LAUSR

Abstract Based on the previous work of the variable wall thickness pipe element Li (2016) , an orthogonal polynomial pipe element is developed in this paper. The orthogonal polynomial theory is applied in the displacement basis functions. By choosing some particular orthogonal polynomials as the basis function, the element mass matrix and total mass matrix are both tri-diagonal matrix, which is meaningful for the explicit dynamical analysis. This paper presents a systematical method of how to design the basis functions. Given the pipe configuration and boundary conditions, a unique basis function can be obtained to generate a tri-diagonal mass matrix accurately. The values of the non-zero terms of the tri-diagonal mass matrix can be pre-calculated. In order to satisfy the displacement circumferential periodical condition and the contact constraint condition, the Lagrangian multiplier method or MPC (multi-points constraint) is applied. The additional force degree is eliminated in the element level so that the tri-diagonal mass matrix is maintained. Since the orthogonal polynomial is applied, a high-order resolution is obtained. To prove the accuracy of this orthogonal polynomial pipe element, the problems of the pipe dynamical buckling propagation are analyzed. The numerical simulation results are compared with experiment results from other papers.