Efficient computation of wave propagation along axisymmetric pipes under non-axisymmetric loading

This paper presents an efficient formulation of the problem of wave propagation along the length of axisymmetric pipes under non-axisymmetric loading such as leaks or new cracks so that wave characteristics in a pipe can be identified without the excessive computational time associated with most current 3D modeling techniques. The axisymmetric geometry of the pipe is simplified by reducing the problem to 2D while the non-axisymmetric loading is represented by the summation of Fourier series. Since the pipe stiffness matrix as conventionally formulated represents the greatest single computational load, the strain–displacement matrix is partitioned in such a way that numerical integration components are decoupled from θ (the angular parameter) and n (the number of Fourier terms). A single numerical integration of the strain–displacement matrix is performed and utilized for all the iterations of Fourier terms to represent the non-axisymmetric load. The numerical formulation is conducted using spectral elements, which also reduce computational time since these elements yield a diagonal mass matrix. The computational efficiency of the developed method is compared with conventional finite element tools.