Element.quad4i
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=========================== | =========================== | ||
| − | |alpha |STD |QM6 | + | |alpha|STD |QM6 | |
| − | + | + | +-----+---------+---------+ |
| 0.00| 0.2424| 1.0000| | | 0.00| 0.2424| 1.0000| | ||
| 1.00| 0.1274| 0.6174| | | 1.00| 0.1274| 0.6174| | ||
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==Patch Test== | ==Patch Test== | ||
[[Image:Example_Quad4i_02.png|thumb|350px|Patch test.]] | [[Image:Example_Quad4i_02.png|thumb|350px|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<sub>x</sub>=0.0001+0.0061''x''+0.0049''y'' and u<sub>y</sub>=-0.0005+0.0042''x''+0.0038''y'', where ''x'' and ''y'' are the nodal coordinates. The calculated displacements in the inner nodes must coincide with the previous defined displacement field. | ||
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| + | 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 [[Example:Example_Quad4i_02|here]]. | The example code can be found [[Example:Example_Quad4i_02|here]]. | ||
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=Implementation= | =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> | + | 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>. |
| − | + | ||
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=Notes= | =Notes= | ||
Latest revision as of 17:34, 9 January 2008
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>.
Contents |
[edit] 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 | - |
[edit] Examples
[edit] 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| ===========================
[edit] 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 ux=0.0001+0.0061x+0.0049y and uy=-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| =================================================
[edit] Comments
Nodes, material and section must be already defined. This element can be only used in plane strain/stress analysis.
[edit] Theory
[edit] 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>.
[edit] Notes
<references/>
[edit] See also
- node module.
- material module.
- section module.
- element module.
- User guide.
