Advanced Topics in Finite Element Methods

For more information and access to documents and online classes visit the OPAL course.

Coverage

Introduction to continuum mechanics
Kinematics of deformation, kinetics and balance laws.
Finite element method for one-dimensional continua
Derivation of strong form, weak form and FEM discretization and implementation for simple structures.
Finite element method for higher-dimensional continua
Derivation of strong form, weak form and FEM discretization and implementation for simple structures.
Material non-linear finite element analysis
1D and 3D plasticity problems: incremental boundary value problem, finite element equation and Newton-Raphson solution scheme.
Geometrically non-linear finite element analysis
Total- und Update-Lagrange formulation for large deformation mechanical problems: linearisation and numerical solution.
Extension to fully coupled multifield problems
Handling of diverse non-linearities arising from coupled problems

Exam of 120 min.

Prof. Dr.-Ing. habil. Markus Kästner
Zeunerbau Zi. 352
Telefon: +49 (351) 463-37555

Dr.-Ing. Mareddy Ambati
Zeunerbau Room 350
Telefone: +49 (351) 463-34388

Fish, J.; Belytschko, T.: A First Course in Finite Elements. Wiley, 2007.
Belytschko, T.; Liu, W. K.; Moran, B.: Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.
Wriggers, P.: Nichtlineare Finite-Element-Methoden. Springer, 2001.
Cottrell, J.A.; Hughes, T.J.R.; Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, 2009.
Pilkey W.D., Wunderlich W.: Mechanics of Structures, Variational and Computational Methods, CRC Press, 2003.
Lewis R.W., Nithiarasu P., Seetharamu K.N.: Fundamentals of the Finite Element Method for Fluid and Heat Flow, Wiley, 2004.