Package for Machine Design

Finite Element Analysis in Structural Mechanics

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Nonuniform temperature field

A nonuniform temperature field has the meaning of the resulting temperature (working temperature) and can be prescribed in any load case.

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

GV set number T 6 V prescribed values

or

GV set number T 6 D 4 record number

and the set thus defined is then assigned to the entire body:

AS load case number /$\dots$ /G set number /$\dots$

The first set form is used to specify the vector directly, whereby the order of the nodes and the order of the components at the nodes must be followed:

OrderNode types
$T$ node of an isoparametric or bar element
corner node of a semi-loof element
$T$ $\Delta T$ midside node of a semi-loof element, see the Reference Manual
$T_\xi$ $T_\eta$ $T_\zeta$node of a beam element, see the Reference Manual

The length of the vector, i.e., the number of prescribed values after the key letter V, must exactly match the number of thermal degrees of freedom of the mesh.

The second set form is used to read the vector from the name.TEM file (a previously computed steady-state or transient temperature field).

Note
The temperature difference is taken relative to the temperature $T_o$. If $T_o=T_w\ne0$ is specified, the temperature field prescribed by the GV set is not taken into account for the calculation of stresses, but is written to the output file name.STR. If the prescribed temperature field is to be taken into account for the calculation of stresses, it is necessary to formally specify $T_w\ne T_o$. The value of $T_w$ then plays no role, since it is overwritten by the GV set.

Example

Let us consider a temperature field for a mesh consisting of isoparametric elements. The number of nodes in the mesh is 22. Each node has one degree of freedom, $T$.

In the GV set, the prescribed values after the key letter V will be in the order $T_1$ $T_2$ $\dots$ $T_{21}$ $T_{22}$.