Optimal design of an annular cantilever beam under pressure, dead weight and thermal loading is considered. The radius of outer profile is taken as the design variable and assumed to be of cubic polynomial shape.
The structure is modeled by finite element method; axisymmetric analysis for pressure and thermal loading, beam element analysis for dead weight and transversal modal analysis.
In the optimal design formulation, constraints are imposed on stress, displacement, eigenvalue and geometry. Stresses and displacements are obtained by superposing the results of axisymmetric analysis and beam analysis. Design sensitivity analysis with respect to the change of the coordinates is necessary and implemented for a generalized steepest descent method. As a numerical example, a long gun barrel is optimized. The optimal profile is found to be highly dependent on the pressure-distance curve for this example.
