The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated wit...The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated with these realizations are also obtained by the contraction method.Further relations among the geometries are revealed.Most geometries fall into pairs.There exists t 1/(ν 2 t) correspondence in each pair.In the viewpoint of differential geometry,there are only 9 geometries,which have right signature and geometrical spatial isotropy.They are 3 relativistic geometries,3 absolute-time geometries,and 3 absolute-space geometries.展开更多
Beam model has been used widely in computer aided engineering for mechanical systems and the simulation results largely depend on the beam model, there are great demand for beam model with high accuracy and efficiency...Beam model has been used widely in computer aided engineering for mechanical systems and the simulation results largely depend on the beam model, there are great demand for beam model with high accuracy and efficiency in simulating the mechanical system with large deformation. In this work, a new model of Timoshenko beam for large deformations is proposed to improve the accuracy and efficiency. Absolute nodal coordinate formulation and geometrically-exact beam formulation, which make the model very suitable to simulate large deformation mechanical system, are first combined in the new beam model, the governing equations are then discrete by finite element methods and numerical difficulties are well solved by applying the shape function strategy. The new beam model is then applied to simulate the mechanical systems with large deformation and the simulations based on the traditional beam model and hexahedron element were also carried out to verify the results. The results show that good precision and efficiency in simulating the mechanical systems with large deformation can be obtained by the new Timoshenko beam model at the same time. The presented new method also serves as a good foundation for other simulation of mechanical systems.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10775140,10975141,10705048,10731080,10975141,11175245 and 11075206)the Fundamental Research Funds for the Central Universities (Grant No. 105116)
文摘The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated with these realizations are also obtained by the contraction method.Further relations among the geometries are revealed.Most geometries fall into pairs.There exists t 1/(ν 2 t) correspondence in each pair.In the viewpoint of differential geometry,there are only 9 geometries,which have right signature and geometrical spatial isotropy.They are 3 relativistic geometries,3 absolute-time geometries,and 3 absolute-space geometries.
基金supported by the National Natural Science Foundation of China(Grant Nos.51605219&51375007)the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20160791&SBK2015022352)+3 种基金the Visiting Scholar Foundation of the State Key Lab of Mechanical Transmission in Chongqing University(Grant Nos.SKLMT-KFKT-2014010&SKLMT-KFKT-201507)the start-up research foundation for new teachers in Nanjing University of Aeronautics and Astronautics(Grant No.1002-YAH16027)the Fundamental Research Funds for the Central Universities(Grant No.NE2016002)the Open Fund Program of the State Key Laboratory of Vehicle Lightweight Design,P.R.China(Grant No.20130303)
文摘Beam model has been used widely in computer aided engineering for mechanical systems and the simulation results largely depend on the beam model, there are great demand for beam model with high accuracy and efficiency in simulating the mechanical system with large deformation. In this work, a new model of Timoshenko beam for large deformations is proposed to improve the accuracy and efficiency. Absolute nodal coordinate formulation and geometrically-exact beam formulation, which make the model very suitable to simulate large deformation mechanical system, are first combined in the new beam model, the governing equations are then discrete by finite element methods and numerical difficulties are well solved by applying the shape function strategy. The new beam model is then applied to simulate the mechanical systems with large deformation and the simulations based on the traditional beam model and hexahedron element were also carried out to verify the results. The results show that good precision and efficiency in simulating the mechanical systems with large deformation can be obtained by the new Timoshenko beam model at the same time. The presented new method also serves as a good foundation for other simulation of mechanical systems.
