1.2.5 Time Dependency for Elements

1.2.5.1 Continuum Elements

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

    (syntax)

a1t1 ...a1tn

are the values of the ambient variables (T , C , M , P ) at times t1 to tn respectively. If only this set of values is specified, then the distribution is uniform: all nodes of the element(s) get the same value. Else, these values are for the first node only, a2t1 to a2tn for the second node until aet1 to aetn for the last node.

    (file.dat)

'TEMPER'
     0. 10. 30.
 1
     0. +200. +300.   0. +200. +300.   0. +200. +300.
     0. +300. +500.   0. +300. +500.   0. +300. +500.
 / 2-8 /
     0. +100. +400.

This example specifies temperatures at times t₁ = 0 , t₂ = 10 and t₃ = 30 . Element 1 has six nodes. The temperatures for the first three nodes are T₁ = 0° , T₂ = 200° and T₃ = 300° and for the last three nodes T₁ = 0° , T₂ = 300° and T₃ = 500° (note that it is not necessary to specify the temperatures for each node on a separate line). The temperatures for all nodes of elements 2 to 8 are T₁ = 0° , T₂ = 100° and T₃ = 400° .

1.2.5.2 Shell Elements

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

    (syntax)

a1t1 ...a1tn

are the average values ($\bar{{T}}$ , $\bar{{C}}$ , $\bar{{M}}$ , $\bar{{P}}$ ) at times t1 to tn respectively. If only this set of values is specified, then the distribution is uniform: all nodes of the element(s) get the same value. Else, these values are for the first node only, a2t1 to a2tn for the second node until aet1 to aetn for the last node.

d1t1 ...d1tn

are the gradients ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P ) at times t1 to tn respectively. For uniform distribution only this set is necessary. Nonuniform distribution requires d2t1 to a2tn for the second node until det1 to detn for the last node.

    (file.dat)

'TEMPER'
     0. 10. 30.
 1
     0. +200. +300.   0. +200. +300.   0. +200. +300.
     0. +300. +500.   0. +300. +500.   0. +300. +500.
     0.   +5.   +2.   0.   +5.   +2.   0.   +5.   +2.
     0.   +7.   +2.   0.   +7.   +2.   0.   +7.   +2.
 / 2-8 /
     0. +100. +400.   0.   +5.   +2.

This example specifies temperatures at times t₁ = 0 , t₂ = 10 and t₃ = 30 . Element 1 has six nodes. The temperatures for the first three nodes are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 200° and $\bar{{T}}_{{3}}^{}$ = 300° and for the last three nodes $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 300° and $\bar{{T}}_{{3}}^{}$ = 500° . The temperature gradients for the first three nodes are $\Delta$T₁ = 0° , $\Delta$T₂ = 5° and $\Delta$T₃ = 2° and for the last three nodes $\Delta$T₁ = 0° , $\Delta$T₂ = 7° and $\Delta$T₃ = 2° . Note that it is not necessary to specify the temperatures for each node on a separate line. The temperatures for all nodes of elements 2 to 8 are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 100° and $\bar{{T}}_{{3}}^{}$ = 400° . The temperature gradients for all nodes are $\Delta$T₁ = 0° , $\Delta$T₂ = 5° and $\Delta$T₃ = 2° . Note that it is not necessary to specify the temperature gradients on a separate line.

1.2.5.3 Beam Elements

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

Two-dimensional    (syntax)

a1t1 ...a1tn

are the average values ($\bar{{T}}$ , $\bar{{C}}$ , $\bar{{M}}$ , $\bar{{P}}$ ) at times t1 to tn respectively. If only this set of values is specified, then the temperature is uniform: all nodes of the element(s) get the same value. Else, these values are for the first node only, a2t1 to a2tn for the second node until aet1 to aetn for the last node.

y1t1 ...y1tn

are the gradients ($\Delta$T , $\Delta$C , $\Delta$M , $\Delta$P ) in the element y direction at times t1 to tn respectively. For uniform distribution only this set is necessary. Nonuniform distribution requires y2t1 to a2tn for the second node until yet1 to yetn for the last node.

Additional for three-dimensional    (syntax)

z1t1 ...z1tn

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.

Uniform, two-dimensional    (file.dat)

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

This example specifies a uniform temperature distribution for a two-dimensional beam element at times t₁ = 0 , t₂ = 10 and t₃ = 30 . The average temperatures are $\bar{{T}}_{{1}}^{}$ = 0° , $\bar{{T}}_{{2}}^{}$ = 200° and $\bar{{T}}_{{3}}^{}$ = 300° for all nodes. The temperature gradients in element y direction at the same times are $\Delta$T₁ = 0° , $\Delta$T₂ = - 10° and $\Delta$T₃ = 15° for all nodes. 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.

Nonuniform, three-dimensional    (file.dat)

'TEMPER'
     0. 10. 30. 50.
 1
     0. +200. +300. +428.    0. +237. +348. +565.   0. +150. +258. +483.
     0.  -10.  +15.  +34.    0.  -12.  +22.  +29.   0.   -8.  +17.  +26.
     0.  -13.  +24.  +62.    0.  -15.  +28.  +45.   0.   -4.  +36.  +61.

This example specifies a nonuniform temperature distribution for a three-dimensional beam element with three nodes at times t₁ = 0 , t₂ = 10 , t₃ = 30 and t₄ = 50 .