Users:General FEM Analysis/Elements Reference/SolidHexa1
Contents 
General Description
Element Type
 This element class provides 3D hexahedral elements with linear (8noded element), partially quadratic (20noded) or quadratic shape functions (27noded)
 The element formulation includes an enhanmced assumed strain (EAS) improvement in order to avoid locking effects. This feature is only available for 8noded elements. EAS can be used within gemoetrical nonlinear analysis, but it might lead to artificial uero energy modes within the regime of big strains. ^{[2]}
Degrees of Freedom
All hexahedral elements use three translatoric degrees of freedom at each node.
They are named Disp_X, Disp_Y, Disp_Z.
Input Parameters
Parameter Description
Compulsory Parameters  
Parameter  Values, Default(*)  Description 

MAT  ELMAT int  Linking to a material input block 
INT_TYPE_HEXA  FULL, REDUCED  Control of integration type 20noded elements are able to perform a uniform reduced integration (2x2x2 instead of 3x3x3) without hourglassing stabilisation 
Optional Parameters  
Parameter  Values, Default(*)  Description 
EAS  int  Flag Enhances Assumed Strains (EAS) method Possible values are:

Example of a Complete Input Block
ELPROP 1: SOLIDHEXA1 MAT = ELMAT 1 INT_TYPE_HEXA = FULL EAS = 0
Inside the property block there is no distinction between linear and quadratic formulated elements. It is possible to define 8noded, 20noded and 27noded elements using one and the same element property (assuming that no EAS is used):
! ElementID PartID ELPROP NodeIDs NEL 1 1 1 1 2 3 4 5 6 7 8 ! 8noded element NEL 2 1 1 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 36 38 39 40 !20noded element NEL 3 1 1 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 66 68 69 70 71 72 73 74 75 76 77 !27noded element
Element Loading
Hexahedral elements are able to carry two types of element loads:
 dead load
 temperature load
Dead Load
Dead weight of an element is computed by multiplying material's denisity (ρ) with gravity's acceleration, which has to be defined inside the load block concearning its direction and size.
An example for a load definition of a concrete structure (assuming linear elastic isotropic material behaviour) with gravity acting in positive zdirection would look like
ELMAT 1 : LIN_ELAST_ISOTROPIC EMOD=3.5e10 ALPHAT=1e5 DENS=2.5e3 NUE=0.2
LDELEM 1 PART=1 TYPE=DEAD D1=0.0 D2=0.0 D3=1.0 VAL=9.81
whereat the finite elemet model is based on SI units (m, N, kg).
Temperature Load
This paragraph only focuses at element specific topics concearing temperature load. For more detailed descriptions please look at the load documentation
For the computation of temperature loads solid elements do not concider any layer of laminate structure within the element. So only the temperature defined for layer number one is considered at each node.
The combination of temperature loading and EAS improvement is possible.
LDELEM 1 TYPE = TEMPERATURE NDSET = 1 LAYER = 1 VAL = +10 NDSET = 2 LAYER = 1 VAL = 10
The EAS Method
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. ^{[3]} ^{[4]}.
To this purpose the straindisplacement relation is enlarged by additional terms which leads to a modified element stiffness matrix:
The following example will show the benefit of EAS improved elements toward purely displacment formulated eightnoded hexahedrals. The investigated system is a tip loaded cantilever wherby the cross section is modeled by one element.
Element HEXA8  Element HEXA8EAS9 
The pure displacement based elements show the well known inplane 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.
In contrast the EAS improved elements are able to eliminate artificial strains arrising from locking, and so tip displacement is described correctly.
References
 ↑ Pictures taken from the notes to the lecture "Advanced Finite Element Methods for Solids, Plates and Shells" given by Carlos Felippa at the University of Colorado at Boulder. http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/ (4th August 2011)
 ↑ W. A. Wall, M. Bischoff, E. Ramm: „A deformation dependent stabilization technique, exemplified by EAS elements at large strains“, in „Computer methods in applied mechanics and engineering“, Vol. 188, 2000, Seiten 859871
 ↑ J.C. Simo, M.S. Rifai: „A class of mixed assumed strain methods and the method of incompatible modes“, in „International Journal for Numerical Methods in Engineeering“, Vol. 29, 1990, pages 15951638
 ↑ U. Andelﬁnger, E. Ramm: „EASElements for twodimensional, threedimensional, plate and shell structures and their equivalence to HRElements“, in „International Journal for Numerical Methods in Engineeering“, Vol. 36, 1993, pages 13111337
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