analysis::nonlinear_dynamic::NonlinearDynamicAnalysis: Newmark-beta with
a full Newton solve on the internal force inside every step — residual
F_ext − f_int(u) − M a(u), consistent Jacobian K_T(u) + M/(beta dt^2),
the same total-Lagrangian St. Venant–Kirchhoff / small-strain seam the
nonlinear static analysis uses, consistent mass assembled once (element
mass is configuration-independent in a total-Lagrangian setting),
undamped, homogeneous Dirichlet only (prescribed interface motion
arrives with the FSI rung). The existing NewmarkStepper stays what it
is: the right tool for constant matrices.
Verified (tests/nonlinear_newmark_csm3.rs):
- linear limit (strains ~1e-9): the TL nonlinear stepper reproduces the
verified linear NewmarkStepper on the same dense M, K, F to a max
deviation of 1.7e-16 — 1.3e-9 of the oscillation amplitude — over 120
steps;
- Turek–Hron CSM3 (35x2 Quad8, dt = 0.005, gravity switched on at rest,
6 s): ux(A) = −14.291 ± 14.291 mm vs the reference −14.305 ± 14.305
(0.1%); uy(A) = −63.644 ± 64.295 mm vs −63.607 ± 65.160 (0.06% mean,
1.3% amplitude); frequency 1.1020 Hz vs 1.0995 (0.23%); two Newton
iterations per step throughout; the undamped amplitude persists
(half-window drift 0.2%).
rtx-fea 564 -> 566 green (full suite).
With this the S-side of the Turek–Hron ladder is complete: statics
(CSM1/CSM2) and dynamics (CSM3) both land on the benchmark. Next rung is
the coupling: FSI1 with the embedded fluid, the TL flag, and rtx-fsi's
transfer rebuilt on the deformed interface each subiteration.
Co-Authored-By: Claude Fable 5 <[email protected]>
