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1D elements I: trusses (rod2, rod3), point masses, rotary inertia, springs and dashpots (#38)
* Model, fem and decks: point masses, rotary inertia, springs, dashpots and rod3 trusses Model: PointMass and Spring definitions (spring | dashpot; to ground or two-point; along a degree of freedom, a vector or the line of the ends) on a set or reference point, resolved per node; ElementKind::Rod3. fem: rod2/rod3 truss kernel on Basis::Line2/Line3 declaring ElementDofs (translations). Decks: Abaqus T3D3, MASS, ROTARYI, SPRING1/2/A, DASHPOT1/2/A; Nastran CONM1, CELAS2, CDAMP2; LS-DYNA ELEMENT_MASS/INERTIA and ELEMENT_DISCRETE; what a format cannot take is reported. Commands model.mass.* and model.spring.*. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * Implicit solver: trusses, point masses, rotary inertia and springs on the DofLayout Trusses declare their translations like solids; point masses, inertia and springs ask the layout for the kinds they need at their nodes (translations, rotations), and reference points they use get six degrees of freedom. The matrix pattern takes rows for those points; dashpots are ignored with a warning. Existing results are bit-identical (hash-checked). Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * Explicit solver: trusses, point masses, springs and dashpots on the node-major layout Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * docs: fem.md on trusses and discrete elements in the layout; regenerate features.md Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * docs: trusses in plane models and corotational explicit trusses Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm --------- Co-authored-by: jyviko <[email protected]> Co-authored-by: Claude Opus 5.5 <[email protected]>
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@@ -997,6 +997,12 @@ the module docs):
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distributing (interpolation) constraint as a least-squares rigid fit with loads spread by
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virtual work, G. H. K. Heirman, W. Desmet, Multibody Syst. Dyn. 24(2):219–234, 2010; the
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reduced matrix product T_fᵀ K T_f row by row, F. G. Gustavson, ACM TOMS 4(3):250–269, 1978.
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- Trusses and discrete elements: the isoparametric bar along its arc, R. D. Cook, D. S. Malkus,
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M. E. Plesha, R. J. Witt, *Concepts and Applications of Finite Element Analysis*, 4th ed.,
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Wiley 2002, §3.6 and §6.2, and Hughes 2000, §1.10; springs k [n nᵀ, −n nᵀ; −n nᵀ, n nᵀ],
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Cook et al. 2002, §2.2 and §2.10; HRZ lumping as above. Verified against the method of joints
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(statically determinate trusses), the three-bar truss, the hanging bar, √(k/m), the two-mass
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chain and the torsional pendulum √(k_t/J).
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- Verification: R. H. MacNeal, R. L. Harder, *A proposed standard set of problems to test finite
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element accuracy*, Finite Elem. Anal. Des. 1(1):3–20, 1985 (patch tests); Lamé, Kirsch,
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Timoshenko and Euler–Bernoulli closed forms; Saint-Venant's principle (tension through a
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@@ -1024,6 +1030,10 @@ again in the module docs):
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14(5):437–449, 1998.
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- Bulk viscosity and its time-step correction: J. von Neumann, R. D. Richtmyer, J. Appl. Phys.
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21(3):232–237, 1950; M. L. Wilkins, J. Comput. Phys. 36(3):281–303, 1980.
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- Springs and dashpots: lagged-velocity damping and the damped stable increment
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Δt ≤ (2/ω)(√(1 + ξ²) − ξ), Belytschko et al. 2014, §6.2–6.3; Gershgorin's bound on
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M^{-1/2} K M^{-1/2} per degree of freedom. Verified against the damped oscillator's decay e^{−ξωt}
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and period 2π/ω_d.
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- Rigid walls as kinematic velocity constraints: T. J. R. Hughes, R. L. Taylor, J. L. Sackman,
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A. Curnier, W. Kanoknukulchai, CMAME 8(3):249–276, 1976.
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- Verification: d'Alembert's solution of the 1D wave equation (front at c t, σ = ρ c v), the
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