Research On GPU Parallel Fast Multipole Boundary Element Method In Structural Analysis

Design is the source of product innovation in enterprises and plays a key role in the core competitiveness of manufacturing industry. The innovative design of products not only satisfies the demands of structural shape, but also meets the requirements of structural performance. Nowadays, CAD and finite element method based CAE softwares are used in geometrical modeling and structural performance analysis respectively in most product designs of enterprises, but it takes much time in the pre-processings between CAD models and CAE models such as model conversion, model simplification and mesh generation. Thus pre-processing simplification and CAD/CAE integration are of great importance to the improvement of product design efficiency. In this dissertation, the boundary element method (BEM) and the fast multipole boundary element method (FMBEM) are intensively studied, and a GPU parallel adaptive FMBEM is presented and used in structural performance analysis of products. Such method can simplify the pre-processings and improve the efficiency of product design, which provides an available method for CAD/CAE software integration. The major research works and contributions of this dissertation can be concluded as follows:(1) The BEM for3D elasticity problems has been studied in detail, including the establishment of boundary integral equations, the element integral methods, the treatment of corner problem, the stress computing on boundary surfaces and generalized minimal residual method (GMRES) etc. In order to address the problem that tractions are discontinuous at corners, a BEM with mixed boundary elements related to boundary conditions is proposed and the mixed boundary elements can be automatically generated according to the topological relation of model’s BREP at corners. Comparing with other BEMs with mixed boundary elements, our method distributes non-conforming elements only at the displacement-given corners, which reduces the extra degrees of freedom introduced by the non-conforming elements and the solving scale of structure analysis.(2) The algorithm theory of the FMBEM is studied. Then a construction method of the dual-information adaptive tree containing both node and element information is presented, which can computes the integrals of high-order elements efficiently. Based on this method, the dual-information FMBEM can reduce the BEM’s complexities of both time and space from O(N2) to O(N), and the computational complexity of element integrals is only one third of the FMBEM with the global node method or node patch method. Furthermore, a rigid body movement method for FMBEM is proposed by combining the FMBEM with given boundary conditions, which is used to compute the1/r2singular integrals and the free-term coefficients.(3) For the purpose of improving the efficiency of the moment-to-local (M2L) translation, the new FMBEM based on the exponential-expansion is researched. The results show that such method obtains high accuracy and remarkable acceleration only if the number of expansion terms is large, and increases the memory cost. Therefore, the child-to-parent M2L translation optimization method is studied as an alternative. The examples show that the child-to-parent M2L can accelerate all the expansion terms almost without memory increment, which is more suitable for structural performance analysis.(4) A CUDA based GPU parallel algorithm of the adaptive FMBEM is presented according to the intrinsic parallelism of boundary elements and knots of the adaptive tree, which accelerates moment expansion, moment-to-moment translation, M2L translation, local-to-local translation and near field direct computing in the FMBEM. The experimental examples show that the parallel algorithm not only obviously accelerates the FMBEM but also obtains load balancing for models with different shapes, which effectively improves the efficiency of structural performance analysis of products.Finally, on the basis of above proposed methods, the software technique and system architecture of CAD/CAE integrated product design have been studied. The CAD/CAE integrated prototype system software has been developed using Visual C++by combining with the3D modeling software InterSolid which owns proprietary intellectual property rights. Whereafter,3D engineering examples with different shapes and complexities are analyzed by the software to verify their structures. The results show that the theories and algorithms in this dissertation have advantages of high computing efficiency, large solving scale and strong adaptability, which have promising future in engineering.