Shape optimization of curves and surfaces considering fairness metrics and elastic stiffness

A method is presented for generating round curves and surfaces allowing discontinuities in tangent vectors and curvatures. The distance of the center of curvature from the specified point is used for formulating the objective function that is a continuous function of the design variables through convex and concave shapes. It is shown that a shell with and without ribs can be generated within the same problem formulation if the minimization problem is converted into a maximization problem and the parameter region where integration is to be carried out is restricted in view of the sign of the curvature. Optimal shapes are also found under constraints on the compliance against static loads. A multiobjective optimization problem is solved by the constraint method to generate a trade‐off design between roundness and mechanical performance.