The physical properties of the symmetric and antisymmetric motions,such as the conservation of the ab- solute angular momentum,the mutual conversions between various forms of energy,have been analysed by using the set...The physical properties of the symmetric and antisymmetric motions,such as the conservation of the ab- solute angular momentum,the mutual conversions between various forms of energy,have been analysed by using the sets of equaticns in p-coordinates controlling the motions in the primitive equation model atmosphere.The results show that only the symmetric component of zoral geopotential difference caused by orography and that of the zonal frictional torque,have contribution to the change of the global angular momentum,and that the mutual conversions between various forms of energy,in addition to those similar to the results in the classical case, irclude those associated with the symmetric and antisymmetric motions.展开更多
There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed a...There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.展开更多
文摘The physical properties of the symmetric and antisymmetric motions,such as the conservation of the ab- solute angular momentum,the mutual conversions between various forms of energy,have been analysed by using the sets of equaticns in p-coordinates controlling the motions in the primitive equation model atmosphere.The results show that only the symmetric component of zoral geopotential difference caused by orography and that of the zonal frictional torque,have contribution to the change of the global angular momentum,and that the mutual conversions between various forms of energy,in addition to those similar to the results in the classical case, irclude those associated with the symmetric and antisymmetric motions.
基金This research is supported by the National Basic Research Program of China(973 Program,Grant No.2014CB047100)the National Natural Science Foundation of China(Grant Nos.41472289,51179185 and 41807275).
文摘There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.
