Course Details
Finite Element Method
Academic Year 2025/26
NDB016 course is part of 1 study plan
NPC-SIS Winter Semester 1st year
Course Guarantor
Institute
Language of instruction
Czech
Credits
3 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
- 1. Introduction to the Finite Element Method (FEM) of solids and structures. Mathematical models and FEM. Detail of models. The basic assumptions for solving problems of mechanics of structures.
- 2. Solution of beam structures. Linear 3D mathematical models. Deformation. Stress. Constitutive equations. Formulation of linear / non-linear tasks.
- 3. Mathematical models of structures for solving engineering problems (2D beam models, bent plates, shells, tasks of heat flow, other force fields). The principle of virtual work.
- 4. Procedure FEM. Formulation of 1D and 2D tasks. Discretization. Equilibrium equation.
- 5. Isoparametric elements. Basic considerations. Stiffness matrix and load vector of 1D and 2D element. Numerical integration to calculate the stiffness matrix and load vectors.
- 6. The finite elements (FE) for beams, plates and shells.
- 7. FEM modelling of structures. The combination of elements. Boundary conditions. Rigid connections. Spring. Singularity.
- 8. Generation of FE mesh. Check-shaped elements and softness meshes. The accuracy of the solution.
- 9. Potential solutions of nonlinear problems via FEM. Geometric, material nonlinearity and contact.
- 10. Identification of a critical load, the collapse of the structure. Matrix notation of stability task in FEM and its solution.
- 11. Software for solving FEM. Pre-processor, solver and post processors.
- 12. Solving problems with stress concentrators.
- 13. Introduction to Extended Finite Element Method.
Exercise
13 weeks, 1 hours/week, compulsory
Syllabus
- 1. Solving simple discrete problems of elasticity.
- 2. Analysis of the derivation of the element stiffness matrix for plane stress. Calculating deformations of simple wall.
- 3. Calculation of the matrix of elasticity constants of the different types of elements.
- 4. Analysis algorithm assembly stiffness matrix and load vector of the different types of elements. Approximate functions for various types of elements.
- 5. Stating stiffness matrix of isoparametric element.
- 6. Numerical integration – application examples. Entering the boundary conditions. Singularity and stress concentration.
- 7. Derivation of finite element of plates and shells.
- 8. Modelling of simple tasks of FEM. The combination of elements. Boundary conditions. Rigid connections. Spring. Joining elements.
- 9. Application software for solving stability – model creation.
- 10. Calculation of critical load and analysis of the results.
- 11. Analysis of modelling structures process. Definition of input data and selection of types of finite elements.
- 12. Analysis of results of the FEM solution of the selected model.
- 13. Stress concentrators. Credit.