How to prescribe a dynamic displacement

ApplicationPLAXIS 2D
VersionPLAXIS 2D
Date created02 December 2019
Date modified02 December 2019

General aspects

In PLAXIS 2D and 3D, providing that the dynamic module is available, a dynamic displacement can be assigned to any cartesian component of a given prescribed displacement to define its evolution with time. As detailed below, the dynamic displacement is only prescribed to the model when both static and dynamic components of displacement are activated.

Activation of a dynamic displacement

To apply a dynamic displacement in a given dynamic phase, the following conditions should be met:

These conditions are illustrated in the figure below for the case of a horizontal acceleration time-history (i.e., an earthquake motion) to be applied to the bottom boundary of a 2D model. It is important to note that:


Time evolution of a dynamic displacement

When a dynamic displacement is active in a given dynamic phase, the value of each of its components (e.g., along x-direction) at each instant of dynamic time, t, is given by:

ux(t) = ux,start,ref x multiplierx(t)

where ux,start,ref is the reference value of the static component of the prescribed displacement and multiplierx(t) is the time-dependent multiplier of the prescribed displacement.

For instance, assuming that, in a 2D analysis, a given x-component of a dynamic displacement would be defined by a reference value, ux,start,ref, of 0.5 m, as well as by a harmonic multiplier defined in terms of accelerations and characterised by an amplitude of 2.0 m/s2, a frequency of 1.0 Hz and a null phase (as shown in the figure below), the dynamic motion applied to the model at 0.25 s would be equal to:
ax (t = 0.25 s) = -0.5 x 2.0 x sin(2 p x 0.25) = -0.5 x 2.0 = -1.0 m/s2.

Supposing now that two consecutive dynamic phases would be computed, the former having a dynamic time interval of 0.25 s, while the latter having a dynamic time interval of 0.75 s, and that time would not be reset at the start of the second dynamic phase, the first quarter of cycle of the sinusoidal motion (i.e., from 0 to 0.25 s) would be applied to the model during the first phase, while the remaining part of the first cycle (i.e., from 0.25 to 1.0 s) would be applied to the model during the second phase. Please note that the same principle applies when a given dynamic signal is defined by a table of values, rather than by a harmonic function.


See also

How to activate a dynamic load

[Tips and Tricks]