SHAPE OPTIMIZATION IN SHELL THEORY: Design Sensitivity of the Continuous Problem

Abstract We consider a non-shallow shell made of an isotropic homogeneous material, working in linear elastic conditions, subjected to a given load. Our aim is to change the shape of the shell so that it resists better towards a given criterion. By shape, we mean essentially the midsurface of the shell. The thickness could be added without any difficulty. The important aspect that we study here is the midsurface. This problem is worked by gradient type methods. We prove that if the criterion depends on the displacement field through a differentiable function, then it depends on the shape in a differentiable manner, because the displacement field is a differentiable function of the shape. Then we present an analytical formula giving the exact gradient of the criteria before any discretization. After that, we explain how to compute numerically an approximation to this exact gradient. Then we give numerical results.