Mathematical Modeling of Dynamics for Partially Filled Shells of Revolution

TL;DR

This paper develops a new analytical and numerical model to study the dynamic behavior of partially filled shells of revolution, reducing a 3D problem to a 1D integral equation with efficient computation.

Contribution

It introduces a novel mathematical model and discrete scheme based on the method of discrete singularities for analyzing shell dynamics with fluid interaction.

Findings

Good agreement with other methods in benchmarking

Demonstrated convergence of the numerical scheme

Model reduces 3D problem to a 1D integral equation

Abstract

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the elastic displacements and the dynamic liquid pressure is developed. The discrete scheme is based on the method of discrete singularities. A code to perform the numerical analysis is developed. Comprehensive benchmarking of the obtained results against other methods is done and good agreement is observed. The convergence of the proposed numerical method is demonstrated. One of the advantages of this new model is that the initial 3D problem is analytically reduced to a 1D integral equation. Moreover, it can handle the behaviour of the pressure in the vicinity of the nodes explicitly and the computational technique used has a quick convergence requiring a negligible amount of CPU time.