4.1 HEXAHEDRON NO.1 WITH 8 NODES

The hexahedron element calculates deflections and stresses in space. It is a transformed element, therefore it can have a wedging form or another oblique-angled form. The transformation is isoparametric. The integration is carried out numerically in all three axises according to Gauss- Legendre. Thus, the integration order can be selected in Z88I1.TXT in the material information lines. The order 2 is mostly sufficient. Hexahedron No.1 is also well usable as a thick plate element, if the plate's thickness is not too small against the other dimensions. The element causes high computing load and needs a lot of memory, because the element stiffness matrix has the order 24*24.

Hexahedrons No.1 can be generated by the mesh generator Z88N from super elements Hexahedrons No.10, but Hexahedron No.1 cannot be used as a super element.

Input:

CAD (see chapter 2.7.2):

Upper plane: 1 - 2 - 3 - 4 - 1, quit LINE function
Lower plane: 5 - 6 -7 - 8 - 5, quit LINE function
1 - 5, quit LINE function
2 - 6, quit LINE function
3 - 7, quit LINE function
4 - 8, quit LINE function

Z88I1.TXT
> KFLAG for cartesian (0) or cylindrical coordinates (1)
> IQFLAG=1 if surface and pressure loads for this element are filed in Z88I5.TXT
> 3 degrees of freedom for each node
> Element type is 1
> 8 nodes per element
> Cross-section parameter QPARA is 0 or any other value, has no influence
> Integration order INTORD for each mat info line. 2 is usually good.

Z88I3.TXT
> Integration order INTORD for stress calculation: Can be different from INTORD in Z88I1.TXT.
0 = Calculation of stresses in the corner nodes
1,2,3,4 = Calculation of stresses in the Gauss points

> any KFLAG, has no influence

> Reduced stress flag ISFLAG:
0 = no calculation of reduced stresses
1 = von Mises stresses in the Gauss points ( INTORD not 0 !)
2 = principal stresses in the Gauss points (INTORD not 0!)
3 = Tresca stresses in the Gauss points (INTORD not 0!)

Z88I5.TXT
This file is optional and only used if in addition to nodal forces surface and pressure loads applied onto element no.1:

> Element number with surface and pressure load [Long]

> Pressure, positive if poiting towards the surface [Double]

> Tangential shear, positive in local r direction [Double]

> Tangential shear, positive in local s direction [Double]

> 4 nodes of the loaded surface [4 x Long]

The local r direction is defined by the nodes 1-2, the local s direction is defined by the nodes 1-4. The local nodes 1, 2, 3 , 4 may differ from the local nodes 1, 2, 3, 4 used for the coincidence.

Results:

Displacements in X, Y and Z
Stresses: SIGXX, SIGYY, SIGZZ, TAUXY, TAUYZ, TAUZX, respectively for corner nodes or Gauss points. Optional von Mises stresses.
Nodal forces in X, Y and Z for each element and each node.