📉 Analysis

An analysis in Alpaca4d is assembled the same way OpenSees assembles one: from a handful of objects, each answering one question. Analysis Settings collects them, and Run Analysis launches OpenSees.

Damping ─────────┐
Test ────────────┼──► Analysis Settings ──┐
Integrator ──────┤                        ├──► Run Analysis ──► AlpacaModel (with results)
Analysis Step ───┘                        │
                        AlpacaModel ──────┘

Natural Vibration and Linear Buckling are the exceptions: they need no settings at all, because they are eigenvalue problems, with nothing to converge.

Components in this tab

Component	Nickname	Answers
Analysis Settings	Analysis Settings	The whole recipe — handler, numberer, system, algorithm, type.
Integrator	Integrator	How the step advances: LoadControl, Newmark, CentralDifference.
Test	Test	When an iteration has converged.
Analysis Step	Analysis Step	How many steps, and how long each one is.
Damping	Damping	Rayleigh damping coefficients.
Run Analysis	Run Analysis	Runs it.
Natural Vibration	Natural Vibration	Modes, periods and frequencies.
Linear Buckling	Linear Buckling	The load factors the model buckles at, and its buckled shapes.

Analysis Settings

Collects everything OpenSees needs in order to solve — constraint handler, numberer, system of equations, convergence test, solution algorithm, integrator and stepping — into the one object Run Analysis takes.

Every input has a default, so an unconnected component already describes a valid linear static analysis. For a dynamic one set AnalysisType to Transient, and give it a Newmark or CentralDifference Integrator, an Analysis Step with Dt, and a Damping.

Integrator

How the analysis advances from one step to the next.

LoadControl scales the loads by a load factor and is the static integrator; Newmark and CentralDifference step forward in time and are the transient ones.

Test

When an iteration inside a step has converged, and how many iterations to allow before the step is declared failed.

NormDispIncr measures how much the model still moves, NormUnbalance how far it is from equilibrium, and EnergyIncr the product of the two. The Relative units compare against the first iteration instead of an absolute tolerance, and FixedNumIter simply iterates a set number of times.

Analysis Step

How many increments the analysis solves, and how long each one lasts.

NumIncr is also how many steps the recorder writes, so it sets how many steps the Results components can read back. A transient analysis needs Dt as well; DtMin, DtMax and Jd let OpenSees shrink the step when a step will not converge.

Damping

Rayleigh damping for every element and node of the model, as a combination of the mass and stiffness matrices:

D = alphaM*M + betaKcurr*Kcurrent + betaKinit*Kinit + betaKcomm*KlastCommit

For a damping ratio at a known circular frequency omega, taken from a Natural Vibration analysis, stiffness-proportional damping is betaKcomm = 2*ratio/omega — so 5% at omega gives 0.1/omega. Only a transient analysis uses damping.

Run Analysis

Writes the assembled model out as an OpenSees script, solves it, and returns the model with its results attached.

Results are recorded to an MPCO file in the AlpacaResults folder beside the Grasshopper document, and read back by the Results components. An MPCO Recorder chooses what the file holds. When a run fails the AlpacaModel output comes out empty — read the log output to find out why.

Natural Vibration

Solves the eigenvalue problem of the model and returns its modes, eigenvalues, periods and frequencies.

It needs no Analysis Settings — an eigenvalue problem has nothing to converge. Connect the assembled model, or an analysed one for the modes of the model it was analysed from — Section Optimiser's last design, say — then feed the solved model to Nodal Displacements to read a mode shape. The participating masses are in its Modal Report menu.

Linear Buckling

Finds the load factors at which the model buckles under its loads, lowest first, and the shapes it buckles into. The first is the critical load factor α_cr, which EN 1993-1-1 compares with 10 to decide whether a frame needs a second-order analysis.

Like Natural Vibration it needs no Analysis Settings. Connect the assembled model, or an analysed one, as for Natural Vibration, and feed the buckled model to Model View to see a mode. Split the beams with Divisions when a member can buckle on its own, between its ends.

What Alpaca4d can analyse

Analysis	How to set it up
Linear static	Analysis Type Static, Integrator LoadControl, Algorithm Linear.
Non-linear static / pushover	Analysis Type Static, Integrator LoadControl, Algorithm ModifiedNewton or KrylovNewton, and a Linear time series to ramp the load.
Eigenvalue / modal	Natural Vibration — no settings needed.
Linear buckling	Linear Buckling — no settings needed.
Linear or non-linear transient	Analysis Type Transient, Integrator Newmark or CentralDifference, plus Damping and a Path time series.
Seismic time history	As transient, with a UniformExcitation pattern.

A first static analysis

The smallest set-up that works:

1. Integrator → unit LoadControl, defaults are fine.
2. Test → unit NormDispIncr, defaults are fine.
3. Analysis Step → NumIncr = 1 for a linear run.
4. Analysis Settings → plug in the Test, the Integrator and the Analysis Step; leave Analysis Type at Static.
5. Run Analysis → the model and the settings.

Then read the Results.