Dynamic

*Dynamic

*Dynamic
<Delta t_0>, <t_step>, <Delta t_min>, <Delta t_max>
<Time integration procedure>

This procedure is used to calculate the response of a structure subject to dynamic loading using a direct integration procedure of the equations of motion. Both following lines are mandatory. In a dynamic step, loads are by default applied by their full magnitude at the start of the step. Other loading patterns can be prescribed by using previously defined amplitudes.

• The first line specifies the time incrementation. Therein \(\Delta t_0\) is the size of the initial time increment, \(t_{step}\) is the overall step time, \(\Delta t_{min}\) is the minimum allowed time increment and \(\Delta t_{max}\) is the maximum allowed time increment.

• <Time integration procedure>

• Use this parameter to choose the time integration method. Note the asterisk starting the keyword.

  • If *Hilber-Hughes-Taylor is chosen, the line may be extended by up to three parameters (=<\(\alpha\)>,<\(\beta\)>,<\(\gamma\)>), defining the Hilber-Hughes-Taylor parameters. The smaller the value of the parameter \(\alpha\), the greater the numerical dissipation (note that \(\alpha \leq 0\) holds). The following options are available:

    • Only the parameter \(\alpha\) is given by the user. \(\beta\) and \(\gamma\) are calculated using the following relations \(\beta=(1-\alpha^2)/4\) and \(\gamma=1/2 - \alpha\). For \(\alpha = 0\) the Newmark's method is recovered. Notice that only then a second order accuracy is achieved in linear problems, otherwise the method has only first order accuracy.

    • All three parameters are given in the following order: \(\alpha, \beta, \gamma\). Note that depending on the user's entries for \(\beta\) and \(\gamma\) the aforementioned relations may be disrespected.

  • If *Backward Euler is chosen, no further information is required. The parameters of the Hilber-Hughes-Taylor time integration scheme are set to \(\alpha=0\), \(\beta=1.0\) and \(\gamma=1.0\). Furthermore, a central differences scheme is used to calculate the time derivatives of the solution. Note that by using the Backward Euler integration scheme, significant damping may be introduced to the calculation.