Course Details

Finite Element Method

Academic Year 2024/25

NDB016 course is part of 1 study plan

NPC-SIS Winter Semester 1st year

Course Guarantor


Language of instruction



3 credits



Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site


13 weeks, 2 hours/week, elective


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.


13 weeks, 1 hours/week, compulsory


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.