Yes. Use a time series to define the sinusoid and apply it in a load (force) pattern or as a prescribed displacement (SP) at the top node.

Prescribed displacement (typical for triaxial axial cycling):

set topNode 1001

set A 1.0e-4 ;# amplitude (m)

set T 0.5 ;# period (s)

timeSeries Trig 1 0.0 1.0e10 -factor $A -period $T -shift 0.0

pattern Plain 1 1 {

sp $topNode 3 1.0 ;# DOF 3 (Z): u(t) = 1.0 * timeSeries = A*sin(...)

}

Sinusoidal load instead:

set P0 1.0e3 ;# peak load (N)

timeSeries Trig 2 0.0 1.0e10 -factor $P0 -period $T

pattern Plain 2 2 {

load $topNode 0.0 0.0 1.0

}

Then run a transient analysis:

constraints Plain; numberer RCM; system BandGeneral

test NormDispIncr 1e-8 10; algorithm Newton

integrator Newmark 0.5 0.25; analysis Transient

set dt 0.001; analyze 5000 $dt

Adjust DOF, amplitude, and period to match your setup.

Hi, Carlos. Thank you very much for your response. But my problem is not getting solved by this method. I tried the time series expression that you suggested, but my material is not degrading or failing like in the case of simple earthquake loading, which is used in the code.

What I think is my material is not considering the degradation in the vertical Y direction even when I apply the load but considers it in the horizontal X direction.

I have added both the Matlab and Tcl files for your reference. You can try running this code and see the difference in the results I am talking about.

The result I am expecting is a decreasing amplitude of the sinusoidal graph like I have attached here, but what I am getting is the consistent amplitude sinusoidal curve. I have attached the photos for your reference, but you can also run the code and check for yourself.

Thanks and regards,

Unqualified comments: Sinusoidity, if one may call it, implies in general constant time-space signal characteristics i.e., amplitude frequency etc. One may understandably make use of convolution related models and filter-theory to advantage and purpose and also re-purpose. Quite universal in application, and also useful in problems, at concept level, as in question.

You can keep the base fixed and then impose a time-history displacement directly at the top node as a boundary condition. Instead of uniform excitation, define a sinusoidal function first and then apply it as an enforced motion on the desired degree of freedom of the top node. This way, the waveform is imposed exactly as intended without needing to fix the top nodes.

Hi Yatharth,

Your script applies base acceleration (UniformExcitation) and fixes pore pressure at the top (fix 3 0 0 1 & fix 4 0 0 1), i.e., drained top boundary. That prevents excess pore‐pressure build-up, so you won’t get the stress decay you expect.

To reproduce the “decreasing stress amplitude” under cyclic triaxial loading:

1. Use displacement-control in Y at the top, not base excitation:

# free pore pressure at top (undrained)

fix 3 0 0 0

fix 4 0 0 0

# move top nodes together

equalDOF 3 4 2

# cyclic axial strain (constant amplitude)

set A 1.0e-4 ;# target displacement

set T 1.0

timeSeries Trig 11 0. 1.e10 -factor $A -period $T

pattern Plain 11 11 { sp 3 2 1.0 }

2. Make it undrained: set very low vperm/hperm (e.g., 1e-9) and don’t fix pore‐pressure DOFs on boundaries you want undrained.

3. Keep gravity → switch to plastic stage → run transient.

With constant axial strain amplitude, effective stress should decay cycle-by-cycle as pore pressure rises.