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
In conceptual and preliminary design, many aspects of mechanical products are most efficiently modeled for simulation using 0D/1D/rigid entities. In vehicle drivelines, for example, these include beams, bushings, bearings, point masses and the like. Combining these models with other product components best represented by 2D/3D CAE models can yield systems models that are highly revealing in design exploration activities such as parameter studies, design of experiments and optimization runs. But bringing multiple levels of fidelity together in a single model has conventionally been a labor-intensive manual process, severely limiting the number of design variants able to be studied this way when not precluding the practice altogether.
While mainstream CAE vendors are beginning to progress on this front, breakthrough technologies addressing the problem are available today that work with the industry’s leading solvers. Continue reading
Design space exploration as an engineering formalism originated in the embedded-systems industry as a set of methodologies for hardware/software co-design, configuration of software product lines, and real-time software synthesis. “The set of all possible design alternatives for a system is referred to as a design-space, and design-space exploration (DSE) is the systematic exploration of the elements in a design-space” (Saxena and Karsai, “Towards a Generic Design Space Exploration Framework,” Proceedings of 2010 IEEE 10th International Conference on Computer and Information Technology).
In mechanical engineering, design space exploration is rooted in the technological domain often referred to as process integration and design optimization, or PIDO, first identified and defined (Jenkins, Daratech, 2001) as software and methods to help:
- Automate and manage the setup and execution of digital simulation and analysis;
- Integrate/coordinate analysis results from multiple disciplines and domains to produce a more holistic model of product performance; and
- Optimize one or more aspects of a design by iterating analyses across a range of parameter values toward specified target conditions.
Design space exploration is both a class of quantitative methods and a category of software tools for systematically and automatically exploring very large numbers of design alternatives and identifying those with the most optimal performance parameters. The mathematical techniques that underpin design space exploration have been long known—and sometimes applied, in cases where the attendant costs in expertise, time and labor could be justified. What’s changing now is the way fresh software technologies are at last converting these powerful but formerly difficult-to-use methods into practical everyday engineering aids. Continue reading
Design optimization is the search for a structural design that is optimal in one or more respects. In all the various methods available for optimization, the design is guided to satisfy operating limits imposed on the response of the structure, and by further limits on the values that the structural parameters can assume. The power of numerical optimization is its ability to rationally and rapidly search through alternatives for the best possible design(s). Continue reading