CIVIL-449 / 6 credits

Teacher(s): Lignos Dimitrios, Saloustros Savvas

Language: English

## 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

## 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

## 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
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 3 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Reference week

Monday, 14h - 16h: Lecture GRA330

Wednesday, 9h - 10h: Lecture GRA332

Wednesday, 10h - 12h: Exercise, TP GRA332

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