Surface traction, pressure

A surface traction acting on the face of an element can be prescribed in any load case. Pressure is a special case of a general surface traction, which can conveniently be specified in the local system of the outward normal.

In the name.i2 file, a vector is first defined using a SV set:

SV set number T 9 V $q_x$ $q_y$ $q_z$

or

SV set number T 6 V $q_n$

and the set thus defined is then assigned to the face of the selected elements:

AS load case number /$\dots$ /S set number E element number list S face number /$\dots$

where

$q_x,q_y,q_z~[\text{Pa}]$ are the components of the stress in the direction of the global axes,
$q_n~[\text{Pa}]$ is the stress perpendicular to the face of the element, acting in the direction of the outward normal of the element face (the pressure $p$ is specified negatively, i.e., $q_n=-p$).

Note
Faces and their local numbers are defined for isoparametric elements and semi-loof elements, see the Reference Manual. For 2D isoparametric elements, the edge of the element is considered its face, since it has a nonzero thickness (and therefore also an area). For semi-loof elements, only one face is defined (the midsurface), whose orientation is given by the normal $\zeta$, see the Reference Manual. A negatively specified pressure acts on the top side of the surface; a positively specified pressure acts on the bottom side of the surface.

Note
More than one assignment of surface tractions to a single element face may occur within a single load case. In that case, the force components are added together.

Note
The components of the vector can depend on the global coordinates $x,y,z$, using any of the available functional dependencies, see the Reference Manual.

Example

Let us consider the hydrostatic water pressure $p=rg(h-z)$ acting on the wall of a container $h=5~\text{m}$, so that $rg=10000~\text{Pa/m}$ and $rgh=50000~\text{Pa}$.

We describe the dependence of the pressure $p$ on the coordinate $z$ using a polynomial dependence $p(z)=50000-10000z$, see the Reference Manual. According to the Reference Manual, the global coordinate $z$ has identification number 3, hence

SV 1 T -6 I 3 V -50000 10000

By specifying the pressure $-p$ using set 1, we tacitly assumed that the normals of all shell elements point into the container. However, the sense of the normals is determined by the topology of the elements, and the normals of all elements need not be oriented consistently, see the Reference Manual. We therefore define another set

SV 2 T -6 I 3 V 50000 -10000

which we assign to the elements whose normal points out of the container.

The assignment will take the form

AS <load case> / …
  /S 1 E <elements> S 1 ; elements with the normal pointing inward
  /S 2 E <elements> S 1 ; elements with the normal pointing outward
  / …