An isogeometric boundary element reanalysis framework based on proper generalized decomposition

Abstract

The aim of this work is to provide a promising way to accelerate the structure design procedure and overcome heavy burden from meshing. The Isogeometric Analysis (IGA) appears in recent years and soon grows up as a powerful means to eliminate gaps between Computer Aided Design (CAD) and Computer Aided Engineering (CAE), due to the abilities of both complicated geometry description in CAD software and unknown field approximation in numerical simulations. The Boundary Element Method (BEM) with IGA is a better seamless integration since the same boundary representation. Relying on this benefit, the model could be recomputed without extra mesh construction, meanwhile, this study introduces the model reduction technique to narrow the reanalysis scale and enhance efficiency. The NURBS surface are used to construct the model geometry and calculation element. The problem is treated as a state evolution process, it is proceed by approximating the problem solution using the most appropriate set of approximation basis, which depend on the Proper Generalized Decomposition (PGD). The IGABEM calculation combined the reduction model strategy is proposed in this paper which allow to accurate and fast resolution of IGABEM problems. Moreover, the CPU time is drastically reduced, the numerical example treated, proves the potentiality of this numerical technique. This provides a proper condition that structure optimization bases on.