The first part of the course includes an introduction to the basic concepts of mathematical modeling in rigid body mechanics. The basics of the Euler method, its refined modifications and Runge-Kutta methods for the numerical solution of problems with initial conditions are considered. The practical part of the section on the numerical solution of motion problems includes the implementation of the Euler method in the problems of glider flight, the problem of projectile flight, the problem of steady motion of an ekranoplan. The numerical solution of problems by students is built in the MatLab software environment. Some of the lectures are devoted to numerical differentiation and integration of tabulated functions. The issues of approximation and interpolation of functions, the basic concepts of the theory of difference schemes are also considered.

The second part of the course is devoted to the finite element method in the mechanics of a solid deformable body and problems of thermal conductivity. The theoretical foundations of the finite element method are considered, as well as the scope of its application. The students will consider typical one-dimensional and two-dimensional finite elements, and their application to solve static and dynamic deformation problems, as well as thermal conductivity problems. During the course, attention is paid to the basic methods of solving systems of linear algebraic equations of large dimension. More classes are devoted to explicit schemes for solving dynamics problems.

— Sergey A. Kholmogorov,
академический руководитель программы

Sergey Kholmogorov

Structural Strength dept. associate professor, PhD