Numerical modeling of elliptical cylindrical shells, containing flowing fluid

Abstract

The paper presents a finite-element algorithm for investigation of the dynamic behavior of elastic shells with arbitrary cross sections containing a flowing fluid. A curvilinear surface of the structure is approximated by a set of plane elements, which are subjected to both membrane and bending forces. Description of the shell motion is based on the variable principle of virtual displacements, which includes the linearized Bernoulli equation for calculation of hydrodynamic pressure. A compressible non-viscous fluid is considered in the framework of the potential theory, the equations of which are transformed with the use of the Bubnov-Galerkin method. The performance of the algorithm is demonstrated by the example of two shells with a circular and elliptical cross section. Numerical simulation have been carried out to analyze the influence of the ratio of the ellipse semi-axes, the linear dimensions of the structure and the level of shell filling on the hydrodynamic stability of the connected "shell-fluid" system.