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 \(fileName&gt; &lt;-time&gt; &lt;-node (\)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 \(vPerm &lt;\)b1=0 \(b2=0&gt;</strong></p></td> </tr> </tbody> </table> <figure> <img src="/OpenSeesRT/contrib/static/Elem9_4QuadUp.png" title="Elem9_4QuadUp.png" alt="Elem9_4QuadUp.png" /> <figcaption aria-hidden="true">Elem9_4QuadUp.png</figcaption> </figure> <table> <tbody> <tr class="odd"> <td><code class="parameter-table-variable">eleTag</code></td> <td><p>A positive integer uniquely identifying the element among all elements</p></td> </tr> <tr class="even"> <td><p><strong>\)Node1,… \(Node9</strong></p></td> <td><p>Nine element node (previously defined) numbers (see figure above for order of numbering).</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">thick</code></td> <td><p>Element thickness</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">matTag</code></td> <td><p>Tag of an NDMaterial object (previously defined) of which the element is composed</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">bulk</code></td> <td><p>Combined undrained bulk modulus B&lt;sub&gt;c&lt;/sub&gt; relating changes in pore pressure and volumetric strain, may be approximated by:</p> <p>B&lt;sub&gt;c&lt;/sub&gt; &amp;asymp; B&lt;sub&gt;f&lt;/sub&gt;/n</p> <p>where B&lt;sub&gt;f&lt;/sub&gt; is the bulk modulus of fluid phase (2.2x10&lt;sup&gt;6&lt;/sup&gt; kPa (or 3.191x10&lt;sup&gt;5&lt;/sup&gt; psi) for water), and n the initial porosity.</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">fmass</code></td> <td><p>Fluid mass density</p></td> </tr> <tr class="odd"> <td><p><strong>\)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:

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