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femorph-solver

  • Getting started
  • User guide
  • Reference
  • Verification
  • Examples
    • API reference
    • Changelog
    • Provenance inventory
  • GitHub
  • Getting started
  • User guide
  • Reference
  • Verification
  • Examples
  • API reference
  • Changelog
  • Provenance inventory
  • GitHub

Section Navigation

  • Quickstart
    • Static cantilever — first example
    • Modal cantilever — first modal example
  • Pre-processing
    • Loading a CDB input deck
    • Building a model from a pyvista grid
  • Analyses
  • Post-processing
    • Exporting results to VTK / ParaView
    • Plotting mode shapes
    • HEX8 — elastic-strain post-processing
  • Elements
  • Verification gallery
    • Irons constant-strain patch test
    • Single-hex uniaxial tension — Hooke’s law + Poisson check
    • Cantilever tip deflection — Euler-Bernoulli closed form
    • NAFEMS LE1 — elliptic membrane (plane stress)
    • Clamped square plate under uniform pressure (NAFEMS LE5)
    • Cantilever under uniformly distributed load — Euler–Bernoulli closed form
    • Cantilever natural frequency — Rao 2017 Table 8.1
    • Fixed-free axial rod — natural frequencies
    • Clamped-clamped beam — first three bending natural frequencies
    • Pinched ring — Castigliano diametrical deflection
    • Cantilever Saint-Venant torsion — rectangular cross-section
    • Simply-supported plate — first transverse bending mode
    • Plate with a circular hole — Kirsch stress concentration
    • Simply-supported plate under uniform pressure (Navier series)
    • Shear-locking demonstration — HEX8 integration variants
    • Cantilever beam under a tip moment
    • Cantilever beam — first four bending modes
    • Clamped-clamped beam under a central point load
    • Simply-supported beam under a central point load
    • Propped cantilever under uniformly-distributed load
    • Mesh-refinement convergence — cantilever Euler-Bernoulli
    • Mesh-refinement convergence — Lamé thick cylinder
    • Lamé thick-walled cylinder under internal pressure
    • Continuous beam over three supports — Clapeyron’s three-moment theorem
    • Cook’s membrane — mesh-distortion benchmark (1974)
  • Examples
  • Analyses
  • Modal analysis

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)

HEX8 — cantilever-plate modal (2 × 40 × 40 hex mesh)
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