Realization And Comparison Of Three Kinds Of Numerical Integrator Programs For Multibody System Dynamics Equations

The simulation results of modern large-scale commercial software have been very close to the experimental results and can be applied to many occasions where the tests are impossible or difficult to conduct.With the development of aerospace,aviation,weapons and other national defense industries,as well as the development of civilian industries such as automobiles and ships,and the rise of smart manufacturing industries,the high demand has been constantly proposed by the industrial community to the basic theory and computational capabilities of multi-body system dynamics software.For the analysis of large-scale multi-body systems,the methods for the formation of standardized modeling and equations as well as the common solver integration are the most important.The differential algebraic equations(DAE)for large-scale multi-body systems are established and solved using suitable integrators is a better way to deal with practical applications.The main research contents of this article are as follows:1.For multibody dynamic systems,including rigid bodies model representing a rigid body systems,the flexible pendulum model representing a large deformatable bodies systems,and the two cylindrical collision model representing a contact-impact systems,the equations of motion are modeled separately in each model of its components which coupled with the constraints that connect the various components are extracted to generate the DAE of the multibody system.2.Establish HHT fixed-step and variable-step integrators,generalized ?fixed-step and variable-step integrators and BDF type 1 and type 2 integrators these three types numerical integrators.First,Using single pendulum and double pendulum models Verifies the correctness of the three types numerical integrators,and then numerically solve the above three representative models,and Adams dynamics software is used to establish the dynamic model of the single and double pendulum and the seven bodies and contact-impact.3.Extract the numerical results of three types of integrators in solving models of different types and compare them with the results obtained from the corresponding Adams dynamic model.The comparison between the flexible pendulum and the contact-impact model is based on the BDF type 1 integrator.The efficiency,solution accuracy and stability are comprehensively summarized as the performance of three types of integrators.4.By comparison.It can be concluded that in the multibody dynamic systems,whether the system is smooth or not,the solving efficiency and accuracy of the BDF integrators are much greater than that of the Generalized?and HHT integrators.The performance of the HHT integrators ranks second,but its solution is unstable and the step failure is the highest.The performance of Generalized?integrators in the worst,but the stability of the solution is the best and the step success rate is the highest;for the fixed-step integrators,the solution efficiency depends on the preset number of the steps and the performance is generally inferior to the corresponding variable-step integrator.