A discrete model for the design sensitivity analysis of multi-layered composite shells of revolution

This paper studies the sensitivity analysis for the optimization of the multi-layered composite axisymmetric shells subjected to arbitrary static loading and free vibrations. The structural analysis is carried out using a two node frustum-cone finite element with 16 degrees of freedom based on Love-Kirchhoff assumptions. The design variables are the angle of orientation of the fibers and/or the vectorial distances from middle surface to upper surface of each ply. The constraint functions are displacements, stresses (Tsai-Hill criterion) and the natural frequency of a specified mode shape. Four types of objective functions can be used: maximum displacement or natural frequency or elastic strain energy and material volume. The design sensitivities are calculated analytically, semi-analytically and by global finite difference. The potentiality of the proposed model and the accuracy of the sensitivities of response are discussed with reference to the applications.