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 !)

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.