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#### ÉLÉMENTS FINIS

#### FINITE ELEMENT MODELING AND COMPUTATIONS IN THE FIELD OF CIVIL ENGINEERING

This collaborative work elaborated by professionals confronted daily to the use of FE methods targets young engineers, who recently graduated from university and often studied exclusively the fundamentals of the FE calculations. Its objective is to answer some...

#### The AFGC Editorial

Thierry Kretz was the president of the AFGC Scientific and Technical Counsel when the finite element task force was launched. He shares his vision of this project.

#### Foreword

#### Introduction

#### PART 1 – THEORETICAL ELEMENTS

#### PART 2 – USEFUL ELEMENTS

#### PART 3 – EXAMPLES AND COMPLETE CASE STUDIES

#### BIBLIOGRAPHY

#### FOLLOW-UP OF ADDS-UP AND MODIFICATIONS

#### Table of contents

EDITORIAL Finite Element (FE) calculations – a paradigm shift Words from the Scientific and Technical Counsel FOREWORD Recommendations and Advice Content – The list of authors Let us know about your comments and feedback to improve the website! I...

#### Finite Element (FE) calculations – a paradigm shift

Finite Element (FE) calculations – a paradigm shift It is no exaggeration to say that FE calculations applied to civil engineering structures are a paradigm shift for structural analysis. Indeed, it is possible to transpose to structural engineering the conce...

#### Preface - Words from the Scientific and Technical Council

Emmanuel Ferrier is the president of the AFGC Scientific and Technical Council. He shares with us his foreword. Preface Numerous students, engineers, scientists, and researchers use numerical methods to develop or use software that will solve engineering pr...

#### Recommendations and Advice Content – The authors

Recommendations and Advice Content – The authors This collaborative work elaborated by professionals confronted daily to the use of FE methods targets young engineers, who recently graduated from university and often studied exclusively the fundamentals of th...

#### Leave us a comment for us to improve the website

Leave us a comment for us to improve the website It could be: a disagreement, a proposal for a better phrasing, a proposal for a bibliography reference, a link to a relevant internet webpage, a practical example illustrated or not, ...

#### A short and broad introduction of the Recommendations and Advice

A short and broad introduction of the Recommendations and Advice Civil engineering construction projects require to justify the work regarding the risks identified upon technical baselines, which are usually based on the current regulation or chosen by the co...

#### Chapter A. Introduction

Chapter A. Introduction When performing a FE calculation of a structure, the modeling assumptions as well as the objectives must be defined. Those goals generally consist of solving: the displacements caused by a static loading (permanent) quasi-static (...

#### Chapter B. Structural Dynamics

Chapter B. Dynamics For many applications such as seismic calculations, collisions, vibrations… it is necessary to consider the dynamic phenomena. The dynamic charges applied to a civil engineering structure belong to two different categories: phenome...

#### Chapter C. Static non-linear calculations

Chapter C. Nonlinear Static calculations Nonlinear calculations are generally time-demanding: a finite element software solves a nonlinear problem as a series of linear problems (incremental process). To prepare this type of calculation the user has to make d...

#### Chapter D. Civil Engineering

Chapter D. Civil Engineering D.1 Civil engineering materials D.1 Civil engineering materials D.2 The categories of structural elements D.2 The categories of structural elements D.3 The steps of construction D.3 The steps of construction

#### Chapter E. Typical post-treatment in Civil Engineering

Chapter E. Typical post-treatment in Civil Engineering Introduction In civil engineering there is a great variety of quantities of interest because of the numerous subjects that can be studied: The nature of the construction considered and its functiona...

#### Chapter F – Geotechnical calculations

Chapter F – Geotechnical calculations Introduction Conventional methods for the design and dimensioning of geotechnical structures mainly aim to analyze the resistance to failure of an isolated structure. These analytical or semi-analytical methods only con...

#### A1. General formulation for linear elastic calculations

A1. A general formulation for linear elastic calculations The two main formulations for linear calculations are displacements-based and stress-based. Most of the software nowadays rely on a displacement formulation because it can easily consider the boundary ...

#### A2. The dimensionality of the model

A2. The dimensionality of the model It is very important to simplify the full-size problem to model the interaction between the structure and its environment. To do so, there are 2 known techniques: the first one consists of transforming the full-size pr...

#### A3. Choosing the finite elements

A3. Choosing the finite elements Choosing the element is an important step. The goal is to select the type of element (its shape, the order of the shape functions associated), and the size of the element. The type and size of the elements define the form and ...

#### A4. Interaction between the structure and its environment

A4. Interaction between the structure and its environment Taking into account the interactions between the structure and its environment: this consideration allows us to reduce the number of discrepancies between the model and the real-life structure. The eff...

#### A5. Estimation of the quality of the approximated numerical solution

A5. Estimation of the quality of the approximated numerical solution The difference between the exact solution of the problem and the approximate one obtained through the finite element method allows us to assess the quality of the solution: this is called “d...

#### B1. Analysis based on a modal search

B1. Analysis based on a modal search A reminder of the concept of simple oscillator – Concept of the elastic response spectrum In the following section, a lot of applied methods return the response of damped oscillators with a degree of freedom often named s...

#### B2. Analysis based on a direct temporal integration

B2. Analysis based on a direct temporal integration Schemes of integration Main Principles: The principle of the different direct integration methods is to divide the studied interval into n smaller intervals of length ∆t = T/n and to verify the equilibriu...

#### B3. Considering damping

B3. Considering damping The damping of a structure’s vibration is related to dissipation phenomena of various origins that can happen inside of a structure. It can be due to viscous phenomena specific to fluid dampers, which can be found in spring boxes or da...