Users:General FEM Analysis/Elements Reference/Quad1

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== The EAS Method ==
 
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The idea of enhanced assumed strains is to enlarge the element srain field by a set of additional strains in order to enable the element to express certain states of displacement without locking due to parasitic strains.
 
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<ref>
 
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J.C. Simo, M.S. Rifai: „A class of mixed assumed strain methods and the method
 
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of incompatible modes“, in „International Journal for Numerical Methods in Engineeering“, Vol. 29, 1990, pages 1595-1638
 
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</ref>
 
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<ref name="AnRa93"> U. Andelfinger, E. Ramm: „EAS-Elements for two-dimensional, three-dimensional,
 
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plate and shell structures and their equivalence to HR-Elements“, in „International
 
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Journal for Numerical Methods in Engineeering“, Vol. 36, 1993, pages 1311-1337 </ref>.
 
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To this purpose the strain-displacement relation is enlarged by additional terms which leads to a modified element stiffness matrix:
 
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[[File:Eas_formulas.JPG|400px|border|center|stiffness matrix concerning EAS improvement]]
 
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The following example will show the  benefit of EAS improved elements toward purely displacment formulated eight-noded hexahedrals. The investigated system is a tip loaded cantilever wherby the cross section is modeled by one element.
 
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{|border="1"
 
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|[[File:Cantilever_locking.JPG |400px| HEXA8]]
 
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|[[File:Cantilever_lockingfree.JPG |400px| HEXA8EAS9]]
 
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|-
 
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| Element HEXA8
 
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| Element HEXA8EAS9
 
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|}
 
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The pure displacement based elements show the well known in-plane shear locking which increases along the cantilever with increasing bending moment. As artificial strain/shear produces artificial stiffness, the tip displacement is extremly under estimated.
 
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In contrast the EAS improved elements are able to eliminate artificial strains arrising from locking, and so tip displacement is described correctly.
 
  
 
== References ==
 
== References ==
 
<references/>
 
<references/>

Revision as of 07:24, 7 September 2010


Contents

General Description

4-noded quad element

Element Type

This class provides a purely displacement formulated four-noded plane stress/plane strain element. It is intended for comparisons and introductory purpose only. The element is only able to perform geometrically linear static computations and cannot carry element loads.

Degrees of Freedom

All nodes of the plane stress/stain element have to be defined in the plane z=0 and all movements take place in this plane. So nodal displacements can be described by the two remaining translatoric degrees of freedom, Disp_X and Disp_Y.

Input Parameters

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
MAT EL-MAT int Linking to a material input block
THICKNESS real Parameter for constant element thickness
INT_TYPE_QUAD FULL Only full integration is available
MODE PSTRESS, PSRTAIN Switch to choose plane stress or plane strain computation


Example of a Complete Input Block 

EL-PROP 1: QUAD1
MAT           = EL-MAT 1
THICKNESS      = 0.1
INT_TYPE_QUAD = FULL
EAS           = PSTRESS    ! choose: PSTRESS, PSTRAIN

 !  ElementID  Part-ID       EL-PROP        Node-IDs
NEL  1           1             1            1  2  3  4

References





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