Nonlinear Mechanics and FEM (FSI-9NMT)

Academic year 2020/2021
Supervisor: prof. Ing. Jindřich Petruška, CSc.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
The aim of the course is to provide students with advanced knowledge and experience with the solution of nonlinear problems of solid mechanics, connected with the topic of PhD dissertation.
Learning outcomes and competences:
Students learn how to solve basic types of nonlinear behaviour in solid mechanics. They can prepare numerical computational model, solve it using some of the commercial FE systems and make a rational analysis of typical problems connected to the PhD dissertation topic.
Prerequisites:
Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations.
Others: basic theory of elasticity, theory and practical knowledge of the FEM.
Course contents:
The course is a follow-up to basic lectures in solid mechanics, which are traditionally limited to linear problems, and introduces the basic nonlinearities. Material nonlinearity is represented by several models of plastic behaviour, viscoelasticity and hyperelasticity.
Next, contact problems, stability, large displacement and large strain problems are presented. Although some classical solutions to selected nonlinear problems are mentioned (Hertz contact, deformation theory of plasticity),
attention is given to numerical solution. Above all, the relation between stability and convergence of numerical solution and physical interpretation of the analysed problem is thoroughly inspected. In the second part, students work on individual projects under the guidance of tutor.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
Final evaluation is based on the ability of active work with a selected FEM system, which is proved by individual preparation and presentation of a semestral project.
Controlled participation in lessons:
Active participation in the course is controlled individually according to the progression of the semestral project.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 1. Introduction to numerical solution of nonlinear problems of solid mechanics
2. Material nonlinearity
3. Stability of structures, bifurcation, buckling
4. Large deformation
5. Contact problems
6. Simulation of material damage, ductile fracture, fracture mechanics
7. Explicit solvers, solution stability, mesh-dependent solutions
8.-12. Solution of individual projects, consultations
13. Presentation of individual projects
Literature - fundamental:
1. T.Belytschko, T.Liu, K.Moran: Nonlinear Finite Elements for Continua and Structures. J.Wiley, New York, 2000
2. G.A.Holzapfel: Nonlinear Solid Mechanics, Wiley, 2000
3. M.A.Crisfield: Non-linear Finite Element Analysis of Solids and Structures 1-2, Wiley, 1991-97
Literature - recommended:
1. M.Okrouhlík, editor: Mechanika poddajných těles, numerická matematika a superpočítače. Ústav termomechaniky AV ČR, Praha, 1997
2. C.Höschl_: Kontaktní úlohy a lisované spoje. Dům techniky ČSVTS Praha, 1985
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-IME-P full-time study --- no specialisation -- DrEx 0 Recommended course 3 1 S
D4P-P full-time study D-APM Applied Mathematics -- DrEx 0 Recommended course 3 1 S
D-APM-K combined study --- -- DrEx 0 Recommended course 3 1 S