This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation the...This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.展开更多
To accommodate the gait and balance disorder of the elderly with age progression and the occurrence of various senile diseases,this paper proposes a novel gait balance training robot(G-Balance)based on a six degree-of...To accommodate the gait and balance disorder of the elderly with age progression and the occurrence of various senile diseases,this paper proposes a novel gait balance training robot(G-Balance)based on a six degree-of-freedom parallel platform.Using the platform movement and IMU wearable sensors,two training modes,i.e.,active and passive,are developed to achieve vestibular stimulation.Virtual reality technology is applied to achieve visual stimulation.In the active training mode,the elderly actively exercises to control the posture change of the platform and the switching of the virtual scene.In the passive training mode,the platform movement is combined with the virtual scene to simulate bumpy environments,such as earthquakes,to enhance the human anti-interference ability.To achieve a smooth switching of the scene,continuous speed and acceleration of the platform motion are required in some scenarios,in which a trajectory planning algorithm is applied.This paper describes the application of the trajectory planning algorithm in the balance training mode and the optimization of jerk(differential of acceleration)based on cubic spline planning,which can reduce impact on the joint and enhance stability.展开更多
文摘This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.
基金Supported by National Key R&D Program of China(Grant No.2019YFB1311404)。
文摘To accommodate the gait and balance disorder of the elderly with age progression and the occurrence of various senile diseases,this paper proposes a novel gait balance training robot(G-Balance)based on a six degree-of-freedom parallel platform.Using the platform movement and IMU wearable sensors,two training modes,i.e.,active and passive,are developed to achieve vestibular stimulation.Virtual reality technology is applied to achieve visual stimulation.In the active training mode,the elderly actively exercises to control the posture change of the platform and the switching of the virtual scene.In the passive training mode,the platform movement is combined with the virtual scene to simulate bumpy environments,such as earthquakes,to enhance the human anti-interference ability.To achieve a smooth switching of the scene,continuous speed and acceleration of the platform motion are required in some scenarios,in which a trajectory planning algorithm is applied.This paper describes the application of the trajectory planning algorithm in the balance training mode and the optimization of jerk(differential of acceleration)based on cubic spline planning,which can reduce impact on the joint and enhance stability.
