On the formulation of a pipe element II: An orthogonal polynomial pipe element

摘要

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.