Dynamic Modeling And Analysis Of The Compliant Bistable Mechanism Based On Absolute Node Coordinate Formulation

Compared with the traditional bistable mechanism,the compliant bistable mechanism has a wide range of applications in aerospace manufacturing,fine processing and measurement,and robot design due to its energy storage characteristics.At present,the modeling of statics and kinematics of compliant bistable mechanisms is relatively mature,meanwhile the corresponding commercial software also has relatively high calculation accuracy,but there are still various problems and limitations for the dynamic modeling of compliant bistable mechanisms.For example,it is difficult to quantify the effect of mechanism deformation on kinetic energy calculation.Therefore,the research on the dynamics of the compliant bistable mechanism will bring high value to the practical engineering application.This thesis uses the Absolute Nodal Coordinate Formulation as the basic modeling method to model and analyze the dynamic characteristics of the compliant bistable mechanism in magnetic field.The work is mainly as follows:(1)According to the theory of the Absolute Nodal Coordinate Formulation,a one-dimensional two-node beam element model is derived,including the element mass matrix,external force matrix and stiffness matrix of the model,from what the dynamic equations are obtained.Based on one-dimensional two-node beam element model,the dynamic model of the flexible pendulum is established,and the free swing process under gravity is numerically simulated,the results are compared with the ANSYS simulation results to verify the accuracy of the model.(2)A compliant bistable mechanism considering the magnetic field is proposed,and it is modeled using the Absolute Nodal Coordinate Formulation:According to the one-dimensional two-node beam element model,the two-dimensional two-node beam element model and the three-dimensional two-node beam element model based on the Absolute Nodal Coordinate Formulation are derived,and the element mass matrix,stiffness matrix,external force matrix of the three-dimensional two-node beam element are obtained,meanwhile the dynamic equations of the element are established;According connect all the nodes in series to establish the dynamic equation of a single beam,complete the modeling and solution of the dynamic equation of the bistable system.By simulating the swing process of the large-deformation flexible pendulum and the small-deformation flexible pendulum,the calculation results are mutually corroborated with the ANSYS simulation results,which shows the accuracy of Absolute Node Coordinate Formulation when dealing with large-deformation flexible beams.(3)Complete the kinematics and dynamics analysis of the compliant bistable mechanism in the magnetic field:Including dynamic stress analysis,bistable characteristic analysis,and also calculated the natural frequency.At the same time,the geometric parameters of the compliant rod and the external force frequency are optimized by using the minimum second steady-state position potential energy,maximum power,and maximum efficiency as the objective functions,some results are compared with ANSYS simulation results and experimental results,verify the accuracy and simplicity of the model(4)Aiming at Poisson locking phenomenon in the modeling and calculation process,a two-dimensional high-order interpolation beam element model is proposed.And the numerical solution algorithm based on generalized-is used for calculation.The calculation of the cantilever beam shows that the model can indeed alleviate the problem of Poisson locking when the Poisson ratio is not zero.