Structural Shape Optimization of Vibrating Axisymmetric and Prismatic Shells

Abstract

Chapter 9 is concerned with structural shape and thickness optimization of vibrating axisymmetric and prismatic plates and shells. The basic algorithm for SSO is described first. Details are subsequently presented concerning the problem definition. Attention is then focused on the sensitivity calculations and problems connected with their accuracy. In the penultimate section some details regarding mathematical programming are given. Finally, various practical aspects of SSO are discussed, such as specification of end conditions, scaling and bounds on design variables. This chapter is also concerned with the SSO of vibrating axisymmetric and prismatic shells. Natural frequencies and mode shapes are determined using curved, variable-thickness, MR FSs and FEs introduced and bench-marked in Chapters 7 and 8. The whole shape optimization process is carried out by integrating FE and FS analysis, cubic spline shape and thickness definitions, sensitivity analysis and mathematical programming. In most cases, the objective is either the maximization of the fundamental frequency or the minimization of the volume by changing the shape or thickness variation of the cross-section of the structure with constraints on the volume or natural frequencies. The SAM and FDM are used to determine the sensitivities of the objective function and constraints to changes in the design variables. Several examples are considered to illustrate and highlight various features of the optimization, including plates, conical shells, box-girder bridges with rectangular or curved planform, axisymmetric branched shells, bells and cylindrical shells.