with eigenvalue calculation routines. The proposed mathematical model has succeeded in maximizing the fundamental frequency without the penalty of increasing the total structural mass. Results show that the approach used in this study is efficient and produces designs having improved dynamic performance as compared with a known baseline design.