This collaborative research is a partnership between the University of California, San Diego, the University of Texas, Austin and Alcoa (Grant Opportunities for Academic Liaison with Industry "GOALI" partner). This research will develop finite elements for virtual sheet metal stamping using NURBS (Non-Uniform Rational B-Splines), the same functions used for representing the geometry in CAD-CAM packages. Current finite element methods approximate the geometry of the sheet metal and the dies with linear interpolation and therefore don't represent curves well. NURBS, however, are used in CAD-CAM because they can represent complicated curves exactly. The easiest advantage to appreciate is a NURBS finite element formulation has the generality in its kinematics to be completely compatible with the CAD-designed die unlike the polynomials used in current finite elements. NURBS are also very well behaved numerically, allowing length to thickness ratios of 1000:1 to be modeled with solid elements, eliminating the zero normal stress assumption of traditional shell formulations. Being able to model the sheet with solid elements allows more general kinematics through the thickness than the linear displacement field in standard shell element formulations, enhancing the accuracy. Introducing NURBS in finite element analysis will therefore increase its accuracy.
This research is directly applicable to all engineering applications requiring the accurate analysis of linear (e.g., vibration) and nonlinear structural response. It initiates collaborative research between two universities and industry. It provides graduate students the rare opportunity to work with industry as part of their research, and will provide under represented groups of undergraduate students an opportunity to participate in research via the McNair Program at UCSD. Additionally, they will gain firsthand experience with industry through the collaboration with Alcoa.
