FREE-VIBRATION ANALYSIS AND OPTIMIZATION OF AXISYMMETRICAL PLATES ANDSHELLS .2. SHAPE OPTIMIZATION

The second part of this paper is concered with the structural shape op timisation of vibrating axisymmetric shells. Natural frequencies and m ode shapes are determined using curved, variable thickness, Mindlin-Re issner FEs introduced and benchmarked in the first part of the paper. The whole shape optimisation process is carried out by integrating FE analysis, cubic spline shape and thicknness definitions, sensitivity a nalysis and mathematical programming. The semi-analytical method is us ed to determine the sensitivities of the objective function and constr aints to changes in the design variables. Several examples are conside red to illustrate and highlight various features of the optimisation, including various plates, a conical shell, a branched shell, and a chu rch bell.