Result objects#

Every solver returns a lightweight dataclass carrying the full-length arrays for every DOF of the original model — even the ones that were prescribed or fell out as rigid-body. That keeps downstream indexing simple: a mode shape of length N lines up 1-to-1 with Model.dof_map(), and slicing by node number Just Works.

StaticResult#

Returned by solve_static() and Model.solve():

Field	Shape	Meaning
`displacement`	`(N,)`	Global displacement at every DOF; zeros at Dirichlet-fixed DOFs.
`reaction`	`(N,)`	Reaction force at constrained DOFs, zeros elsewhere.
`free_mask`	`(N,)` bool	`True` where the DOF was solved (not Dirichlet, non-trivial diagonal).

result = solve_static(K, F, prescribed={0: 0.0, 1: 0.0, 2: 0.0})
u_tip = result.displacement[dof_map_tip]
R_total_y = result.reaction[1::3].sum()   # Σ of all UY reactions

ModalResult#

Returned by solve_modal() and Model.modal_solve():

Field	Shape	Meaning
`omega_sq`	`(n_modes,)`	Eigenvalues \(\omega^2 = (2\pi f)^2\); numerically negative values are clipped to 0.
`frequency`	`(n_modes,)`	Cyclic frequencies \(f\) in Hz (\(\sqrt{\omega^2} / (2\pi)\)).
`mode_shapes`	`(N, n_modes)`	Each column is a full-length eigenvector.
`free_mask`	`(N,)` bool	`True` where the DOF participated in the eigenproblem.

result = solve_modal(K, M, prescribed=fixed, n_modes=10,
                     eigen_solver="arpack", sigma=-1.0)
first_bending = result.mode_shapes[:, 6].reshape(-1, 3)   # 6 rigid-body modes skipped
f1 = result.frequency[6]

TransientResult#

Returned by solve_transient() and Model.transient_solve():

Field	Shape	Meaning
`time`	`(n_steps + 1,)`	Time grid including \(t = 0\).
`displacement`	`(n_steps + 1, N)`	Displacement history.
`velocity`	`(n_steps + 1, N)`	Velocity history.
`acceleration`	`(n_steps + 1, N)`	Acceleration history.

result = solve_transient(K, M, F=load, dt=1e-4, n_steps=1000,
                         prescribed=fixed)
u_tip_t = result.displacement[:, dof_map_tip]   # tip vs time

CyclicModalResult#

Returned by solve_cyclic_modal() — one per requested harmonic index. See Cyclic-symmetry modal analysis.

Field	Shape	Meaning
`harmonic_index`	`int`	The k for this result.
`n_sectors`	`int`	Number of sectors in the full rotor.
`omega_sq` / `frequency`	`(n_modes,)`	Eigenvalues and Hz frequencies at this k.
`mode_shapes`	`(N, n_modes)` complex	Base-sector complex mode shape; imaginary part is identically 0 for k=0 and k=N/2.

See also#

Strain and stress recovery — deriving \(\varepsilon\) and \(\sigma\) from displacement.
Visualisation and export — getting the arrays into pyvista for plotting.
The Model — what Model.dof_map() returns.