Research On The Stability Of Numerical Algorithms For Multi-body Dynamics Differential-algebraic Equations

With the rapid development of national economy and national defense construction,the requirements for dynamic performance of some mechanical system products are improving,therefore,it is necessary to analyze and predict the dynamic characteristics of large and complex mechanical systems accurately and rapidly,and design more efficient and stable numerical algorithm to satisfy the numerical simulation requirements of system dynamics.The A-stable and L-stable method over time intervals for differential-algebraic equations of multibody system dynamics is presented in this paper.The solution format is established based on equidistant nodes and non-equidistant nodes such as Chebyshev nodes and Legendre nodes.Based on Ehle's theorem and conjecture,the unknown matrix and vector in the A-stable and L-stable solution formula are obtained by comparing with Pade approximation.The format is further extended to obtain undetermined matrices and vectors of any node.Newton iteration method is used during the solution process.Taking the planar two-link manipulator system as an example,the differential-algebraic equations of each index are obtained,the results of L-stable method based on equidistant nodes are compared for different number of nodes in the time interval and the step size in the simulation,and also compared with the classic Runge-Kutta method,A-stable method based on non-equidistant nodes,Gauss method of B-stable,Radau IA,Radau IIA and Lobatto IIIC methods of L-stable.At the same time,the constructed A-stable method based on equidistant nodes is compared with the Lobatto IIIA and Lobatto IIIB methods of A-stable,and the experimental results are tested and analyzed for the accuracy.The results show that the A-stable and L-stable methods have the advantages of good stability and high precision,and can guarantee the constraints under long-time simulation,and is suitable for multibody system dynamics simulation under long-term conditions.Taking the new structure of negative Poisson ratio concave model as an example,this structure is analyzed and a mathematical model is established to obtain the differential-algebraic equation.The constructed L-stable method is used for numerical simulation,and compared with Runge-kutta method and discrete variational method.The results can satisfy the constraints better and solve the breach of contract of more complex models well.