According to the corresponding relations between general forces and general displacements, the balancing and geometrical equations of elasticity are multiplied by the corresponding virtual quantities, integrated with ...According to the corresponding relations between general forces and general displacements, the balancing and geometrical equations of elasticity are multiplied by the corresponding virtual quantities, integrated with volume and area, and then added algebraically. Proceeding to the next step, by substituting constitutive relation and considering that body force and surface force are both fellow forces, the generalized quasi-variational principles with the two kinds of variables of the first type are established in non-conservative systems. Through substituting another constitutive relation, using similar methods as above, the generalized quasi-variational principles with the two kinds of variables of the second type are established in non-conservative systems. By using the generalized quasi-complementary energy principles with the two kinds of variables of the first type, a method for solving two kinds of variables (internal force and deformation) is given for non-conservative systems of the typical fellow forces.展开更多
The reasons for studying single flexible body dynamics are that on one hand,it is the basis of flexible multi-body dynamics.If the theory of the single flexible body dynamics has been deeply studied,the theory of flex...The reasons for studying single flexible body dynamics are that on one hand,it is the basis of flexible multi-body dynamics.If the theory of the single flexible body dynamics has been deeply studied,the theory of flexible multi-body dynamics will be researched easily.On the other hand,it has its unique and important applications.Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics.Taking the interceptor as an example,this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics.Taking the launch of rocket as an example,it has illustrated the features of"one force for two effects"in a single flexible body dynamics.With an example of the extending flexible beam coupled with the spacecraft attitude,it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics.Finally,a number of related problems are discussed.展开更多
In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is bri...In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products.Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved.The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established.The applicability and validity of the proposed method are demonstrated by three engineering examples.The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step.展开更多
A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An add...A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.展开更多
基金partly financially supported by the National Natural Science Foundation of China(Grant No.10272034)the Natural Science Foundation of Harbin(Grant No.HEUF04003).
文摘According to the corresponding relations between general forces and general displacements, the balancing and geometrical equations of elasticity are multiplied by the corresponding virtual quantities, integrated with volume and area, and then added algebraically. Proceeding to the next step, by substituting constitutive relation and considering that body force and surface force are both fellow forces, the generalized quasi-variational principles with the two kinds of variables of the first type are established in non-conservative systems. Through substituting another constitutive relation, using similar methods as above, the generalized quasi-variational principles with the two kinds of variables of the second type are established in non-conservative systems. By using the generalized quasi-complementary energy principles with the two kinds of variables of the first type, a method for solving two kinds of variables (internal force and deformation) is given for non-conservative systems of the typical fellow forces.
基金Supported by the National Natural Science Foundation of China(Grant No.10272034)the Doctoral Education Foundation(Grant No.20060217020)the Natural Science Foundation of Harbin Engineering University(Grant No.HEUF04003)
文摘The reasons for studying single flexible body dynamics are that on one hand,it is the basis of flexible multi-body dynamics.If the theory of the single flexible body dynamics has been deeply studied,the theory of flexible multi-body dynamics will be researched easily.On the other hand,it has its unique and important applications.Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics.Taking the interceptor as an example,this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics.Taking the launch of rocket as an example,it has illustrated the features of"one force for two effects"in a single flexible body dynamics.With an example of the extending flexible beam coupled with the spacecraft attitude,it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics.Finally,a number of related problems are discussed.
基金This work was supported by the National Nature Science Foundation of China(Grant 11772026)Defense Industrial Technology Development Program(Grants JCKY2017208B001 and JCKY2018601B001)Beijing Municipal Science and Technology Commission via project(Grant Z191100004619006),and Beijing Advanced Discipline Center for Unmanned Aircraft System.
文摘In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products.Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved.The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established.The applicability and validity of the proposed method are demonstrated by three engineering examples.The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step.
文摘A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.
