Meshfree Integration of Geometric Design and Engineering Analysis

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This grant provides funding for developing a new technology for seamless integration of geometric design and engineering analysis tools using a new hybrid computer representation. The new representation combines an implicit function representation of the geometric model with a piecewise continuous model of the analysis problem. Such representations can be constructed automatically and support meshfree analyses of spatially distributed problems, where the spatial discretization no longer needs to conform to the geometric domain or boundary conditions. Specific goals of this project include: (1) development of a modeling theory based on the new hybrid representation, with focus on computational and numerical properties; (2) design and implementation of a framework and software environment integrating geometric design and analysis, based on the new hybrid representation; (3) formulation, experimental studies, and comparison of computed meshfree solutions with other known solutions and/or experimental results; and (4) investigating application of the new technology to problems that are difficult to solve with traditional methods, in particular to shape optimization and simulation problems with time-varying geometries.If successful, this research has the potential to realize major gains in the product development cycle by integrating geometric design and analysis across models, disciplines, and levels of abstraction. Elimination of the difficult and time-consuming meshing procedures should allow major advances in automating solutions to the problems that today require lengthy manual constructions, tedious analysis, and special-purpose tools.