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
Academic program information
English
training language
80 000 RUR
participation fee
14 days
course duration
Bachelor course undergraduates
Engineering Master degree undergraduates
To pass the training successfully, B2 level of proficiency in English language is needed. You do not have to submit a language certificate
Mathematical modeling and ordinary differential equation solution
Differential equations and mathematical models. Steps of mathematical modeling
Numerical approximation. Euler Method of order-1 differential equation solution
Refined Euler Method
Runge-Kutta methods
Numerical integration. Newton-Cotes equations. Composite formula of the Trapezoid Method
Function interpolation and approximation. Applications and differences
Finite Element Method
Basics of Finite element method
Unidimensional case of heat transfer
Two-dimensional case of heat transfer
Non-stationary problem of thermal conductivity. Equation system solution
FEM in deformable body dynamics
"Flat" problem of Theory of Elasticity
Academic supervisor: Sergey A. Kholmogorov, PhD, Associate professor of the Structural Strength department E-mail: SAKholmogorov@kai.ru
Apply to the course right now! Shift 3 admission deadline: July, 10