🔍 Which analysis

Each analysis answers a different question about the same model. A static analysis gives the displacements and forces under the loads; Natural Vibration the modes and periods; Linear Buckling the load factor the structure becomes unstable at; a time history the response as it happens; and a moment–curvature analysis how one cross-section behaves up to failure. Pick the analysis by the question.

At a glance

You want	Analysis	Set up with
Displacements, forces and stresses under the loads	Linear static	Run Analysis and Analysis Settings, one step
The same, where supports lift, bars go slack or displacements are large	Non-linear static	Run Analysis, the Newton algorithm, several steps
Periods, frequencies, mode shapes, participating masses	Natural vibration	Natural Vibration, no settings
Whether and when the structure buckles, α_cr	Linear buckling	Linear Buckling, no settings
The response to a ground motion, an impact, a machine	Time history	Run Analysis, AnalysisType Transient
How a cross-section cracks, yields and fails	Moment–curvature	Moment Curvature, a section on its own

Static analysis

A static analysis finds where the structure comes to rest under its loads, with no inertia. It is what Run Analysis does with AnalysisType Static and the LoadControl Integrator, and an Analysis Settings left with its defaults already describes one. A linear model needs one step: one step of LoadControl with Lambda 1 applies the whole load.

A model is non-linear when its stiffness changes as it moves. In Alpaca4d that comes from:

• Compression Only supports, which let go when the node lifts;
• tension-only and compression-only Trusses, which go slack;
• large displacements: trusses are always corotational, and a shell can be made corotational with Is Corotational.

Such a model needs the load in steps. Each step adds the Integrator's Lambda to a pseudo-time, a Linear time series turns that time into a load factor that ramps up, and the Test decides when the iterations of a step have converged. The algorithm matters: Linear does one solve with no iteration, and on a non-linear model it still reports success, with the unconverged first guess. Newton, the default, re-forms the tangent stiffness every iteration. It costs about 20 % more on an elastic model, and is what lets a non-linear step converge at all. Run Analysis warns when the algorithm is Linear and the model has one-way bars or supports.

Natural Vibration

An eigenvalue problem: the modes the structure vibrates in, with their periods and frequencies. There is nothing to converge, so it needs no settings. It is the first analysis worth running on a new model, because a first period far from what you expect means the mass or the stiffness is wrong.

It needs mass, which comes from the material densities and from Mass Points. Gravity Load adds force, not mass. A mode has no size of its own, so each is read with its largest translation 1. The modal report gives the participating masses, and the frequencies are what Damping is tuned to.

Linear Buckling

The load factors at which the structure buckles under its loads, lowest first, and the shapes it buckles into. The first is the critical load factor ${\alpha }_{cr}$, which EN 1993-1-1 compares with 10 to decide whether a frame needs a second-order analysis. It also gives the buckling length of a member for a design check.

It is linear: elastic, about the undeformed shape, with no imperfections. So ${\alpha }_{cr}$ is the elastic critical load factor, not the load the structure can carry: for that, a non-linear static analysis with the imperfections modelled is the tool. Beams buckle in bending only, so lateral-torsional buckling is left to Utilisation. Shells and solids buckle too. A member that can buckle on its own, between its ends, has to be split with Divisions.

Time history

When inertia matters, time is real: a ground motion, an impact, a machine. Run Analysis then runs with AnalysisType Transient, and the pieces change with it:

• Integrator. Newmark, implicit; with γ = 0.5 and β = 0.25, the defaults, it is unconditionally stable and adds no numerical damping. CentralDifference is explicit and stable only for a time step below the critical step of the smallest, stiffest element, which suits short, sharp events.
• Analysis Step. NumIncr × Dt is the duration. Dt has to sample both the input signal and the highest mode of interest.
• Damping. Without it a dynamic model rings indefinitely. Rayleigh damping is tuned to frequencies from Natural Vibration.
• Loads. A time series carries the signal: a Path of times and values, a Trigonometric wave, or a record read from a file. A ground motion is a UniformExcitation pattern, which shakes the whole base in one direction.

Velocities and accelerations are recorded only by a transient analysis. History on the result components reads every step at once.

Moment–curvature

A section-level analysis, not one of the model. A fibre section gives each small area of the cross-section a non-linear material law, and Moment Curvature pushes its curvature under a held axial force to the ultimate state. Out come first yield, the ultimate moment, the ductility and an effective cracked stiffness, all from the material laws. Interaction Domain gives instead what the section carries at the ultimate limit state, for every combination of N, My and Mz.

A fibre section cannot yet be assigned to a beam of the model, whose sections are elastic. The tab is marked βeta.

See also

• Analysis — the objects an analysis is made of
• Analysis Settings — the algorithm, the system and the analysis type
• Time History — choosing a time series
• Moment Curvature — fibre sections
• Results — reading what an analysis found
• Alpaca4d and OpenSees — what happens when an analysis runs