Linear

A Linear Time Series defines a time–history where the load factor $\lambda$ varies linearly with time:

$$\lambda(t) = c_\text{factor} \, t$$

where $c_\text{factor}$ is a constant slope. This is useful when you want loads to ramp up (or down, if negative) at a constant rate as the analysis time increases.

🔧 Grasshopper component

The Linear Time Series (Alpaca4d) component creates an Alpaca4d linear time series that can be connected to load pattern or excitation components.

• Input

  • LinearFactor: Linear scale factor $c_\text{factor}$ that multiplies time $t$.

    • Type: Number

    • Default: 1.0

    • Effect: The load factor increases (or decreases) proportionally to time: doubling the analysis time doubles the load factor.

• Outputs

  • TimeSeries: Alpaca4d Linear time series object, to be plugged into components that require a time series.

  • Graph: A list of values representing the time series, typically visualised as a straight line increasing with time.

📈 When to use a linear time series

• Use it when

  • You want a ramp load that grows from zero to a target value over a given duration.

  • You need to gradually apply loads to avoid sudden jumps (e.g. quasi‑static ramping in nonlinear analysis).

  • You are modelling a linearly increasing excitation intensity.

• Do not use it when

  • The load should be constant in time → use a Constant time series.

  • The load follows a recorded or arbitrary signal → use a Path / Time History time series.

  • The load is cyclic or periodic → use a Trigonometric time series.

🔗 Relation to OpenSees

Alpaca4d’s linear time series is conceptually equivalent to the OpenSees Linear timeSeries:

timeSeries Linear $tag -factor $cFactor

timeSeries('Linear', tag, '-factor', cFactor)

where cFactor corresponds to the LinearFactor input in the Alpaca4d Grasshopper component.