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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...

B4. Specificities of the seismic analysis Spectral response – Specific case of earthquakes The principle of the method is, for a given seismic direction, to construct the maximum responses from the loading spectrum at all points, mode by mode, then, to accum...

C1. Mechanical non-linear problems Description of possible non-linearities The non-linearity of a mechanical problem comes from the fact that the coefficients of the equilibrium equation depend on the displacements of the solid itself in equilibrium....

C2. Why performing non-linear calculations As in many areas of physics, it is only reasonable to undertake a non-linear calculation after having a good idea of the "end of the story". In other words, how the structure will evolve until it becomes unstable. Be...

C3. Implementation The correct method consists of always proceeding step by step so that non-linearities are not introduced all at once: Performing an initial calculation with an elastic constitutive law before using non-linear ones, Performing a ca...

C4. Convergence issues? Symptoms and solutions As opposed to linear elastic calculations, non-linear calculations can perform iterations indefinitely, never verifying the stopping criterion, but they can also be interrupted abruptly at a given load increment ...

D1. Civil engineering materials The objective of this chapter is to highlight the peculiarities of civil engineering materials regarding FE modeling. Among those, there are the particularities of the civil engineering materials themselves (concrete, timber, s...

D2. Different categories of structural elements  Here are presented the peculiarities of these elements regarding FE calculations.  Reinforced concrete elements Considering the delayed phenomena – Usually, the project engineer is interested in the r...

D3. The different construction phases  Studying the phases of construction has two objectives: to ensure the stability of the structure in the various transitional states leading to the final state, to calculate the effects that have the assembly on...

E1. Generalities The different post-treated quantities may change significantly according to the objective of the finite element analysis. Usually the studied quantities in the pre-dimensioning phase (a sketch or preliminary draft) are different from those s...

E2. Quantities in Dynamics Time-dependent analyses Post-processing of time-dependent quantities does not present any major difficulty as long as one is not interested in targeting a precise instant or in characterizing a single representative value a...

E3. The specific case of reinforced concrete Overview of the common methods for designing the reinforcement of plate elements There are mainly 3 methodologies applicable to plates that can be consulted using the following references: Johansen fr...

F1. Geometric aspects  One of the advantages of the FE method is the possibility of describing the exact geometry of the structures even during the various construction phases. CAD-like pre-processing tools make it easy to generate very complex geometries. On...

F2. Material non-linearities  In geotechnics, it is very rare to be able to study a structure exclusively using linear behavior assumptions (except for certain dynamic analyses). It may be useful to first perform a linear calculation, to check that the geomet...

F3. Soil-structure interactions Geotechnical structures often combine layers of soil with metal or concrete structures, which are generally much stiffer than soil. The interaction may be limited to a few points where the structure rests on the ground, or it m...

F4. Hydraulic effects Hydromechanical coupling Another peculiarity of geotechnical calculations concerns the role of water in soils. When a mechanical load is rapidly applied to a saturated layer of soil, instantaneous deformation, and pressurization...

F5. Uncertainties and recommendations  Uncertainties There are many sources of uncertainty in geotechnics. The first is the relative lack of knowledge of the geometry of the soil layers that make up the solid being studied. In addition to the geologi...

F6. Normative aspects: Principles of the Eurocode 7 Numerical modeling always had a particular relationship with calculation standards, which essentially focus on the verification of ultimate limit states by calculating safety coefficients or the equilibrium ...

F7. Modeling in Dynamics   Because of the continuous and unconfined nature of geomaterials, the treatment of dynamic problems in "soil" media differs from the treatment of dynamic problems associated with classical civil engineering structures. While for mos...

F8. Characteristic scales Firstly, to frame the discussion about soil dynamics problems, it is necessary to distinguish the characteristic scales relative to the definition of the physical phenomena studied in these problems. These scales are: the geolog...