Double Numerical Integration Method And Its Application In Absolute Application Research Of Node Coordinate Beam Element

In recent decades,the absolute nodal coordinate method has attracted the attention of many experts and scholars at home and abroad.Compared with the traditional modeling method,the absolute nodal coordinate method has higher accuracy in dealing with large scale motion and large deformation problems.Therefore,the absolute nodal coordinate method in flexible multibody system dynamics in more and more applications,on the absolute nodal coordinate method paper also increased year by year,but most of these papers is the research unit model and the elastic force of the unit description,few people study for the Dan Yuanmo type of computational efficiency and accuracy of the problem.To solve the finite element model is built up based on the absolute nodal coordinate method,the key lies in solving the model of internal force and stiffness matrix,because the absolute displacement accuracy of the node depends entirely on the stiffness matrix and force matrix precision,so research on new numerical integration method for solving the stiffness matrix and force matrix is a very meaningful work.Based on the tradit ional mechanical quadrature method and Gauss Legendre integral method,puts forward two new numerical integration method,and examples show that the proposed method in the numerical integration method in computational efficiency and accuracy are better tha n the traditional,the details are as follows:(1)general survey on the development of multi body system dynamics and the absolute nodal coordinate method and numerical integral method in dynamics of flexible multibody system in detail,and introduces the related knowledge of continuum mechanics and the absolute nodal coordinate method,and the process of modeling the absolute nodal coordinate based on beam element is derived in detail.(2)by studying the traditional mechanical quadrature method and the Gauss Legendre integral method,we have designed two new numerical integration methods: the new numerical integration method based on the first derivative and the composite Gauss Legendre integral method.The mechanical quadrature method is different from t he traditional model,numerical quadrature method based on derivative attribute evaluation problem for the calculation of integral integrand function values and the first derivative of the original function,can avoid solving the integrand;the number of nodes of Gauss Legendre integral method could be used to obtain results with higher accuracy,is a very commonly used numerical methods,but when the integral interval is large,the accuracy of Gauss quadrature Legendre integral method is not ideal,in order to solve this problem,this paper re processing of the Gauss Legendre integral method,derived composite Gauss Legendre integral method,this method can avoid the Gauss Legendre integral method for integral interval becomes larger and the defects of quadrature accuracy.(3)using displacement mode displacement mode and Kerkkanen O mar and Shabana is proposed for modeling examples,and then uses two new numerical integral method constructed in this paper to solve the problem,and the calculated results were compared with the Gauss Legendre integral method is obtained by comparing the results,the results show that the proposed methods in computing efficiency and accuracy are better than the Gauss Legendre integral method.