Two-dimensional shape optimal design†

This paper treats shape optimal design of two-dimensional structures. Sensitivity of cost and constraint functions to changes in the shape of the structure are obtained by applying theorems from the calculus of variations and by using consistent first-order approximations of functions arising in an optimal design problem. A generalized steepest descent algorithm is presented for determination of the optimum shape. The method is applied to a load carrying shear plate that models a component of the high pressure seal in a gun launched high velocity projectile.