4.10 HEXAHEDRON NO.10 WITH 20 NODES

This is a curvilinear Serendipity volume element with square shape functions. The transformation is isoparametric. The integration is carried out numerically in all axises according to Gauss- Legendre. Thus, the integration order can be selected in Z88I1.TXT in the material information lines. The order 3 is good. This element calculates both displacements and stresses very exactly. The quality of the displacement and stress calculations are far better than the results of the hexahedron element No.1.

Hexahedron No.1 also applies well for thick plate elements, if the plate's thickness is not too small compared to the other dimensions.

The element causes an enormous computing load and needs an extreme amount of memory because the element stiffness matrix has the order 60*60. Pay attention to surface and pressure loads when using forces, cf. chapter 3.4. It is easier to enter these loads via the surface and pressure loads file Z88I5.TXT.

The nodal numbering of the element No.10 must be done carefully and must exactly match the sketch below. Pay attention to the location of the axis system ! The possible error message " Jacobi determinant zero or negative " is a hint for incorrect node numbering.

Hexahedron No.10 can be generated by the mesh generator Z88N from super elements Hexahedron No.10. Thus, the Hexahedron No.10 is well suited as super element. Hexahedron No.10 can also generate 8-node Hexahedrons No.1, see chapter 4.1.

Hexahedron No.10 is recommended for all sort of deflection and stress computation in space. Though its need for memory and computing power is enormous, this element gives precise results for displacements and stresses. Or use it as superelements for meshing Hexahedrons No.1 with 8 nodes.

Input:

CAD (see chapter 2.7.2):
Upper plane: 1 - 9 - 2 - 10 - 3 - 11 - 4 -12 - 1, quit LINE function
Lower plane: 5 - 13 - 6 - 14 - 7 - 15 - 8 - 16 - 5, quit LINE function
1 - 17 - 5, quit LINE function
2 - 18 - 6, quit LINE function
3 - 19 - 7, quit LINE function
4 - 20 - 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 10
> 20 nodes per element
> Cross-section parameter QPARA is 0 or any value, has no influence
> Integration order INTORD for each mat info line. 3 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

> KFLAG , any, 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.10:

> 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.