Analysis types
Linear static, modal, linear buckling and second-order — what each analysis assumes, what it returns and how to read the result.
Analysis types 2 min read
Elementarium ships four analysis types. Each answers a different question, and each rests on assumptions that decide whether the answer means anything.
Every analysis is a named setup stored with the project, and you may have as many as you like. Two setups that differ only in the solver or the mass matrix are a cheap check on each other. Each setup keeps its own results and can be pinned to its own viewer panel.
In this section
- 01Choosing a linear solverConjugate gradients with Jacobi, incomplete Cholesky or multigrid, or a direct factorisation — what each does, how to watch it, and when the choice matters.
- 02Linear bucklingCritical load factors and buckling shapes — what α_cr means, why it is an upper bound, and how to use it for second-order effects.
- 03Linear static analysisThe workhorse analysis — what K u = f actually assumes, what it returns, and where linearity stops being a reasonable model.
- 04Modal analysisNatural frequencies and mode shapes — mass modelling, participation factors and what the numbers are good for.
- 05Second-order analysisP-Δ and P-δ solved by iteration, geometric imperfections to EN 1993-1-1 §5.3, and why a second-order result cannot be superposed.
- 06Verifying the solverClosed-form cases you can build in ten minutes to test the solver — beams, frames, columns, plates, frequencies — with the expected error of each.
The four at a glance
| Analysis | Solves | Combinations |
|---|---|---|
| Linear static | Factored sum of load-case results; no further solve | |
| Modal | None; needs mass (load cases enter only if converted to mass) | |
| Linear buckling | One run per load state or permutation | |
| Second-order | , iterated | One run per combination or permutation |
Choosing the analysis
| Question | Analysis | Returns |
|---|---|---|
| What are the forces and deflections under this combination? | Linear static | Displacements, internal forces, reactions |
| Is this floor going to feel lively? | Modal | Frequencies, mode shapes, participating mass |
| How much margin is there against instability? | Linear buckling | Critical load factor , buckling shapes |
| Does sway matter for the design forces? | Linear buckling, then judgement | compared with the code threshold |
| What are the forces once the sway is accounted for? | Second-order | Amplified displacements, internal forces and reactions |
The assumptions, and which analysis relaxes which
Every analysis in the current release is linear elastic. Three of the four also write equilibrium on the undeformed shape; second-order analysis writes it on the deformed one. All four assume small rotations: second-order here means P-Δ and P-δ, not a large-displacement analysis.
| Assumption | Static, modal, buckling | Second-order |
|---|---|---|
| Material stays elastic — no yielding, cracking or creep | Yes | Yes |
| Equilibrium written on the undeformed shape | Yes | No — on the deformed one, iterated |
| Supports do not gap, lift off or change stiffness | Yes | Yes |
| Sections stay plane and prismatic between nodes | Yes | Yes |
| Results superpose, so combinations are a factored sum | Yes | No — each combination is its own run |
Material and contact nonlinearity (yielding, cracking, supports that lift off) are on the roadmap and not in the current release. Geometric nonlinearity is: see second-order analysis.
Reading results critically
Deflected shape first, then the reaction sum, then one hand check, and only then the peaks. The four questions are written out once, in Troubleshooting, and Your first analysis walks through them on a real model.
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