A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the c...A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G2 continuous spline approximation of conic section when using the subdivision scheme,and the effectiveness of this method is demonstrated by some numerical examples.展开更多
As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the ...As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics(SPH) method is used to model the compressible fluid, the natural coordinate formulation(NCF) and absolute nodal coordinate formulation(ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit(GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.展开更多
基金Supported by the NSF of China(11101230 and 11371209)
文摘A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G2 continuous spline approximation of conic section when using the subdivision scheme,and the effectiveness of this method is demonstrated by some numerical examples.
基金supported by the 111 China Project(Grant No.B16003)the National Natural Science Foundation of China(Grant Nos.11290151,11702022,and 11221202)
文摘As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics(SPH) method is used to model the compressible fluid, the natural coordinate formulation(NCF) and absolute nodal coordinate formulation(ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit(GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.
