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Course unit

Limiting behaviours

Last updated: 22/02/2024

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Course Director(s):

KLOCKER Helmut

General Description:

The unit includes two class courses. The first deals with structural dimensioning under dynamic stress loads (seismic). The second focuses on fracture mechanics.

Key words:

Structure Dynamics Fracture Mechanical engineering

Number of teaching hours

40

Fields of study

Mechanical Engineering

Teaching language

French

Intended learning outcomes

On completion of the unit, the student will be capable of: Classification level Priority
Understanding Structural vibration 3. Apply null
Understanding structural fracture modes under dynamic stress loads 2. Understand
Applying the mechanics of linear fracture 3. Apply
Understanding the mechanics of non-linear fracture 2. Understand
Calculating effects of cyclic loading 3. Apply

Learning assessment methods

Percentage ratio of individual assessment Percentage ratio of group assessment
Written exam: 60 % Project submission: 40 %
Individual oral exam: 0 % Group presentation: 0 %
Individual presentation: 0 % Group practical exercise: 0 %
Individual practical exercise: 0 % Group report: 0 %
Individual report: 0 %
Other(s): 0 %

Programme and content

Type of teaching activity Content, sequencing and organisation
Flipped Class

Structural dynamics

Students will be led to reflect on the impact of dynamic phenomena on structural dimensioning. The common thread of the course is the concrete case study of actual seismic response of civil engineering structures. Students will implement regulations, acting as a design study engineer, while establishing the links with theoretical aspects. They will also be taught to use finite element software programmes to simulate the dynamic response of model structures.

  1. Dynamics of rigid structures
    1. Fundamental principles of dynamics
    2. Energy theorems
  2. Elementary oscillator
    1. Dynamic response and resonance
    2. Ordinary loading
    3. Application to seismic problems
  3. Vibration of discrete structures
    1. Notions of natural modes of vibration
    2. Resolution methods
    3. Application to seismic problems
  4. Vibration of continuous structures
    1. Continuum dynamic balance
    2. Beam vibration
    3. Resolution methods using finite elements
Flipped Class

Fracture mechanics

Fracture mechanics is a basic tool for engineers in materials science and mechanical engineering. Following a presentation of the fundamental concepts and principle mechanisms of fracture, a detailed presentation will be given of linear fracture mechanics. The mechanics of non-linear fracture will be studied through the integral concept. Materials fatigue will be introduced in a heuristic manner. The course is based on theoretical sessions, supervised studies and practical courses.

Chapter I : Introduction

Chapter II : Linear elastic fracture mechanics

I.    Stress concentration

II.   Griffith criterion

III. Strain energy release rate

IV. R curves and instability

V.   Stress analysis: stress intensity factor

VI.  Relation between G and K

VII. Crack tip plastic zone

Chapitre III : Elastic plastic fracture mechanics

I. Crack opening displacement (CTOD)

II. J-integral

Chapitre IV : Various fatigue notions

I. Cyclic loading: Wöhler curves

II. Empirical law of crack propagation