Path

A Path Time Series defines the relationship between time $t$ and load factor $\lambda$ using user‑specified discrete points:

$$\lambda(t_i) = \lambda_i \quad \text{for} \quad i=1,\dots,n$$

Values between the specified times are typically obtained by linear interpolation. This allows you to reproduce arbitrary time histories, such as recorded ground motions or experimental signals.

🔧 Grasshopper component

The Path Time Series (Alpaca4d) component creates an Alpaca4d path time series from lists of times and values.

• Inputs

  • Times: List of time values $t_i$ $[s]$.

    • Type: List of numbers

    • Requirement: Must be in ascending order and have the same length as Values.

  • Values: List of corresponding load factors $\lambda_i$.

    • Type: List of numbers

    • Requirement: Same count as Times; defines the raw shape of the time series.

  • LoadFactor: Global scale factor $c_\text{factor}$ applied to all Values.

    • Type: Number

    • Default: 1.0

    • Effect: The effective load factor is $\lambda(t) = c_\text{factor} \cdot \lambda_\text{path}(t)$.

• Outputs

  • TimeSeries: Alpaca4d PathTimeSeries object, to be used wherever a time series is required.

  • Graph: A list of values describing the time–history, useful for plotting or checking the input signal in Grasshopper.

📈 When to use a path time series

• Use it when

  • You need to apply recorded time histories (e.g. earthquake acceleration, measured force or displacement).

  • The load pattern is non‑standard and cannot be described by simple analytical functions.

  • You want full control over the shape of the excitation in time.

• Do not use it when

  • A simple constant or linear ramp is sufficient → use Constant or Linear time series.

  • The loading is purely harmonic or periodic → use a Trigonometric time series.

🔗 Relation to OpenSees

Alpaca4d’s path time series corresponds to the OpenSees Path timeSeries:

timeSeries Path $tag -time {t1 t2 ... tn} -values {v1 v2 ... vn} -factor $cFactor

timeSeries('Path', tag,
           '-time',  [t1, t2, ..., tn],
           '-values',[v1, v2, ..., vn],
           '-factor', cFactor)

where:

• the Times input maps to the -time list,

• the Values input maps to the -values list,

• the LoadFactor input corresponds to cFactor.