Course detail

# Finite Element Method

Mathematical models and FEM, basic assumptions, linear 3D models, constitutive relations, design models for solving engineering problems (planar beam task models, bent plates, shells, tasks of heat flow), process solutions, variant of formulation of FEM, discretization, derivation matrix stiffness of the 2D element, equilibrium equations. Isoparametric elements, numerical integration to calculate the stiffness matrix and load vector elements for solving various problems, generation FE mesh and the influence on the accuracy of the solution, singularity, the possibility of nonlinear problems solving and problems of FEM stability, software based on FEM.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Static analysis of statically determinate and indeterminate planar beam structures with straight and curved centreline; calculation of deformations via unit forces method; force method; influence support relaxation and the influence of temperature changes; theory of strength and failure; stress and strain in point of the solid, the principal stresses.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

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.

Aims

Not applicable.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Classification of course in study plans

• Programme NPC-SIS Master's, 1. year of study, winter semester, 3 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise

13 hours, compulsory

Teacher / Lecturer