1.2.6 Time Dependency for Nodes

1.2.6.1 Nodes Attached to Continuum Elements

For nodes attached to continuum elements the ambient variable (T , C , M , P ) must be specified.

    (syntax)

at1 ...atn

are the values of the ambient variables (T , C , M , P ) at times t1 to tn respectively.

    (file.dat)

'TEMPER'
NODES
     0. 10. 30.
 1
     0. +200. +300.
 / 2-8 /
     0. +100. +400.

This example specifies temperatures at times t₁ = 0 , t₂ = 10 and t₃ = 30 . The temperatures for node 1 are T₁ = 0° , T₂ = 200° and T₃ = 300° . The temperatures for nodes 2 to 8 are T₁ = 0° , T₂ = 100° and T₃ = 400° .

1.2.6.2 Nodes Attached to Shell Elements

For nodes attached to shell elements, the average value of the ambient variable ($\bar{{T}}$ , $\bar{{C}}$ , $\bar{{r}}$ ) and its gradient through the thickness ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P ) must be specified.

    (syntax)

at1 ...atn

are the average values ($\bar{{T}}$ , $\bar{{C}}$ , $\bar{{M}}$ , $\bar{{P}}$ ) at times t1 to tn respectively.

dt1 ...dtn

are the gradients ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P )) at times t1 to tn respectively.

    (file.dat)

'TEMPER'
NODES
     0. 10. 30.
 1
     0. +200. +300.
     0. +5. +2.
 / 2-8 /
     0. +100. +400.
     0. +7. +2.

This example specifies temperatures at times t₁ = 0 , t₂ = 10 and t₃ = 30 . The temperatures for node 1 are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 200° and $\bar{{T}}_{{3}}^{}$ = 300° . The temperature gradients for node 1 are $\Delta$T₁ = 0° , $\Delta$T₂ = 5° and $\Delta$T₃ = 2° . The temperatures for nodes 2 to 8 are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 100° and $\bar{{T}}_{{3}}^{}$ = 400° . The temperature gradients for nodes 2 to 8 are $\Delta$T₁ = 0° , $\Delta$T₂ = 7° and $\Delta$T₃ = 2° .

1.2.6.3 Nodes Attached to Beam Elements

For nodes attached to beam elements, the value of the ambient variable (T , C , M , P ) and its gradient ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P [§1.2]) must be specified. For nodes attached to three-dimensional beam elements two gradients must be specified: in element y and z direction respectively.

Two-dimensional    (syntax)

at1 ...atn

are the average values ($\bar{{T}}$ , $\bar{{C}}$ , $\bar{{M}}$ , $\bar{{P}}$ ) at times t1 to tn respectively.

yt1 ...ytn

are the gradients ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P ) in the element y direction at times t1 to tn respectively.

Additional for three-dimensional    (syntax)

zt1 ...ztn

are the values of the gradients ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P ) in the element z direction. Further description and conditions analogous to the y gradients.

Two-dimensional    (file.dat)

'TEMPER'
NODES
     0. 10. 30.
 / 1-8 /
     0.  +200.   +300.
     0.   -10.    +15.

This example specifies a uniform temperature distribution for nodes which are attached to two-dimensional beam elements. The temperatures are given for times t₁ = 0 , t₂ = 10 and t₃ = 30 . For nodes 1 to 8 the average temperatures are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 200° and $\bar{{T}}_{{3}}^{}$ = 300° . The temperature gradients in element y direction at the same times and for the same nodes are $\Delta$T₁ = 0° , $\Delta$T₂ = - 10° and $\Delta$T₃ = 15° . This means that at t₁ the upper and lower fiber in y direction have the same temperature, at t₂ the upper fiber in y direction is 10° colder than the lower fiber and at t₃ the upper fiber in y direction is 15° warmer than the lower fiber.