Nine Four Node Quad u-p Element
Nine_Four_Node_QuadUP is a 9-node quadrilateral plane-strain element. The four corner nodes have 3 degrees-of-freedom (DOF) each: DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p). The other five nodes have 2 DOFs each for solid displacement. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium.
Please click here for examples.
OUTPUT INTERFACE:
Pore pressure can be recorded at an element node using OpenSees Node Recorder:
recorder Node <-file \(fileName> <-time> <-node (\)nod1 $nod2 …)> -dof 3 vel
See OpenSees command manual (McKenna and Fenves 2001) for nodal displacement, velocity, or acceleration recorders.
The valid queries to a Nine_Four_Node_QuadUP element when creating an ElementRecorder are ‘force’, ‘stiffness’, or ‘material matNum matArg1 matArg2 …’, where matNum represents the material object at the corresponding integration point.
element 9_4_QuadUP $eleTag $Node1 $Node2 $Node3 $Node4 $Node5 $Node6 $Node7 $Node8 $Node9 $thick $matTag $bulk $fmass $hPerm \(vPerm <\)b1=0 \(b2=0></strong></p></td> </tr> </tbody> </table> <figure> <img src="/OpenSeesRT/contrib/static/Elem9_4QuadUp.png" title="Elem9_4QuadUp.png" alt="Elem9_4QuadUp.png" /> <figcaption aria-hidden="true">Elem9_4QuadUp.png</figcaption> </figure> <table> <tbody> <tr class="odd"> <td><code class="parameter-table-variable">eleTag</code></td> <td><p>A positive integer uniquely identifying the element among all elements</p></td> </tr> <tr class="even"> <td><p><strong>\)Node1,… \(Node9</strong></p></td> <td><p>Nine element node (previously defined) numbers (see figure above for order of numbering).</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">thick</code></td> <td><p>Element thickness</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">matTag</code></td> <td><p>Tag of an NDMaterial object (previously defined) of which the element is composed</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">bulk</code></td> <td><p>Combined undrained bulk modulus B<sub>c</sub> relating changes in pore pressure and volumetric strain, may be approximated by:</p> <p>B<sub>c</sub> &asymp; B<sub>f</sub>/n</p> <p>where B<sub>f</sub> is the bulk modulus of fluid phase (2.2x10<sup>6</sup> kPa (or 3.191x10<sup>5</sup> psi) for water), and n the initial porosity.</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">fmass</code></td> <td><p>Fluid mass density</p></td> </tr> <tr class="odd"> <td><p><strong>\)hPerm, \(vPerm</strong></p></td> <td><p>Permeability coefficient in horizontal and vertical directions respectively.</p></td> </tr> <tr class="even"> <td><p><strong>\)b1, $b2 |
Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0) |
Code Developed by: UC San Diego (Dr. Zhaohui Yang):
UC San Diego Soil Model: