Lehrinhalte
The lecture covers the fundamentals of the finite element methods and its application in
material science. Specifically, the focus is on strong and weak forms of linear elasticity
and heat conduction problems. Finite element formulations as well as its implementation
for linear elasticity and heat conduction problems will be discussed.
1. Review of Basics of tensor calculus, Linear algebra, Continuum mechanics
(kinematics) and Material mechanics (Hooks law)
2.Weak form construction for 1D bar and truss-based FE problem
3.Learning about the Galerkin approach for a general solid and construction of the weak
form for a general PDE
4.Finite element (1): concept of Shape functions and discretised version of the weak form
5. Finite element (2): construction of residual vector and Stiffness matrix
6.Finite element (3): learning about numerical integration and post-processing.
7. Multiphysics problems: focusing on a simple thermo-mechanical problem (Strong form
Weak form)
8.Thermo-mechanical problem (finite element discretization)
9.Discussions towards nonlinear FE (simple plasticity model)
If time permits:
10. Multi-scaling and Machine learning in FE
Literatur
1. T. I. Zohdi and P. Wriggers, An Introduction to Computational Micromechanics.
Springer, 2010.
2.Zienkiewicz OC, Taylor RL, Zhu JZ. The finite element method: its basis and
fundamentals. Elsevier; 2005.
3. Jacob, Fish, and Belytschko Ted. A first course in finite elements. Wiley, 2007.
4.Lecture notes on FE by Prof. Carlos A. Felippa: https://quickfem.com/wpcontent/uploads/
Offizielle Kursbeschreibung
The student will learn about the fundamental concept behind the finite element method
as one of the most promising and wide-used computational schemes at different scales.
In addition, they learn about the mathematical representation of material behavior
within a computational framework. Apart from the theory, they learn how a finite
element code in a simple program works and how they can implement their own coding
for new problems. They should be able to apply their understanding to other governing
equations in different branches and applications of material science. The courses also
prepare them for future and more advance topics in computational material mechanics
and science, such as studies on plasticity and damage progression in solids.
Zusätzliche Informationen
Final Module Examination:
Module Examination: 3 mid quizzes (30%), Final project (70%)
Online-Angebote
moodle
The lecture covers the fundamentals of the finite element methods and its application in
material science. Specifically, the focus is on strong and weak forms of linear elasticity
and heat conduction problems. Finite element formulations as well as its implementation
for linear elasticity and heat conduction problems will be discussed.
1. Review of Basics of tensor calculus, Linear algebra, Continuum mechanics
(kinematics) and Material mechanics (Hooks law)
2.Weak form construction for 1D bar and truss-based FE problem
3.Learning about the Galerkin approach for a general solid and construction of the weak
form for a general PDE
4.Finite element (1): concept of Shape functions and discretised version of the weak form
5. Finite element (2): construction of residual vector and Stiffness matrix
6.Finite element (3): learning about numerical integration and post-processing.
7. Multiphysics problems: focusing on a simple thermo-mechanical problem (Strong form
Weak form)
8.Thermo-mechanical problem (finite element discretization)
9.Discussions towards nonlinear FE (simple plasticity model)
If time permits:
10. Multi-scaling and Machine learning in FE
Literatur
1. T. I. Zohdi and P. Wriggers, An Introduction to Computational Micromechanics.
Springer, 2010.
2.Zienkiewicz OC, Taylor RL, Zhu JZ. The finite element method: its basis and
fundamentals. Elsevier; 2005.
3. Jacob, Fish, and Belytschko Ted. A first course in finite elements. Wiley, 2007.
4.Lecture notes on FE by Prof. Carlos A. Felippa: https://quickfem.com/wpcontent/uploads/
Offizielle Kursbeschreibung
The student will learn about the fundamental concept behind the finite element method
as one of the most promising and wide-used computational schemes at different scales.
In addition, they learn about the mathematical representation of material behavior
within a computational framework. Apart from the theory, they learn how a finite
element code in a simple program works and how they can implement their own coding
for new problems. They should be able to apply their understanding to other governing
equations in different branches and applications of material science. The courses also
prepare them for future and more advance topics in computational material mechanics
and science, such as studies on plasticity and damage progression in solids.
Zusätzliche Informationen
Final Module Examination:
Module Examination: 3 mid quizzes (30%), Final project (70%)
Online-Angebote
moodle
Semester: WT 2022/23