Bivariate Splines for Geometric Modeling

聚合物产品的最终性能在很大程度上取决于工艺条件，如低速率、加工模具的形状和冷却温度，这些在数学模型中表示为条件参数。从这个意义上说，粘弹性流体行为的建模提供了对聚合物产品（如纤维和薄膜）结构的基本解释。模拟纤维和薄膜加工过程的有限元计算方法是聚合物工业中的一个新发展，本文的目的是将数学优化技术引入粘弹性流体的数值模拟中，以确定聚合物产品的最佳工艺条件。两个研究项目涉及的建议：电影铸造和涡量最小化问题。总体战略将是整合最近开发的粘弹性模型和优化技术，以满足通过各种控制机制，如形状控制和边界控制的目标。作为薄膜流延问题的方程求解器，将使用商业软件包Poly ow，该软件包模拟各种设置下的薄膜和纤维加工。对于另一个问题，有限元codecurrently正在开发中将被使用。在求解优化问题时，目前的研究成果将扩展到更一般的高维粘弹性区域。

ABSTRACT0204174Marian NeamtuVerderbilt UniversityThe final properties of polymer products are largely determined by process conditions such a low rate, shape of processing die and cooling temperature, which are represented as condition parameters in mathematical models. In this sense, modeling viscoelastic fluid behavior provides a fundamental explanation of the structure of polymer products such as fibers and films. Advances in the finite element computational methodologies for simulating the fiber and film process is a recent development in polymer industries.The goal of this work is to introduce mathematical optimization techniques into the nu-merical simulation of viscoelastic fluid, in order to determine optimal process conditions for polymer products. Two research projects are involved in the proposal: film casting and a vorticity minimization problem. The overall strategy will be to integrate recently developed viscoelastic models and optimization techniques in order to meet objectives through various control mechanisms such as shape control and boundary control. As an equation solver for the film casting problem, the commercial software package Poly ow, which simulates film and fiber processing in various settings, will be used. For the other problem, a finite element codecurrently under development will be used. In solving the optimization problems, recent resultsfrom current research will be extended to the more general and high dimensional viscoelasticregime.