# PART 1 – THEORETICAL ELEMENTS

#### Chapter A. Introduction

Chapter A. Introduction When performing a FE calculation of a structure, the modeling assumption...

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

A1. A general formulation for linear elastic calculations The two main formulations for linear c...

#### A2. The dimensionality of the model

A2. The dimensionality of the model It is very important to simplify the full-size problem to mo...

#### A3. Choosing the finite elements

A3. Choosing the finite elements Choosing the element is an important step. The goal is to selec...

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

A4. Interaction between the structure and its environment Taking into account the interactions b...

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

A5. Estimation of the quality of the approximated numerical solution The difference between the ...

#### Chapter B. Structural Dynamics

Chapter B. Dynamics For many applications such as seismic calculations, collisions, vibrations… ...

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

B1. Analysis based on a modal search A reminder of the concept of simple oscillator – Concept of...

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

B2. Analysis based on a direct temporal integration Schemes of integration Main Principles: T...

#### B3. Considering damping

B3. Considering damping The damping of a structure’s vibration is related to dissipation phenome...

#### B4. Specificities of the seismic analysis

B4. Specificities of the seismic analysis Spectral response – Specific case of earthquakes The ...

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

Chapter C. Nonlinear Static calculations Nonlinear calculations are generally time-demanding: a ...

#### C1. Mechanical non-linear problems

C1. Mechanical non-linear problems Description of possible non-linearities The non-line...

#### C2. Why performing non-linear calculations

C2. Why performing non-linear calculations As in many areas of physics, it is only reasonable to...

#### C3. Implementation

C3. Implementation The correct method consists of always proceeding step by step so that non-lin...

#### C4. Convergence issues? Symptoms and solutions

C4. Convergence issues? Symptoms and solutions As opposed to linear elastic calculations, non-li...

#### Chapter D. Civil Engineering

Chapter D. Civil Engineering D.1 Civil engineering materials D.1 Civil engineering materials D...

#### D1. Civil engineering materials

D1. Civil engineering materials The objective of this chapter is to highlight the peculiarities ...

#### D2. Different categories of structural elements

D2. Different categories of structural elements Here are presented the peculiarities of these e...

#### D3. The different construction phases

D3. The different construction phases Studying the phases of construction has two objectives: ...

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

Chapter E. Typical post-treatment in Civil Engineering Introduction In civil engineering there ...

#### E1. Generalities

E1. Generalities The different post-treated quantities may change significantly according to the...

#### E2. Quantities in Dynamics

E2. Quantities in Dynamics Time-dependent analyses Post-processing of time-dependent qu...

#### E3. The specific case of reinforced concrete

E3. The specific case of reinforced concrete Overview of the common methods for designing th...

#### Chapter F – Geotechnical calculations

Chapter F – Geotechnical calculations Introduction Conventional methods for the design and dim...

#### F1. Geometric aspects

F1. Geometric aspects One of the advantages of the FE method is the possibility of describing t...

#### F2. Material non-linearities

F2. Material non-linearities In geotechnics, it is very rare to be able to study a structure ex...

#### F3. Soil-structure interactions

F3. Soil-structure interactions Geotechnical structures often combine layers of soil with metal ...

#### F4. Hydraulic effects

F4. Hydraulic effects Hydromechanical coupling Another peculiarity of geotechnical calc...

#### F5. Uncertainties and recommendations

F5. Uncertainties and recommendations Uncertainties There are many sources of uncertai...

#### F6. Normative aspects: Principles of the Eurocode 7

F6. Normative aspects: Principles of the Eurocode 7 Numerical modeling always had a particular r...

#### F7. Modeling in Dynamics

F7. Modeling in Dynamics Because of the continuous and unconfined nature of geomaterials, the...

#### F8. Characteristic scales

F8. Characteristic scales Firstly, to frame the discussion about soil dynamics problems, it is n...