A comparison amongst different shape control methods for shell optimization

For shape optimization many different parameterization methods are currently used, all of them aim at both minimizing the number of design variables and increasing the control on the shape of the structure. This study compares two different approaches to parameterize the shell shape: the first is to define a geometric surface representation, like Bézier, the design variables are provided by the Cartesian coordinates of the control points. In the second approach a design velocity field using natural vibration modes of the initial geometry is defined. The objective surface geometry is determined by a scaled combination of the vibration modes. An optimization problem of shell structure is solved by these two approaches for comparison. The objective function is defined as total strain energy, and the gradient-based sequential quadratic programming algorithm is used. The goal of the research is to investigate the capabilities of the above methods trying to emphasize advantages and drawbacks of both of them.