Motion Accuracy Reliability Analysis Of Flexible Multibody System Based On Improved Domain Decomposition Method

At present,there are two main methods to deal with the flexible deformation in the study of the reliability of the kinematic accuracy of mechanisms considering the elastic deformation:the kinematic-elastic dynamic method and the hybrid coordinate method.The first method does not consider the coupling effect of flexible deformation and large motion of the system on the dynamic response of the system.The second method is based on the hypothesis of small deformation and small rotation,which leads to the inaccuracy of the model itself.Absolute nodal coordinate method was proposed based on continuum mechanics,and it can more accurately describe the system dynamics of large deformation and large rotation.In this paper,based on the absolute nodal coordinate method,the dynamic equation of large deformation flexible multibody system is established,and the augmented Lagrangian multiplier method is used to solve the differential-algebraic equations.In order to improve the efficiency of dynamic analysis,an improved domain decomposition method is proposed.Finally,based on the above research,the kinematic accuracy reliability analysis of large deformation flexible multibody system is carried out.The main research contents can be summarized as follows.(1)The geometric description of beam element and plate element based on the absolute node coordinate method is introduced.The mass matrix,generalized external force matrix,elastic force matrix and Jacobian matrix of the element are derived.The dynamic equations of the system are obtained by the above parts.(2)The augmented Lagrangian multiplier method is applied to solve the differential algebraic equations of flexible multibody system based on the absolute node coordinate formulation,and the mass orthogonal projection is used to correct velocity and acceleration.The dynamic problems of beam pendulum and plate pendulum are simulated based on MATLAB and the validity of augmented Lagrangian multiplier method is verified.In addition,the correctness of the finite element description for rigid system,small deformation system and large deformation system is also verified.(3)Based on the finite element tearing and interconnecting methods,an improved domain decomposition method is proposed to solve the dynamic problems in parallel.Based on the C++,the parallel strategy is implemented on the OpenMP.The accuracy and validity of the parallel strategy are verified by numerical examples,and the parallel performance of the algorithm is studied..(4)Based on the research of modeling and solving methods of flexible multi-body system,the dynamic characteristics of the slider crank system composed of the flexible rectangular plate and the slider are analyzed.The reliability of the dynamic displacement accuracy of the slider crank mechanism is analyzed by Monte Carlo method based on the first crossing theory.