Course detail
Nonlinear Mechanics and FEM
FSI-9NMTAcad. year: 2021/2022
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
Learning outcomes of the course unit
Prerequisites
Others: basic theory of elasticity, theory and practical knowledge of the FEM.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
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-IME-P Doctoral 1 year of study, summer semester, recommended course
- Programme D-APM-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