A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2:Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control upon elastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body system variational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and joint modeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,while allowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from a Hill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,an effective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models the muscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated by utilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies, models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone and tendon.

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 1:Model Development

In this paper we develop an elasto-dynamic model of the human arm for use in neuro-muscular control and dynamic interaction studies.The motivation for this work is to present a case for developing and using non-quasistatic models of human musculo-skeletal biomechanics.The model is based on hybrid parameter multiple body system(HPMBS)variational projection principles.In this paper,we present an overview of the HPMBS variational principle applied to the full elasto-dynamic model of the arm.The generality of the model allows one to incorporate muscle effects as either loads transmitted through the tendon at points of origin and insertion or as an effective torque at a joint.Though the technique is suitable for detailed bone and joint modeling,we present in this initial effort only simple geometry with the bones discretized as Rayleigh beams with elongation, while allowing for large deflections.Simulations demonstrate the viability of the mcthod for use in the companion paper and in future studies.

Application of the generalized quasi-complementary energy principle to the fluid-solid coupling problem

The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.

Design and Dynamics Simulation of a Novel Double-Ring-Plate Gear Reducer

A patented double-ring-plate gear reducer was designed and its dynamic performance was simulated. One unique characteristic of this novel drive is that the phase angle difference between two parallelogram mechanisms is a little less than 180 degree and four counterweights on two crankshafts are designed to balance inertia forces and inertia moments of the mechanisms. Its operating principle, advantages, and design issues were discussed. An elasto-dynamics model was presented to acquire its dynamic response by considering the elastic deformations of ring-plates, gears, bearings, etc. The simulation results reveal that compared with housing bearings, planetary bearings work in more severe conditions. The fluctuation of loads on gears and bearings indicates that the main reason for reducer vibration is elastic deformations of the system rather than inertia forces and inertia moments of the mechanisms.

Investigation of power-type variational principles in liquid-filled system

Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.

An artificial neural network based deep collocation method for the solution of transient linear and nonlinear partial differential equations

A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is proposed.The developed method is applied to solve problems governed by the Sine–Gordon equation(SGE),the scalar wave equation and elasto-dynamics.Two methods are studied:one is a space-time formulation and the other is a semi-discrete method based on an implicit Runge–Kutta(RK)time integration.The methodology is implemented using the Tensorflow framework and it is tested on several numerical examples.Based on the results,the relative normalized error was observed to be less than 5%in all cases.

Dynamical cavitation and oscillation of an anisotropic incompressible hyper-elastic sphere

Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of finite elasto-dynamics.An exact differential equation between the radius of the cavity and the applied load is obtained.The curves for the variation of the maximum radius of the cavity with the load and the phase diagrams are obtained by vibration theories and numerical computation.It is shown that there exists a critical value for the applied load.When the applied load is larger than the critical value,a spherical cavity will suddenly form at the center of the sphere.It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillation,and oscillation of the anisotropic sphere is not the same as that of the isotropic sphere.