1.2 Ambient Time Dependency

If the actual properties of a material are influenced by the temperature, the concentration, the maturity, or the pressure then you must specify the time dependency of these ambient phenomena in table 'TEMPER' [§1.2.1], 'CONCEN' [§1.2.2], 'MATURI' [§1.2.3], or 'PRESSU' [§1.2.4] respectively. These tables list the temperature T , concentration C , maturity M , or pressure P as a function of time for each node of the specified elements or for each specified node.

When executing time steps, DIANA interpolates the T -, C -, M -, or P -field for the step time. The temperatures and/or concentrations in combination with expansion coefficients $\alpha$ and/or $\gamma$ are used to determine expansion strains. The pressure differences during the time step give an element load. All ambient phenomena are taken into account for the ambient dependent material properties, if any.

Element types.

Ambient time dependency can be specified for three categories of elements [§1.2.5], or for nodes attached to one of these categories [§1.2.6]:

• Continuum elements: numerically integrated isoparametric elements for trusses, plane stress, plane strain, axisymmetry and solids. These elements require one single value per node.

• Shell elements: all curved, infinite and axisymmetric shell elements. These elements require two values per node: a mean value and a gradient ($\Delta$ ) over the thickness.

• Beam elements: all two-dimensional and three-dimensional beam elements. Two-dimensional beam elements require two values per node: a mean value and a gradient ( $\Delta_{{y}}^{}$ ) over the thickness. Three-dimensional beam elements require an additional gradient ( $\Delta_{{z}}^{}$ ).

  The meaning of the gradients depends on the input of the beam cross-section in table 'GEOMET' [Vol. Element Library]. If the cross-section is specified with a predefined shape or with a profile, then the gradient is the difference between the value in the `positive' and the `negative' fiber. If the cross-section of a class-I beam element is specified with an arbitrary shape, then DIANA does not know the distance between the extreme fibers. Therefore, you must specify the gradients per unit length, e.g. for temperature  dT/y and  dT/z .