forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
8ca2dddeec
Theory cases for the nonlinear solver, each frozen as a fixture: uniaxial stretch of a neo-Hookean block to twice its length (closed form), the nonlinear patch test on a distorted hex8 mesh, a quarter turn of the same mesh (objectivity: zero stress), the elastica of a hex20 cantilever at P L²/(E I) = 1, 2, 5, 10 against Bisshopp–Drucker (0.2–0.5 %), and the inflation of a thick neo-Hookean tube by a follower pressure against Rivlin's closed form (0.08 % at the bore). A finite-strain Cook's membrane is pending its transcribed reference. docs/fem.md describes the formulation, the material point interface, the follower-pressure choice and what nonlinear steps refuse; the literature, parity and roadmap pages follow. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
9 lines
587 B
Markdown
9 lines
587 B
Markdown
# Large-deflection cantilever (elastica)
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A cantilever L = 10, b = 1, h = 0.5 (L/h = 20) of 40 × 1 × 2 hex20 elements, clamped at x = 0,
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E = 10⁴, ν = 0 (an elastic material in a nonlinear step: St Venant–Kirchhoff, exact for large
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rotations with these small strains), under a dead vertical tip force P spread over the end face.
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Four steps at P L²/(E I) = 1, 2, 5 and 10 (rotations of the tip 0.46 to 1.43 rad). The tip's
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neutral-axis node (10, 0, 0.25) is compared with the elastica (Bisshopp–Drucker), whose values
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were computed by shooting and agree with Mattiasson's table.
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