feat(examples): migrate TH-141 sample to declarative layout (WU-6)

Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment,
15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest
to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) +
per-element element.toml (kind + scalars; examples carry `source`). Content .typ
files copied byte-identical (no math corruption); per-element main.typ + meta.toml
dropped (wiring is now generated). Part order matches source exactly; 5 lemmas
have no proof.typ (optional); no cross-file imports / paralearn refs / figs.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
This commit is contained in:
2026-06-22 01:33:40 +08:00
parent 752a5c661d
commit c73a2c903f
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kind = "lemma"
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设固体体积 $V$、表面积 $A$,应变 $epsilon$ 为均匀小量。体相单位体积的自由能 $f_b = Y epsilon^2 \/ 2$,表面单位面积的自由能 $gamma(epsilon)$,总自由能
$ F = V f_b + A gamma(epsilon) . $
对均匀拉伸 $V epsilon$ 求导得单位横截面承担的应力
$ sigma_("tot") = (partial F) / (partial (V epsilon)) = Y epsilon + A / V dot (dif gamma) / (dif epsilon) , $
@总应力。
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对横截面被均匀拉伸的固体,单位横截面承担的总应力为
$ sigma_("tot") = Y epsilon + A / V dot (dif gamma) / (dif epsilon) , $ <总应力>
其中 $Y$ 为杨氏模量、$epsilon$ 为应变、$A \/ V$ 为表面积与体积之比。第一项为体相弹性贡献,第二项为表面贡献。