4.7 PLANE STRESS ELEMENT NO.7 WITH 8 NODES

This is a curvilinear Serendipity plane stress element with square shape functions. The transformation is isoparametric. The integration is carried out numerically in both axises according to Gauss- Legendre. Consequently, the integration order can be selected in Z88I1.TXT in the material information lines. The order 3 is mostly sufficient. This element calculates both displacements and stresses very exactly. The integration order can be chosen again for the stress calculation. The stresses are calculated in the corner nodes (good for an overview) or calculated in the Gauss points (substantially more exactly). Pay attention to edge loads when using forces, cf. chapter 3.4. It is easier to enter edge loads via the surface and pressure loads file Z88I5.TXT. You may combine this element with elements no.3 (not recommended) or elements no.14 (good).

Plane Stress Elements No.7 can be generated by the mesh generator Z88N from super elements Plane Stress Elements No.7 or No.11 . Thus, the Plane Stress Element No.7 is well suited as super element.

Plane Stress Element No.7 is recommended for all sort of plane stress computation. This element is well-balanced in respect to the precision of displacement and stress calculation as well as to its needs for memory and computing power.

Input:

CAD (see chapter 2.7.2): 1-5-2-6-3-7-4-8-1

Z88I1.TXT
> KFLAG for cartesian (0) or polar coordinates (1)
> IQFLAG=1 if edge loads for this element are filed in Z88I5.TXT
> 2 degrees of freedom for each node
> Element type is 7
> 8 nodes per element
> Cross-section parameter QPARA is the element thickness
> Integration order INTORD per each mat info line. 3 is usually good.

Z88I3.TXT
> Integration order INTORD: Basically, it is a good idea to use the same value as chosen in Z88I1.TXT , but different values are permitted
0 = Calculation of the stresses in the corner nodes
1,2,3,4 = Calculation of the stresses in the Gauss points

> KFLAG = 0: Calculation of SIGXX, SIGYY and TAUXY
> KFLAG = 1: Additional calculation of SIGRR, SIGTT and TAURT

> 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 edge loads applied onto element no.7:

> Element number with surface and pressure load [Long]

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

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

> 2 corner nodes and one mid node of the loaded surface [3 x Long]

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

Results:

Displacements ino X and Y.
Stresses: The stresses are calculated in the corner nodes or Gauss points and printed along with their locations. For KFLAG = 1 the radial stresses SIGRR, the tangential stresses SIGTT and the accompanying shear stresses SIGRT are computed additionally (makes only sense if a rotational-symmetric structure is available). For easier orientation the respective radiuses and angles of the nodes/points are printed. Optional von Mises stresses
Nodal forces in X and Y for each element and each node.