Legacy · Mechanical validation · §8.3 / Fig. 6a

Solid cylinder (Fig. 6a)

Separable thermal field — fundamental mode in a long cylinder. §8.3 / Figure 6(a).

Article: Part I · DOI 10.70271/rirc.v1n2a007

Mechanical material: Itumbiara — $\nu=0.20$; $\alpha_T=10\times10^{-6}\,^{\circ}\mathrm{C}^{-1}$. Diffusivity: $h^{2}=0.10\,\mathrm{m}^{2}/\mathrm{d}$ (do not confuse with $a_T$). Idea: $T=\theta(t)\,h(\mathbf{x})$ ⇒ $\sigma_{ij}=g_{ij}(\mathbf{x})\,S(t)$.

Control points (all Fig. 6 cases): ref_fig6_pontos_controle.csv.

Schematic

PDF sheet: folha_cilindro_macico.pdf

Data sheet

Input files

• ref_cilindro_macico_theta.csv — $\theta(t)$
• Material: Itumbiara

Output figures

Output files

• ref_cilindro_macico_g.csv — spatial kernel $g$
• ref_cilindro_macico_S.csv — $S_{\mathrm{ref}}$ and $S_{\mathrm{inc}}$
• ref_cilindro_macico_sigma_theta_corte.csv

Time mesh and tolerance

The public CSVs for $S(t)$ and $\sigma_\theta$ use age_grid(3, 123, 240) (240 nodes from $t_0=3\,\mathrm{d}$ to $123\,\mathrm{d}$). The incremental algorithm is order ~1 in $\Delta t$; on this mesh the discretization bias is of order 0.2 % along the curve (independent check with a 61 440-point mesh and extrapolation: published $S_{\mathrm{inc}}(9.05\,\mathrm{d})$ $-3.6987$ vs converged $-3.6908$; peak $\sigma_\theta$ $0.58325$ vs $0.58210$). A 2nd-order solver that agrees with the CSV to ~0.2 % is aligned with the reference published on this mesh — not necessarily with a finer continuous limit.

How to validate

1. Reproduce $g_{ij}(r)$ and compare with *_g.csv.
2. Build $\varepsilon^*=\alpha_T\theta/(1-\nu)$; obtain $S(t)$ vs *_S.csv (same mesh or declare yours).
3. $\sigma_\theta(r_{\mathrm{corte}},t)=g_\theta S(t)$ vs *_sigma_theta_corte.csv.