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

doc. Ing. Petr Hradil, Ph.D.

Institute

Institute of Structural Mechanics

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

https://www.vut.cz/en/students/courses/detail/295811

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.