Parametric shape optimization “searches the space spanned by the design variables to minimize or maximize some externally defined objective function” (Jiaqin Chen, Vadim Shapiro, Krishnan Suresh and Igor Tsukanov, Spatial Automation Laboratory, University of Wisconsin–Madison, “Parametric and Topological Control in Shape Optimization,” Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference). “In other words, parametric shape optimization is essentially a sizing problem that is a natural extension of parametric computer-aided design.
“The downside of parametric shapes is that they do not provide any explicit information about the geometry or topology of the shape’s boundaries. This, in turn, leads to at least two widely acknowledged difficulties: boundary evaluation may fail, and topological changes in the boundaries may invalidate boundary conditions or the solution procedure.”
Non-parametric optimization, by contrast, operates at the node/element level to derive an optimal structure. It can offer greater design freedom, and can make use of existing CAE models without the need for parameterization. “The main advantage of non-parametric shape optimization is the ease of setup, avoiding tedious parameterization that may be too restrictive with respect to design freedom” (Michael Böhm and Peter Clausen, FE-DESIGN GmbH, “Non-Parametric Shape Optimization in Industrial Context,” PICOF (Problèmes Inverses, Contrôle et Optimisation de Formes) ’12). “One of the major disadvantages on the other hand is that the CAD interpretation of the shape optimization result is not trivial.” Continue reading