Multiparametric shape optimal design of disks

The external boundary of a structure described by a set of design parameters undergoes shape modification. Arbitrary stress, strain and displacement functionals are defined within the domain of the structure and its first- and second-order sensitivities with respect to varying structural shape are discussed. The optimal shape design problem is then formulated and solved using the first- and second-order sensitivity information. The iterative analysis-redesign algorithm is formulated using the finite element method. Some illustrative examples are included.