FEM in Engineering Computations II (FSI-RNU-A)

Academic year 2020/2021

Supervisor:	prof. Ing. Jindřich Petruška, CSc.
Supervising institute:	ÚMTMB	all courses guaranted by this institute
Teaching language:	English
Aims of the course unit:
The aim of the course is to provide students with theoretical knowledge and elementary experience with the solution of most frequent types of nonlinear problems of solid mechanics.
Learning outcomes and competences:
Students learn how to classify basic types of nonlinear behaviour in solid mechanics, they will learn their characteristics and classical solutions for some types of problems. They can prepare numerical computational model, solve it using some of the commercial FE systems and make a rational analysis of typical problems with divergence of the iterative process of solution.
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. Next, contact problems, 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 by the FEM. Above all, the relation between stability and convergence of numerical solution and physical interpretation of the analysed problem is thoroughly inspected in seminars.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Requirements for successful passing : - active participation in seminars, - good results in the written test of basic knowledge, - individual preparation and presentation of seminar assignments.
Controlled participation in lessons:
Attendance at practical training is obligatory. The absence (in justified cases) is compensated by additional assignments according to the instructions of the tutor.
Type of course unit:
Lecture	13 × 2 hrs.	optionally
Computer-assisted exercise	13 × 2 hrs.	compulsory
Course curriculum:
Lecture	1. Introduction to nonlinear problems of solid mechanics 2. Incremental theory of plasticity and its implementation in FEM systems, Deformation theory of plasticity 3. Elasto-plastic bending of beams, plastic hinge and plastic collaps 4. Elasto-plastic response to cyclic loading 5. Residual stress 6. Contact problems - classical solution 7. Strategy of contact solution in FEM, characteristics of contact elements 8. Large displacement and strain - alternative formulations of strain tensors 9. Large displacement and strain - continued 10. Engineering vs. natural stress and strain, evaluation of materiál flow curve in natural coordinates 11. Stability of thin-walled structures as a nonlinear problem of mechanics 12. Explicit formulation of FEM in nonlinear problems of mechanics 13. Convergence of numerically solved nonlinear problem

Computer-assisted exercise	1. Convergence of iterative solution of nonlinear problem - numerical demonstrations 2. Plasticity in FEM - solution of selected tasks 3. Plasticity in FEM - solution of selected tasks 4. Start of seminar project 5. Plastic collaps 6. Residual stress 7. Tutorial of seminar project 8. Solution of contact problem by FEM 9. Tutorial of seminar project 10. Solution of large displacement problem by FEM 11. Solution of stability of shell 12. Example of an explicit FEM solver 13. Presentation of seminar projects

Literature - fundamental:
1. G.A.Holzapfel: Nonlinear Solid Mechanics, Wiley, 2000
2. D.R.J.Owen, E.Hinton: Finite Elements in Plasticity, Pineridge Press, 1980
3. K.-J.Bathe: Finite Element Procedures, Prentice Hall, 1996
4. M.A.Crisfield: Non-linear Finite Element Analysis of Solids and Structures 1-2, Wiley, 1991-97
Literature - recommended:
5. M.Okrouhlík, editor: Mechanika poddajných teles, numerická matematika a superpocítace, Ústav termomechaniky AV CR, Praha, 1997
6. C.Höschl: Kontaktní úlohy a lisované spoje, Dum techniky CSVTS Praha, 1985
7. E.Pešina: Základy užité teorie plasticity, SNTL Praha, 1966