Course detail
Nonlinear Mechanics and FEM
FSI-9NMTAcad. year: 2023/2024
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.
Language of instruction
Mode of study
Guarantor
Entry knowledge
Others: basic theory of elasticity, theory and practical knowledge of the FEM.
Rules for evaluation and completion of the course
Active participation in the course is controlled individually according to the progression of the semestral project.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
M.A.Crisfield: Non-linear Finite Element Analysis of Solids and Structures 1-2, Wiley, 1991-97 (EN)
T.Belytschko, T.Liu, K.Moran: Nonlinear Finite Elements for Continua and Structures. J.Wiley, New York, 2000 (EN)
Recommended reading
M.Okrouhlík, editor: Mechanika poddajných těles, numerická matematika a superpočítače. Ústav termomechaniky AV ČR, Praha, 1997
Elearning
Classification of course in study plans
- Programme D-APM-P Doctoral 1 year of study, summer semester, recommended course
- Programme D-IME-P Doctoral 1 year of study, summer semester, recommended course
- Programme D-APM-K Doctoral 1 year of study, summer semester, recommended course
- Programme D-IME-K Doctoral 1 year of study, summer semester, recommended course
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Elearning