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Shells and beams: MITC4/MITC3 shells, Timoshenko beams, six-DOF nodes (M4) (#47)

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* fem: MITC4/MITC3 flat shells and Timoshenko beams with profile properties (ElementDofs STRUCTURAL)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* solver: shells and beams on the DofLayout beside solids, 2D elements and trusses; analytic verification and tagged benchmarks

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* engine: probe rotations, reaction moments and shell and beam element results; docs for shells and beams

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

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Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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Irakli KourtisClaude Opus 5.5jyviko
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docs/solvers/literature.md
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@@ -1003,6 +1003,24 @@ the module docs):
Cook et al. 2002, §2.2 and §2.10; HRZ lumping as above. Verified against the method of joints
(statically determinate trusses), the three-bar truss, the hanging bar, √(k/m), the two-mass
chain and the torsional pendulum √(k_t/J).
- Shells: E. N. Dvorkin, K.-J. Bathe, *A continuum mechanics based four-node shell element for
general nonlinear analysis*, Engineering Computations 1(1):77–88, 1984 (MITC4 shear tying);
K.-J. Bathe, E. N. Dvorkin, IJNME 21(2):367–383, 1985 (the flat-plate form); P.-S. Lee,
K.-J. Bathe, *Development of MITC isotropic triangular shell finite elements*, Computers &
Structures 82(11–13):945–962, 2004 (MITC3); T. J. R. Hughes, F. Brezzi, *On drilling degrees of
freedom*, CMAME 72(1):105–121, 1989 (drilling penalty); facet shells, O. C. Zienkiewicz,
R. L. Taylor, D. D. Fox, *The Finite Element Method for Solid and Structural Mechanics*, 7th
ed., 2014, ch. 9–10.
- Beams: J. S. Przemieniecki, *Theory of Matrix Structural Analysis*, McGraw-Hill 1968, §5.6;
Z. Friedman, J. B. Kosmatka, Computers & Structures 47(3):473–481, 1993 (interdependent
Timoshenko interpolation); G. R. Cowper, J. Appl. Mech. 33(2):335–340, 1966 (shear
coefficients); S. P. Timoshenko, J. N. Goodier, *Theory of Elasticity*, 3rd ed., 1970, §109
(torsion of a rectangle); W. D. Pilkey, *Analysis and Design of Elastic Beams*, Wiley 2002
(thin-walled shear areas and torsion).
- Shell benchmarks (published values, tagged, not the analytic gate): Scordelis–Lo roof 0.3024
(MacNeal & Harder 1985); pinched cylinder 1.8248 · 10⁻⁵ (T. Belytschko, H. Stolarski, W. K.
Liu, N. Carpenter, J. S.-J. Ong, CMAME 51(1–3):221–258, 1985). Plate: S. Timoshenko,
S. Woinowsky-Krieger, *Theory of Plates and Shells*, 2nd ed., 1959, §30 (Navier).
- Verification: R. H. MacNeal, R. L. Harder, *A proposed standard set of problems to test finite
element accuracy*, Finite Elem. Anal. Des. 1(1):3–20, 1985 (patch tests); Lamé, Kirsch,
Timoshenko and Euler–Bernoulli closed forms; Saint-Venant's principle (tension through a