Nonlinear analysis of structures
Summary
This course provides an introduction to the nonlinear modelling of civil engineering structures.
Content
The course is based on assignments in which students either implement the nonlinear analysis from scratch (for models with truss elements) or use an open-source software (for models with beam elements). The topics that are covered are the following:
- Truss models: Hand calculations and finite element calculations of truss models with material and geometric nonlinearity;
- Nonlinear material laws: Plasticity, Continuum Damage Mechanics, Smeared Crack Models
- Beam element formulations: Total and incremental compatibility and equilibrium relations of beams, accounting for large displacements. Differential equations for Euler-Bernoulli and Timoshenko beams. Sectional analysis of RC sections. Beam formulations with concentrated and distributed plasticity approaches (force-based and displacement-based).
- Nonlinear analyses: Solution methods for nonlinear static and dynamic analysis. Damping models.
- Review of past blind prediction tests and comparison between numerical and experimental results.
- Use of nonlinear simulations in civil engineering practice.
Keywords
Nonlinear analysis, beam-column elements, seismic assessment, geometric nonlinearities, material nonlinearities
Learning Prerequisites
Required courses
CIVIL-321 Numerical modelling of solids and structures (or similar)
Courses on structural mechanics
Learning Outcomes
By the end of the course, the student must be able to:
- Implement nonlinear finite element approaches for truss elements
- Assess / Evaluate the consequences of modelling hypotheses on analysis results
- Choose appropriate finite element formulations for nonlinear structural analysis problems
- Develop models that represent the essentials of the nonlinear response of structures
Transversal skills
- Plan and carry out activities in a way which makes optimal use of available time and other resources.
- Set objectives and design an action plan to reach those objectives.
- Use a work methodology appropriate to the task.
- Communicate effectively with professionals from other disciplines.
- Access and evaluate appropriate sources of information.
- Use both general and domain specific IT resources and tools
- Communicate effectively, being understood, including across different languages and cultures.
- Identify the different roles that are involved in well-functioning teams and assume different roles, including leadership roles.
Teaching methods
Lectures, exercices
Expected student activities
Solution of assignments, active participation in case studies (in-class exercices)
Assessment methods
Assignments
Project during the semester
Final exam
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
Resources
Ressources en bibliothèque
Moodle Link
Prerequisite for
Master projects in seismic engineering, assessment of existing structures
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Nonlinear analysis of structures
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Nonlinear analysis of structures
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Nonlinear analysis of structures
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Nonlinear analysis of structures
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Nonlinear analysis of structures
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional