Skeletal Reduction of Thin Mechanical Components

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Thin mechanical components are ubiquitous and constitute a multi-billion dollar industry; examples include outer-shell of automobiles and aircrafts, most plastic components, etc. Like all mechanical components, they are subject to rigorous computational analysis before production. Existing analysis techniques for thin components, for historical reasons, are based on the mid-surface of a thin component. Unfortunately, the mid-surface is often ill defined for complex objects. This has led to fragile and inaccurate algorithms. This project proposes to use of the skeleton of a solid, abandoning the notion of a "mid-surface" approach. The skeleton, unlike the mid-surface, is well defined and can be computed uniquely for a solid. Initial investigation shows that this would result in robust algorithms, involving the combination of the Kantorovich principle of dimensional reduction with the unique topological and geometrical properties of skeleton representation. If successful, the research would lead to a fundamentally new and unified theory of thin component analysis consisting of an unambiguous and complete mathematical language of skeletal reduction, and associated algebra. The mathematical principles would also be of interest to researchers involved in the broad area of boundary value problem analysis. Dissemination of the findings of the research will be articulated to University of Wisconsin students through a graduate course, and students and researchers elsewhere through seminars. It is also the intention to facilitate a transfer of technology of the ensuing theory and algorithms to the CAD/CAE industry. An environmental impact of the project is in the plastics industry where components are almost exclusively thin; better analysis techniques have the potential of significantly reducing the tonnage of plastics used (and discarded) today.