Collaborative Research: Isogeometric Boundary Element Analysis

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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.