Element.quad4i

The following article describes the use of the element.quad4i command. This command defines a four-node non-conforming quad based on the work of R.L. Taylor, P.J Beresford & E.L. Wilson<ref>R.L. Taylor, P.J Beresford and E.L. Wilson, "A non-conforming element for stress analysis", International Journal for Numerical Methods in Engineering, Vol. 10, pp.1211-1219 (1976)</ref>.

Syntax

element.quad4i(id,node1,node2,node3,node4,mat)

where

Parameter	description	type	default
id	The elemental id	integer	-
node1-4	The elemental nodes	integer	-
mat	The element material	integer	-

Examples

Mesh distortion test

Mesh distortion test.

The example code can be found here.

===========================
|alpha|STD      |QM6      |
+-----+---------+---------+
| 0.00|   0.2424|   1.0000|
| 1.00|   0.1274|   0.6174|
| 2.00|   0.0846|   0.5337|
| 3.00|   0.0703|   0.5271|
| 4.00|   0.0597|   0.5044|
===========================

Patch Test

Patch test.

A typical patch test. The outer nodes are ordered anti-clockwise as 1(0.0, 0.0), 2(9.0, 0.0), 3(8.0, 8.0) and 4(0.0, 6.0) while the inner nodes are arranged similarly as 5(2.5, 2.0), 6(6.5, 1.5), 7(5.5, 5.0) and 8(2.5, 5.0). A displacement field is given in the outer nodes defined by u_x=0.0001+0.0061x+0.0049y and u_y=-0.0005+0.0042x+0.0038y, where x and y are the nodal coordinates. The calculated displacements in the inner nodes must coincide with the previous defined displacement field.

The displacement field (displacement vector magnitude) is plotted in the picture on the left, while the results are shown in the next table.

The example code can be found here.

=================================================
|   |     Analytical      |     Numerical       |
+---+----------+----------+----------+----------+
|id |ux        |uy        |ux        |uy        |
+---+----------+----------+----------+----------+
|  5|  0.025150|  0.017600|  0.025150|  0.017600|
|  6|  0.047100|  0.032500|  0.047100|  0.032500|
|  7|  0.058150|  0.041600|  0.058150|  0.041600|
|  8|  0.039850|  0.029000|  0.039850|  0.029000|
=================================================

Comments

Nodes, material and section must be already defined. This element can be only used in plane strain/stress analysis.

Implementation

The implementation of this element follows closely the work of T.J.R. Hughes<ref>T.J.R. Hughes, "The Finite Element Method: Linear Static and Dynamic Finite Element Analysis"', Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1997, pp.243-248.</ref>.

Notes

<references/>

See also

• node module.
• material module.
• section module.
• element module.
• User guide.