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

这项合作研究是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(GRANT Opportunities for学术联络与行业“GOALI”合作伙伴)之间的伙伴关系。这项研究将使用NURBS(非均匀有理B-Splines)开发用于虚拟板料冲压的有限元，该函数与CAD-CAM软件包中用于表示几何的函数相同。现有的有限元方法用线性插值法逼近板料和模具的几何形状，因此不能很好地表示曲线。然而，在CAD-CAM中使用NURBS是因为它们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，与当前有限元中使用的多项式不同，它与CAD设计的模具完全兼容。NURBS在数值上也表现得很好，允许用实体单元模拟1000：1的长厚比，消除了传统壳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，能够使用实体单元对板材进行建模，从而允许通过厚度进行更一般的运动学分析，从而提高精度。因此，将NURBS引入有限元分析将提高有限元分析的精度。本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。它推动了两所大学和产业界之间的合作研究。它为研究生提供了难得的与行业合作的机会，作为他们研究的一部分，并将为未被代表的本科生群体提供机会，通过加州大学圣迭戈分校的麦克奈尔项目参与研究。此外，他们还将通过与美国铝业的合作获得与行业相关的第一手经验。

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.