Lectures:
1. Introductory lecture, the basic idea of the finite element method, history of
method, possibilities of application of the method in engineering problems.
2. Matrix algebra, types of matrices, methods for solving systems of linear algebraic equations, conditions for their solvability.
3. Differential operators, the basic equations of the theory of elasticity and strength.
4. Energy principles, principle of virtual work, Lagrange principle
Galerkin method, Ritz method.
5. Discretization of analyzed area, the principle of discretization, finite element types (Linear, planar and spatial).
6. Function approximation for a particular type of finite element, basis functions,
stiffness matrix and its properties.
7. One-dimensional role - beam variant of FEM.
8. Two-dimensional problem, the basic equations and relations.
9. Finite elements in spatial tasks.
10. The finite element method in continuum mechanics.
11. Geotechnical software applications of finite element method.
12. Program system PLAXIS (characteristic preeprocesor, postprocessor).
13. Program system TUNNEL 3D modeling spatial problems by
finite elements.
14. The possibilities of combination the finite element method and method of boundary integrals.
Exercise:
1. Home exercise - introduction to training programs and organizations.
2. Flexible plate deflection equations.
3. Solving boundary value problems using Ritz variational method.
4. One-dimensional finite element task.
5. Static solutions of arc lining using REVYZ.
6. Program system FEAT - creating a model, input data, evaluation of results.
7. Static solutions of the support construction using FEAT.
8. Interpolation of the solution of plane triangle task, setting the base
function.
9. Functional of potential energy.
10. Slope stability solution using the program system PLAXIS.
11. Modeling of the stability of underground workings using PLAXIS software system.
12. Utilization of the software PHASES for modeling of geotechnical problems.
13. Spatial modeling of the stability of the tunnel using the program system TUNNEL 3D.
14. Monitoring and evaluation of programs and credits.
Tasks:
1. Determination of stress-strain and stability state of the slope using FEM
2. Static and stability design of tunnel supports using finite
elements.
1. Introductory lecture, the basic idea of the finite element method, history of
method, possibilities of application of the method in engineering problems.
2. Matrix algebra, types of matrices, methods for solving systems of linear algebraic equations, conditions for their solvability.
3. Differential operators, the basic equations of the theory of elasticity and strength.
4. Energy principles, principle of virtual work, Lagrange principle
Galerkin method, Ritz method.
5. Discretization of analyzed area, the principle of discretization, finite element types (Linear, planar and spatial).
6. Function approximation for a particular type of finite element, basis functions,
stiffness matrix and its properties.
7. One-dimensional role - beam variant of FEM.
8. Two-dimensional problem, the basic equations and relations.
9. Finite elements in spatial tasks.
10. The finite element method in continuum mechanics.
11. Geotechnical software applications of finite element method.
12. Program system PLAXIS (characteristic preeprocesor, postprocessor).
13. Program system TUNNEL 3D modeling spatial problems by
finite elements.
14. The possibilities of combination the finite element method and method of boundary integrals.
Exercise:
1. Home exercise - introduction to training programs and organizations.
2. Flexible plate deflection equations.
3. Solving boundary value problems using Ritz variational method.
4. One-dimensional finite element task.
5. Static solutions of arc lining using REVYZ.
6. Program system FEAT - creating a model, input data, evaluation of results.
7. Static solutions of the support construction using FEAT.
8. Interpolation of the solution of plane triangle task, setting the base
function.
9. Functional of potential energy.
10. Slope stability solution using the program system PLAXIS.
11. Modeling of the stability of underground workings using PLAXIS software system.
12. Utilization of the software PHASES for modeling of geotechnical problems.
13. Spatial modeling of the stability of the tunnel using the program system TUNNEL 3D.
14. Monitoring and evaluation of programs and credits.
Tasks:
1. Determination of stress-strain and stability state of the slope using FEM
2. Static and stability design of tunnel supports using finite
elements.