Mathematical Modeling of Dynamics for Partially Filled Shells of Revolution

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 bench-marking 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.