# TKT4197 - Nonlinear Finite Element Analysis

### Examination arrangement

Examination arrangement: Home examination

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 4 hours

### Course content

Classification of nonlinearities (geometrical, material and boundary conditions). Strain- and stress measures for large displacements/deformations. Mathematical models for elastic and elastoplastic materials. Geometrical stiffness and linearized buckling. Formulation of the nonlinear finite element method. Numerical integration of dynamically excitated systems. Implicit/explicit time integration. Incremental-iterativ solution methods for nonlinear static and dynamic problems. Modelling of nonlinear boundary conditions. Impact- and contact problems.

### Learning outcome

TKT4197 is a specialization course within the field of study structural engineering at MTBYGG and MTING. The course provides an introduction to the theoretical foundation for nonlinear finite element analysis, as well as skill and understanding of the practical use of computer programs for numerical simulation of nonlinear finite element analysis.

Nonlinear finite element analysis has the following learning objectives:

Knowledge:
The candidate should have knowledge of:
- Description of the nonlinear behavior
- Classification of nonlinearities (geometric, material and boundary conditions)
- Characterization of critical points in the load-displacement diagram
- How to establish and use the total and incremental equilibrium equations
- Incremental-iterative solution methods
- General knowledge of automatic load incrementation and arclength methods
- Material models for elastic and elastic-plastic materials
- Numerical methods for the direct integration of dynamically excited systems
- Modelling and solution methods for nonlinear boundary conditions (contact)
- Stress and strain measures for the description of large strain
- Basic assumptions of linearized buckling.

Skills:
The candidate can:
- Conduct simple deformation and buckling analysis of nonlinear bar and beam systems by hand calculation methods
- Derive incremental stiffness relation for the bar elements based on the expression of potential energy
- Use a general finite element program to model and solve simple nonlinear static and dynamic problems in a qualified manner
.
General knowledge:
The candidate can:
- Nonlinear solution methods
- Numerical methods for direct time integration
- The finite element method for calculating the nonlinear response
- The methodological basis for program-controlled non-linear calculations
- Difference in carrying out linear and nonlinear calculations based on first and second order theory
Linearized buckling - phenomenology and the mathematical description.

### Learning methods and activities

Lectures and homework assignments (including analytical and computer problems). 2/3 of the homework assignments must be approved to take the final exam. The lectures and exercises are in English when students who do not speak Norwegian take the course. If the teaching is given in English the Examination papers will be given in English only. Students are free to choose Norwegian or English for written assessments.

### Compulsory assignments

• Analytical and computer exercises

### Further on evaluation

If there is a re-sit examination, the examination form may be changed from written to oral.

### Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

### Course materials

R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt: Concepts and Application of Finite Element Analysis, 4th ed., Wiley, 2002. Forelesningsnotater.

### Credit reductions

Course code Reduction From To
TKT4516 7.5 01.09.2010
More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2020

No.of lecture hours: 2
Lab hours: 6
No.of specialization hours: 4

Language of instruction: English

Location: Trondheim

Subject area(s)
• Structural Mechanics
Contact information
Course coordinator:

Department of Structural Engineering

Phone:

# Examination

#### Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam
Autumn ORD Home examination 100/100

Release 2020-12-19

Submission 2020-12-19

Release 09:00

Submission 13:00

• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

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