Analyses#
Runnable examples organised by the kind of analysis rather than which element happens to be used. Each sub-gallery walks through the full loop — build the model, solve, interpret the result — for one analysis family.
\(K u = F\). Cantilever deflections, plane-stress / plane-strain problems, single-element patch tests.
\(K \varphi = \omega^2 M \varphi\). Plate modes, SDOF oscillators, beam cantilever frequencies.
\(M \ddot u + C \dot u + K u = F(t)\) via Newmark-β.
Cyclic-symmetry modal on a base sector with phase constraints.
Cyclic-symmetry modal#
Modal analysis of rotationally periodic structures — compute the full rotor’s spectrum from a single base sector plus phase constraints.
Cyclic-symmetry travelling-wave pair — bladed rotor
Harmonic analysis#
Frequency-response sweeps via modal superposition — \((K - \omega^2 M + i\,\omega C)\,u(\omega) = F\). The complex receptance is back-substituted from a precomputed eigenbasis at every excitation frequency.
SDOF receptance — closed form vs modal superposition
Modal analysis#
Free-vibration modes — \(K \varphi = \omega^2 M \varphi\). Plate modes, SDOF oscillators, beam cantilever frequencies.
HEX8 — cantilever-plate modal (2 × 40 × 40 hex mesh)
Static analysis#
\(K u = F\) with Dirichlet BCs. The workhorse analysis — one factorisation, one back-solve.
Transient analysis#
Time-domain simulations of the equation of motion \(M \ddot u + C \dot u + K u = F(t)\) using Newmark-β.
