.. _ASDShellQ4: ASDShellQ4 Element ^^^^^^^^^^^^^^^^^^ This command is used to construct an ASDShellQ4 element object. The ASDShellQ4 element is a 4-node general purpose thick shell element with the following features: #. The membrane behavior is enhanced with the **AGQ6-I** [ChenEtAl2004]_ formulation, which makes the element almost insensitive to geometry distortion, as opposed to standard iso-parametric elements. #. The drilling DOF is treated with the **Hughes-Brezzi** [HughesEtAl1989]_ formulation, with special care to avoid membrane locking, using a 1 point quadrature plus stabilization. #. The plate bending part is treated using the **MITC4** [DvorkinEtAl1984]_ [BatheEtAl1985]_ formulation, to avoid the well known transverse shear locking behavior of thick plate elements. #. It can be used to model both **flat** and **warped** geometries. #. Kinematics can be either **linear** or **corotational**. The corotational kinematics is based on the work of Felippa et al., i.e. the **EICR** [Felippa2000]_ [FelippaEtAl2005]_ (Element Independent Corotational formulation). Finite rotations are treated with Quaternions. #. It uses a full 2x2 Gauss quadrature, so it has a total of 4 integration points. .. function:: element ASDShellQ4 $eleTag $n1 $n2 $n3 $n4 $secTag <-corotational> .. csv-table:: :header: "Argument", "Type", "Description" :widths: 10, 10, 40 $eleTag, |integer|, unique integer tag identifying element object $n1 $n2 $n3 $n4, 4 |integer|, the four nodes defining the element (-ndm 3 -ndf 6) $secTag, |integer|, unique integer tag associated with previously-defined SectionForceDeformation object -corotational, |string|, "optional flag, if provided, the element uses non-linear kinematics, suitable for large displacement/rotation problems" .. figure:: ASDShellQ4_geometry.png :align: center :figclass: align-center Nodes, Gauss points, local coordinate system, warped and flat geometry .. note:: Valid queries to the ASDShellQ4 element when creating an ElementRecorder object are: * '**force**', '**forces**', '**globalForce**', or '**globalForces**': * Internal forces at the element's nodes. * Orientation: global coordinate system. * Size: 24 columns of data, 6 components for each one of the 4 nodes. * '**material $secTag $secArg1 ... $secArgN**': * Section response at section **$secTag** * **$secTag** is the 1-based index of the integration point (1 to 4). * '**$secArg1 ... $secArgN**' are the arguments required by the SectionDeformationObject at the requested integration point. .. admonition:: Example 1. **Tcl Code** .. code-block:: tcl # set up a 3D-6DOFs model model Basic -ndm 3 -ndf 6 node 1 0.0 0.0 0.0 node 2 1.0 0.0 0.0 node 3 1.0 1.0 0.0 node 4 0.0 1.0 0.0 # create a fiber shell section with 4 layers of material 1 # each layer has a thickness = 0.025 nDMaterial ElasticIsotropic 1 1000.0 0.2 section LayeredShell 11 4 1 0.025 1 0.025 1 0.025 1 0.025 # create the shell element using the small displacements/rotations assumption element ASDShellQ4 1 1 2 3 4 11 # or you can use the corotational flag for large displacements/rotations (geometric nonlinearity) element ASDShellQ4 1 1 2 3 4 11 -corotational # record global forces at element nodes (24 columns, 6 for each node) recorder Element -xml force_out.xml -ele 1 force # record local section forces at gauss point 1 (8 columns: | 3 membrane | 3 bending | 2 transverse shear |) # note: gauss point index is 1-based recorder Element -xml force_gp1_out.xml -ele 1 material 1 force # record local stresses at fiber 1 of gauss point 1 (5 columns: Szz is neglected (0) ) # note: fiber index is 1-based (while in beams it is 0-based!) recorder Element -xml stress_gp1_fib0_out.xml -ele 1 material 1 fiber 1 stress 2. **Python Code** .. code-block:: python # set up a 3D-6DOFs model model('Basic', '-ndm', 3, '-ndf', 6) node(1, 0.0, 0.0, 0.0) node(2, 1.0, 0.0, 0.0) node(3, 1.0, 1.0, 0.0) node(4, 0.0, 1.0, 0.0) # create a fiber shell section with 4 layers of material 1 # each layer has a thickness = 0.025 nDMaterial('ElasticIsotropic', 1, 1000.0, 0.2) section('LayeredShell', 11, 4, 1,0.025, 1,0.025, 1,0.025, 1,0.025) # create the shell element using the small displacements/rotations assumption element('ASDShellQ4', 1, 1,2,3,4, 11) # or you can use the corotational flag for large displacements/rotations (geometric nonlinearity) # element('ASDShellQ4', 1, 1,2,3,4, 11, '-corotational') # record global forces at element nodes (24 columns, 6 for each node) recorder('Element', '-xml', 'force_out.xml', '-ele', 1, 'force') # record local section forces at gauss point 1 (8 columns: | 3 membrane | 3 bending | 2 transverse shear |) # note: gauss point index is 1-based recorder('Element', '-xml', 'force_gp1_out.xml', '-ele', 1, 'material', '1', 'force') # record local stresses at fiber 1 of gauss point 1 (5 columns: Szz is neglected (0) ) # note: fiber index is 1-based (while in beams it is 0-based!) recorder('Element', '-xml', 'stress_gp1_fib0_out.xml', '-ele', 1, 'material', '1', 'fiber', '1', 'stress') Code Developed by: **Massimo Petracca** at ASDEA Software, Italy. .. [ChenEtAl2004] | Chen, Xiao-Ming, et al. "Membrane elements insensitive to distortion using the quadrilateral area coordinate method." Computers & Structures 82.1 (2004): 35-54. (`Link to article `_) .. [HughesEtAl1989] Hughes, Thomas JR, and F. Brezzi. "On drilling degrees of freedom." Computer methods in applied mechanics and engineering 72.1 (1989): 105-121. (`Link to article `_) .. [DvorkinEtAl1984] Dvorkin, Eduardo N., and Klaus-Jurgen Bathe. "A continuum mechanics based four-node shell element for general non-linear analysis." Engineering computations (1984). (`Link to article `_) .. [BatheEtAl1985] Bathe, Klaus-Jurgen, and Eduardo N. Dvorkin. "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation." International Journal for Numerical Methods in Engineering 21.2 (1985): 367-383. (`Link to article `_) .. [Felippa2000] Felippa, Carlos A. "A systematic approach to the element-independent corotational dynamics of finite elements". Technical Report CU-CAS-00-03, Center for Aerospace Structures, 2000. (`Link to article `_) .. [FelippaEtAl2005] Felippa, Carlos A., and Bjorn Haugen. "A unified formulation of small-strain corotational finite elements: I. Theory." Computer Methods in Applied Mechanics and Engineering 194.21-24 (2005): 2285-2335. (`Link to article `_)