Kononenko I. Mathematical modeling of dynamics for partially filled shells of revolution

Object of the research is the dynamic behavior of compound shells of revolution partially filled with liquid. Aim of the research is development of mathematical models to analyze the dynamic behavior of compound shells of revolution partially filled with fluid, and the construction of the relevant discrete mathematical models for numerical experiments. The variational principles, methods of potentials, boundary integral equations, discrete singularities and object-oriented programming are used. A new mathematical model of compound shells of revolution partly filled with an ideal incompressible fluid is built. A method of numerical analysis for movement of a shell without fluid based on a variational principle of elasticity is improved. The methods for determining the fluid pressure are improved. For the first time for this mathematical model the behavior of the solution in the vicinity of the nodes is studied. For the first time a theorem for the limiting value of the double layer potential normal derivative for the integrals with the finite part sense by Hadamard of the functions defined on an open contour is formulated and proved. For the first time the discrete mathematical model of compound shells of revolution with a liquid which is based on the method of discrete singularities is built. The results were used to create computer monitoring technology to operating state volume of chemically active substances in the department of strength and structural optimization at A.N. Podgorny IPMash. The developed mathematical method and software system are used for educational purposes at V.N. Karazin Kharkiv National University.