NONLINEAR PROCEDURES IN FINITE ELEMENT ANALYSIS

CE524

Course Code: CE524
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Master's Degree With Thesis

Year of Study

Semester

ECTS

Name of Lecturer(s)

Learning Outcomes

At the end of this course, the students;

Formulate nonlinear finite element equations based on the principles of continuum mechanics,
Simulate material and geometric nonlinear behaviors using appropriate constitutive models,
Resolve convergence issues in complex problems and select appropriate iterative solution methods,
Analyze the nonlinear response of realistic structural systems using advanced finite element software.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Materially and geometrically nonlinear problems in engineering, incremental equations of motion for nonlinear problems in solid mechanics, general procedures for the solution of nonlinear equations of discrete problems, microstructural basis for material nonlinearities, rheological models for basic modes of material behavior, instantaneous plasticity and numeric procedures for instantaneous plastic material behavior, viscoplasticity and creep, numerical procedures for viscoplastic analysis.

Course Contents

WEEK	TOPICS
1^st Week	Introduction: Foundations of nonlinear analysis and departure from linear assumptions.
2^nd Week	Continuum Mechanics: Stress and strain measures (Piola-Kirchhoff stresses, Green-Lagrange strains).
3^rd Week	Lagrangian Formulations I: Total Lagrangian (TL) approach and its derivation.
4^th Week	Lagrangian Formulations II: Updated Lagrangian (UL) approach and frame of reference.
5^th Week	Material Nonlinearity I: Hyperelasticity and rubber-like material models.
6^th Week	Material Nonlinearity II: Theory of plasticity, yield criteria, and hardening laws.
7^th Week	Geometric Nonlinearity: Large displacements, large strains, and finite rotations.
8^th Week	Midterm
9^th Week	Numerical Solution Strategies I: Newton-Raphson and Modified Newton-Raphson methods.
10^th Week	Numerical Solution Strategies II: Arc-length methods, load control, and displacement control schemes.
11^th Week	Convergence & Stability: Convergence tolerances, error analysis, and energy balance.
12^th Week	Boundary Nonlinearity: Contact mechanics, friction models, and penalty vs. Lagrange multipliers.
13^th Week	Nonlinear Dynamic Analysis: Stability of time integration schemes in nonlinear regimes.
14^th Week	Computational Implementation: Advanced modeling using FEA software (e.g., ABAQUS, ANSYS, OpenSees).
15^th Week	Case Studies: Post-buckling analysis (Snap-through/Snap-back) and failure modeling.

Recommended or Required Reading

1. Finite Element Procedures, Bathe K. J., Prentice Hall, 1996.
2. Concepts and Applications of Finite Element Analysis, Cook R. D., Plesha M. E., Malkus D. S., John Wiley & Sons, 1989.
3. Methods of Analysis for Earthquake Resistant Structures, Earthquake Engineering from Engineering Seismology to Performance-Baseed Engineering, Flippou F. C., Fenves G. L., CRC Press.
4. Computational Inelasticity, Simo J. C., Hughes T. J. R., Springer.

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers
Presentation

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	30
Assignment	1	10
Quiz	1	20
Total(%)		60
Contribution of In-term Studies to Overall Grade(%)		60
Contribution of Final Examination to Overall Grade(%)		40
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz	1	50	50
Individual or group work	14	3	42
Preparation for Final exam	1	80	80
Course hours	14	3	42
Preparation for Midterm exam	1	60	60
Laboratory (including preparation)
Final exam	1	2	2
Homework	1	20	20
Quiz	1	2	2
Total Work Load			300
Total Work Load / 30 (h)			10
ECTS Credit of the Course			10

Language of Instruction

English

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4
K1	X	X	X
K2
K3	X		X	X
K4	X	X	X	X
K5
K6
K7
K8
K9
K10
K11				X