Real-time Boundary Element Stress Analysis

Abstract

Significant improvements in the efficiency of the mechanical design process can be made through interactive stress analysis, in which re-analysis is performed in real-time on models with continuously updating geometry. Once the initial model has been constructed and solved, and matrix representations stored for re-use, the boundary element (BE) system may be rapidly modified and re-solved if the engineer chooses to apply geometric perturbations to parts of the model. The aim is to provide real-time feedback of stress contours to the engineer as the geometry is dynamically modified. Following a successful demonstration of these techniques in two-dimensions, in this work we focus on accelerating the re-analysis of small problems of three-dimensional elasticity to provide this rapid feedback for solids. Three primary areas need to be considered to accelerate the re-solution of boundary element problems. These are re-meshing the model, updating the boundary element system of equations and re-solution of the system. Geometric changes should be accommodated whilst retaining as much of the existing mesh as possible, thus allowing the majority of the previous system of equations to be re-used for the new analysis. For the small problems under consideration, a reusable intrinsic sample point (RISP) integration scheme is shown to accelerate reconstruction of the system of equations. Significant time savings can be made in the iterative solution by preconditioning the updated system with the LU decomposition of the original system, providing a convergence rate suitable for real-time simulations. Using these techniques, real-time analysis can be achieved for some 3D simulations. It is anticipated that this can have a major impact on the way computational mechanics simulations are used in conceptual design.