Collaborative Research: GOALI: Virtual Sheet Metal Stamping Using Isogeometric Analysis

这项合作研究是由加州大学圣地亚哥分校、德克萨斯大学奥斯汀分校和美国铝业公司（与行业学术联络的资助机会“目标”合作伙伴）合作进行的。本研究将使用NURBS（非均匀有理b样条）开发虚拟钣金冲压的有限元，与用于表示CAD-CAM包中的几何形状的函数相同。目前的有限元方法是用线性插值逼近金属板和模具的几何形状，因此不能很好地表示曲线。NURBS之所以在CAD-CAM中使用，是因为NURBS可以精确地表示复杂的曲线。最容易理解的优点是NURBS有限元公式在运动学上具有通用性，与cad设计的模具完全兼容，而不像当前有限元中使用的多项式。NURBS在数值上的表现也很好，允许用实体单元模拟1000:1的长厚比，消除了传统壳体公式的零法向应力假设。与标准壳单元公式中的线性位移场相比，能够用实体单元对板材进行建模可以通过厚度进行更一般的运动学分析，从而提高了精度。因此，在有限元分析中引入NURBS将提高其精度。该研究直接适用于所有需要精确分析线性（如振动）和非线性结构响应的工程应用。它启动了两所大学和工业界之间的合作研究。它为研究生提供了与行业合作的难得机会，作为他们研究的一部分，并将为代表性不足的本科生群体提供通过加州大学圣地亚哥分校麦克奈尔项目参与研究的机会。此外，他们将通过与美国铝业公司的合作获得第一手的工业经验。

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.