Two-Dimensional Shape Optimization

In order to optimize the shape of a structure, one naturally has to be able to control the shape of its boundary using some design variables. In Sect. 6.3.2, the sensitivity analysis for shape optimization of sheets was described. It was concluded that the nodal sensitivities, i.e. the partial derivatives of the nodal positions with respect to the design variables were needed. These sensitivities will depend on how the shape is represented and also on how the finite element mesh is generated. In this chapter we will discuss how the nodal sensitivities may be calculated for two-dimensional structures such as plane sheets or axisymmetric bodies.