Collaborative Research: Isogeometric Boundary Element Analysis

该合作研究奖的研究目标是开发方法，使工程师能够使用他们的计算机辅助设计（CAD）模型进行应力分析，而无需传统有限元分析所需的耗时网格生成。研究方法将等几何分析与边界元技术相结合。等几何分析使用与用于工程分析的CAD模型相同的基函数。这些基函数的例子包括非均匀有理b样条（NURBS）和t样条。传统的数值方法，如有限元分析，使用低次的分段连续多项式。因此，需要一个网格生成步骤来将几何图形的CAD表示转换为数值分析可以使用的表示。直接使用CAD基函数可以省去这一步。目前CAD基函数的局限性是它们只能表示曲面。为了避开这个限制，我们将使用边界元素技术，它直接与表面表示一起工作。如果成功，这项研究的结果将允许工程师在初步设计过程中使用他们的CAD模型快速执行结构分析。在设计阶段进行详细分析的高成本限制了工程师能够探索的设计空间范围，并使真正的创新设计变得昂贵。通过减少分析的时间和成本，设计工程师将能够生产出在重量、性能和成本方面更优化的设计。由于数值分析将直接与CAD模型参数化的设计空间一起工作，因此也将促进自动设计优化，从而允许优化程序在较少的人为干预和校正下工作。

The research objective of this collaborative research award is to develop methods that allow engineers to perform stress analysis using their computer aided design (CAD) models without the time consuming mesh generation required by traditional finite element analysis. The research approach combines isogeometric analysis with boundary element technology. Isogeometric analysis uses the same basis functions that are used in the CAD models for engineering analysis. Examples of these basis functions include non-uniform rational B-splines (NURBS) and T-Splines. Traditional numerical methods, such as finite element analysis, use piecewise continuous polynomials of low degree. A mesh generation step is therefore required to convert the CAD representation of the geometry to one that the numerical analysis can use. Using CAD basis functions directly allows us to eliminate this step. The current limitation with CAD basis functions is they only represent surfaces. To sidestep this limitation, we will use boundary element technology, which works directly with surface representations. If successful, the results of this research will allow engineers to rapidly perform structural analyses with their CAD models during the preliminary design process. The high cost of doing detailed analysis during the design phase limits the scope of the design space that engineers are able to explore, and makes truly innovative design expensive. By reducing the time and cost of analysis, design engineers will be able to produce designs that are more optimal in terms of weight, performance, and cost. Automatic design optimization will also be facilitated since the numerical analysis will work directly with the design space parameterized by the CAD models, allowing optimization programs to work with less human intervention and correction.