8. Post-treatment#
8.1. Analysis of the overall behavior of the structure#
8.1.1. Maximum travel and effort#
The analysis of the evolution of movements and reactions to supports (shear forces, normal forces and global bending moments) provides important elements for understanding the overall behavior of a structure.
Remarks
It is convenient to use the keyword OBSERVATIONafin to save all the results for a given point and not for the whole structure.
8.1.2. Determining the oscillator spectrum#
The determination of the oscillator spectrum of an accelerogram \(a(t)\) is available by the operator CALC_FONCTION [U6.62.04] with the keyword SPEC_OSCI: it is obtained by numerical integration of the Duhamel equation by the Nigam method [R5.05.01]. This command provides the absolute pseudo-acceleration spectrum and, upon request, the pseudo-speed spectrum or the relative displacement spectrum.
In general, the user should always check that the frequency range used to calculate the oscillator spectrum is consistent with the frequency content of the input signal. This is all the more crucial if one seeks to obtain, for example, the asymptotic value of pseudo‑acceleration. In some cases, the SPEC_OSCI keyword’s default frequency list may be too restrictive.
8.1.3. Natural frequencies#
The analysis of the evolution of the natural frequencies of a structure during loading provides a good indication of the state of damage of the structure. The phenomena of cracking reduce the overall stiffness of the structure and a drop in frequency is observed. If the natural frequencies and the damping of the damaged structure are determined, it is then possible to perform a spectral seismic response calculation on it.
The determination of the natural frequencies of the damaged structure is possible using the keyword MODE_VIBR of the DYNA_NON_LINE [U4.53.01] operator. This is a method for performing a vibratory modal analysis (natural frequencies and associated modes) on the global stiffness and mass matrices of DYNA_NON_LINE. Since the natural frequencies of the structure must be calculated for a damaged elastic stiffness matrix, it is necessary to have put the structure back to rest before calculating the natural frequencies by the operator MODE_VIBR. Refer to test case SDNV106 [V5.03.106] for more details.
Another possibility consists in carrying out, after seismic loading and after the structure has been put to rest, a loading of the « white noise » type at a low level of stress using Code_Aster. A Fourier analysis of the response obtained is then carried out in order to determine the natural frequencies of the damaged structure.
8.1.4. Balance of dissipated energies#
The calculation of the energies on all or part of the structure is done by the operator POST_ELEM u4.81.22: the kinetic energy, the elastic deformation energy, the total deformation energy, the total deformation energy, the work of external forces, the dissipation energy for the plate elements of the DKTG family with the laws of global behavior of reinforced concrete GLRC_DM and DHRC. However, the viscous damping energy is currently not calculated, nor is the deformation energy for softening laws such as ENDO_ISOT_BETON. In addition, the calculation of the work of external forces is carried out on the basis of a portion of the nodal forces and does not take into account inertia or damping forces.
The energy balance should therefore be carried out with care.
With the keyword ENERGIEde, you can also use the DYNA_NON_LINEfaire operator to calculate the energy balance over the entire structure, including the viscous damping energy. It is stored in name table PARA_CALC. It is extracted with the RECU_TABLE [U4.71.02] command.
8.2. Analysis of the local behavior of the structure#
8.2.1. Introduction#
The field calculation options mentioned in this chapter are defined in CALC_CHAMP [U4.81.04].
Concrete
The analysis of damage isovalue maps makes it possible to understand the local behavior of a structure. It is possible to determine the maximum levels of stress and cracking achieved at certain points in the structure.
Note
If it is observed that only a few finite elements are very severely damaged, it may be a phenomenon of localization of the damage due to the softening behavior model used. This phenomenon causes the response to be dependent on the mesh. In order to determine whether or not there is a location, it is recommended to repeat the calculation by re-meshing the suspected area more finely. If we observe that the damage has occurred again on a single mesh band (reduction of the damaged area), it is because we have localization.
It should be noted that models for delocalizing laws of behavior by regularizing deformation are not yet currently available in nonlinear dynamics in Code_Aster (cf. § 4.4.4 ) .
Armatories
The analysis of the isovalue maps of the cumulative plastic deformations in the reinforcements makes it possible to determine the level of plasticization achieved in the steels.
8.2.2. Local modeling (massive elements)#
There is no post-treatment specificity in this case. So it is not detailed here.
Concrete
The constraints at the nodes are directly calculated by element SIGM_ELNO.
Armatories
Similarly, membrane grid elements (GRILLE_MEMBRANE) or bar elements (BARRE) are post-processed by calculating the associated constraints SIGM_ELNO.
Note
In HPP, we directly calculate the deformations at the nodes by elements EPSI_ELNOà from the displacements.
8.2.3. Multilayer plate and shell elements#
Concrete
For multi-layer shells, the constraints by elements at the nodes (SIGM_ELNO) are post-processed from the constraints at the integration points of each layer (SIEF_ELGA) calculated during a non-linear calculation. If you want to obtain these constraints in a particular layer and position, you must use the POST_CHAMP operator.
These constraints are calculated in the local coordinate system of the shell defined by the user in the AFFE_CARA_ELEM command. Internal variables can be post-processed in the same way (VARI_ELNO).
Armatories
Off-center grid elements (GRILLE_EXCENTRE) or bar elements (BARRE) can be post-processed simply by calculating the associated constraints SIGM_ELNO.
8.2.4. Elements of multifibre beams#
For multifibre beams, there is currently no option for calculating the stresses in the fibres directly in CALC_CHAMP. However, it is possible to recover the constraints in the fibers by using the operands for locating a field in the operator RECU_FONCTION:
/NOEUD = no, [node]
/GROUP_NO = grno, [gr_node]
/MAILLE = ma, [mesh]
/GROUP_MA = grma, [gr_mesh]
/POINT = nupoint, [I]
/SOUS_POINT = nusp, [I]
The nupoint integer specifies the number of the Gauss point whose value we want to retrieve (case of cham_elem « at points of GAUSS « ).
The integer nusp specifies the number of the sub-point, that is to say of the fiber, on which the constraints are measured (cf. the mesh in section § 3.4).
It is thus possible to analyze the stresses and deformations in concrete fibers and in steel fibers.
8.2.5. « Global » plate elements and shells#
In this modeling, the stresses and deformations in the thickness of the shell are not directly available. However, it is possible to reconstruct the deformation field (but not the stress field) for a given dimension based on the generalized force and deformation fields.
Since the deformation field is considered linear in the section, we have:
\(\{\begin{array}{c}{\varepsilon }_{x}(z)={\varepsilon }_{x}^{\mathrm{tot}}+z{\kappa }_{x}^{\mathrm{tot}}\\ {\varepsilon }_{y}(z)={\varepsilon }_{y}^{\mathrm{tot}}+z{\kappa }_{y}^{\mathrm{tot}}\end{array}\)
with \({\varepsilon }_{x}^{\mathrm{tot}}\), \({\varepsilon }_{y}^{\mathrm{tot}}\), \({\kappa }_{x}^{\mathrm{tot}}\), and \({\kappa }_{y}^{\mathrm{tot}}\) the generalized deformations and \({\varepsilon }_{x}(z)\) and \({\varepsilon }_{y}(z)\) the deformations in the thickness of the overall shell.
8.2.6. Discrete elements carrying laws of linear or non-linear behavior#
In this modeling, we directly have the displacements (or even rotations) of the end nodes of the discrete elements, but also the forces that pass through them. In addition, in the case of a non-linear law of behavior, cf. [R5.03.17], we have access to the values of various internal variables useful for analyzing detailed functioning (anelastic contribution, energy dissipated, etc.).