5. Implementation and post-treatments#
The eccentricity is introduced by the optional keyword EXCENTREMENT at the level of AFFE_CARA_ELEM in the same way as the thickness according to the methods defined in the introduction. When this keyword is not present the eccentricity is zero by default.
5.1. Application of efforts and couples#
All calculations are done in the sketch coordinate system (mesh plane). If forces or torques are defined in relation to another coordinate system, the user must make the necessary transformations for FORCE_ARETE and FORCE_NODALE to return to the mesh coordinate system. For FORCE_COQUE the user will be able to specify the plan for applying the efforts and the conversion to the calculation frame will be automatic.
The concept of an effort implementation plan is thus introduced in AFFE_CHAR_MECA by the keyword PLAN under FORCE_COQUE. This application plane is different from the reference plane or draft plane on which the mesh is based. For this keyword we will define the following four possibilities for applying forces: “INF” “” MOY “” SUP “” “MAIL”. “INF “”MOY” and “SUP” mean that the forces are applied to the lower, middle and upper plate skin respectively. “MAIL” means that the forces are applied at the level of the reference plane or mesh plane. By default, the forces will be applied to the mesh plane of the plate. This includes TE0032 FORCE_COQUE efforts.
As a coordinate system local to the element, when forces and torques are applied to “MOY”, the simple transition relationship is used:
\(\begin{array}{c}{c}_{x}^{\text{'}}\mathrm{=}{c}_{x}\mathrm{-}{\text{df}}_{y}\\ {c}_{y}^{\text{'}}\mathrm{=}{c}_{y}+{\text{df}}_{x}\end{array}\)
to bring the forces and torques into the mesh coordinate system where the calculations are made.
As a coordinate system local to the element, when forces and torques are applied to “SUP”, the simple transition relationship is used:
\(\begin{array}{c}{c}_{x}^{\text{'}}\mathrm{=}{c}_{x}\mathrm{-}(d+h\mathrm{/}2){f}_{y}\\ {c}_{y}^{\text{'}}\mathrm{=}{c}_{y}+(d+h\mathrm{/}2){f}_{x}\end{array}\)
As a coordinate system local to the element, when forces and torques are applied to “INF”, the simple transition relationship is used:
\(\begin{array}{c}{c}_{x}^{\text{'}}\mathrm{=}{c}_{x}\mathrm{-}(d\mathrm{-}h\mathrm{/}2){f}_{y}\\ {c}_{y}^{\text{'}}\mathrm{=}{c}_{y}+(d\mathrm{-}h\mathrm{/}2){f}_{x}\end{array}\)
If the efforts are given in the global frame of reference of the element, we use transition relationships of the type: \({c}^{\text{'}}\mathrm{=}c+(d+\varepsilon h\mathrm{/}2)n\mathrm{\wedge }f\) where \(c\) is defined in relation to the coordinate system “INF” “” MOY “” SUP “with \(\varepsilon\) equal to -1, 0 and 1, respectively. When there is no eccentricity, the previous formula reduces to \({c}^{\text{'}}\mathrm{=}c+\varepsilon h\mathrm{/}\mathrm{2n}\mathrm{\wedge }f\).
Note:
For loads FORCE_ARETE or FORCE_NODALE or * **the forces and torques can only be expressed in relation to the mesh coordinate system. If the user only knows them* in relation to the middle sheet of the plate, he will have to change the coordinate system himself in order to have the expression of the forces and torques in relation to the mesh surface. The relationship to use is \({c}^{\text{'}}\mathrm{=}c+\mathit{dn}\mathrm{\wedge }f\) where \(d\) is the distance between the calculation plane and the loading plane oriented by the normal to the shell. It is obvious that the user has an interest in the loading plane being the mesh plane, but it is not always possible to make these two planes coincide as can be seen on the left part of Figure 2.1-a.
5.2. Application of boundary conditions while traveling#
For displacement-type boundary conditions, the user should pay attention to the fact that they can only be applied to the mesh coordinate system. The transition relationships with respect to conditions given on the middle sheet are as follows:
\(\begin{array}{c}{\theta }_{\text{ref}}\mathrm{=}{\theta }_{\text{moy}}\\ {u}_{\text{ref}}\mathrm{=}{u}_{\text{moy}}\mathrm{-}{\theta }_{\text{moy}}\mathrm{\wedge }\mathit{dn}\end{array}\)
5.3. Post-treatments#
For post-treatments, the results by default, such as generalized efforts, are given in the coordinate system corresponding to the design plan. To have them in the other guides, the user must indicate the post-processing plan and the changes of reference points will be automatic.
For the post-processing of generalized efforts, they can be calculated in the middle sheet of the shell via the POST_CHAMP/COQUE_EXCENT command.