B modeling ============== Characteristics of modeling ----------------------------------- .. image:: images/Shape4.gif .. _RefSchema_Shape4.gif: +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |Modeling DKTG (QUAD4) | + .. image:: images/10000000000001E0000001E04FCDAA3B7314596F.png + + | :width: 2.1953in | - Boundary conditions: | + :height: 2.2654in + + | | | + + + | | | + +. Rating :math:`\mathit{A2A4}`: :math:`\mathit{DZ}\mathrm{=}0` + | | | + + - Symmetry conditions + | | | + + + | | | + + + | |. Side :math:`\mathit{A1A2}`: :math:`\mathit{DY}\mathrm{=}\mathit{DRX}\mathrm{=}0`. Side :math:`\mathit{A1A3}`: :math:`\mathit{DX}\mathrm{=}\mathit{DRY}\mathrm{=}0` | + + + | | The slab is symmetric with respect to planes :math:`(X\mathrm{=}0)` and :math:`(Y\mathrm{=}0)`, the calculations are carried out on a quarter of the slab. | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Characteristics of the mesh ---------------------------- Number of knots: 169 Number of meshes and type: 144 QUAD4 Tested features ----------------------- The macro command POST_COQUE makes it possible to extract the forces and the deformations at any point in the shell. Tested values --------------- .. csv-table:: "**Identification**", "**Reference Type**", "**Reference**", "**Tolerance (%)**" ":math:`\mathrm{DZ}(\mathrm{A1})` ", "'ANALYTIQUE'", "2.433 10-4"," 6%" ":math:`\mathrm{MXX}(\mathrm{A1})` ", "'ANALYTIQUE'", "4050. "," 2%" ":math:`\mathrm{KXX}(\mathrm{A1})` ", "'ANALYTIQUE'", "7.21 10-4"," 5%" +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |**Identification** |**Reference type**|**Reference**|**Tolerance (%)**| +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{MXX}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |4044.05 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{KXX}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |7.1995 10-4 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ * The quantities are expressed in the coordinate system defined by the nautical angles :math:`\alpha \mathrm{=}33°` and :math:`\beta \mathrm{=}12°`. .. csv-table:: "**Identification**", "**Reference Type**", "**Reference**", "**Tolerance (%)**" ":math:`\mathrm{DZ}(\mathrm{A1})` ", "'ANALYTIQUE'", "2.433 10-4"," 6%" ":math:`\mathit{MXX}(\mathit{A1})` ", "'NON_REGRESSION'", "2848.64", "1.e-6" ":math:`\mathit{MYY}(\mathit{A1})` ", "'NON_REGRESSION'", "1201.35", "1.e-6" ":math:`\mathit{MXY}(\mathit{A1})` ", "'NON_REGRESSION'", "-1849.92", "1.e-6" ":math:`\mathit{KXX}(\mathit{A1})` ", "'NON_REGRESSION'", "5.0713 10-4", "1.e-6" ":math:`\mathit{KYY}(\mathit{A1})` ", "'NON_REGRESSION'", "2.1387 10-4", "1.e-6" ":math:`\mathit{KXY}(\mathit{A1})` ", "'NON_REGRESSION'", "-3.2933 10-4", "1.e-6" +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |**Identification** |**Reference type**|**Reference**|**Tolerance (%)**| +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{MXX}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |2844.46 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{MYY}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |1199.59 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{MXY}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |-1847.21 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{KXX}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |5.0639 10-4 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{KYY}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |2.1356 10-4 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ |:math:`\mathit{KXY}`|:math:`\mathit{M133}`|:math:`\mathit{Point}4`|'NON_REGRESSION' |-3.2885 10-4 |1.e-6 | +--------------------+---------------------+-----------------------+------------------+-------------+-----------------+ notes --------- The coefficients of the following elasticity matrices, used during the calculations, were calculated with :math:`{\nu }_{b}\mathrm{=}0`: 1. Membrane elasticity matrix: :math:`\left\{\begin{array}{ccc}4614.& 0& 0\\ 0& 4614.& 0\\ 0& 0& 2142.\end{array}\right\}{10}^{6}N\mathrm{/}m` 2. Flexural elasticity matrix: :math:`\left\{\begin{array}{ccc}5.617& 0& 0\\ 0& 5.617& 0\\ 0& 0& 2.57\end{array}\right\}{10}^{6}N\mathrm{/}m` To be certain of staying within the elastic domain, the elastic limits, expressed in the orthotropy coordinate system, are set arbitrarily to a very high value: Elastic limits in positive flexure: Direction :math:`x`: :math:`{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}` Direction :math:`y`: :math:`{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}` Elastic limits in negative flexure: Direction :math:`x`: :math:`–{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}` Direction :math:`y`: :math:`–{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}` As the structure remains in the elastic domain, the kinematic recall coefficient (Prager constant) can take any value.