Use the Thermal Expansion subnode to add an internal thermal strain caused by changes in temperature. It is possible to model bending due to a temperature gradient in the thickness direction of the shell.

Thermal expansion can be modeled for the Linear Elastic Material, Layered Linear Elastic Material, or Layered Hyperelastic Material. The thermal expansion can be applied to arbitrary layers in a multilayered shell when the Composite Materials Module analysis is available.

This section is present when this node is added under Layered Linear Elastic Material or Layered Hyperelastic Elastic Material node. In this section, select the layers in which thermal expansion needs to be modeled.

For a multilayered shell, it is often easiest to add one Thermal Expansion node per layer, if the temperature input is manual.

If the same layer is selected in two Thermal Expansion nodes being active on the same boundary, the second definition will override the previous.

The Volume reference temperature Tref is the temperature at which there are no thermal strains. As a default, the value is obtained from a Common model input. You can also select User defined to enter a value or expression for the temperature locally.

The Temperature T is by default obtained from a Common model input. You can also select an existing temperature variable from a heat transfer interface (for example, Temperature (htsh/sol1)), if any temperature variables exist. or manually enter a value or expression by selecting User defined. This is the midsurface temperature of the shell, controlling the membrane part of the thermal expansion. For layered shells, it is the mid-layer temperature for each layer.

If needed, you can add a through-thickness temperature gradient in the Thermal Bending section.

From the Coefficient of thermal expansion α list, select From material to use the coefficient of thermal expansion from the material, or User defined to enter a value or expression for α. Select Isotropic, Diagonal, or Symmetric to enter one or more components for a general coefficient of thermal expansion tensor α. When a nonisotropic coefficient of thermal expansion is used, the axis orientations are given by the coordinate system selection in the parent node.

Enter the Temperature difference in thickness direction ΔTz. This is the temperature difference between the top and bottom surfaces.

From the list, select Temperature difference in thickness direction or Temperature gradient in thickness direction.

When Temperature difference in thickness direction is selected, enter the temperature difference ΔTz between the top surface of the topmost of the selected layers and bottom surface of the bottommost of the selected layers.

When Temperature gradient in thickness direction is selected, enter the temperature gradient T’ in the direction from the bottom surface to the top surface.

Physics tab with Linear Elastic Material, Layered Linear Elastic Material or Layered Hyperelastic Material node selected in the model tree: