# Cylindrical Shell Buckling > Use when you must compute the buckling of a curved unstiffened circular cylindrical shell with the NASA SP-8007 knockdown method: the axial-compression knockdown factor from the shell radius and thickness, the axial critical buckling stress 0.605*gamma*E*t/r, the bending knockdown factor, the bending critical moment, the cross-section ovalization collapse moment, and the plasticity correction factor. Produces the knockdown factors, the critical stress and moments, and the governing verdict between bifurcation and ovalization collapse for a curved-shell stability check. Trigger: cylindrical shell buckling, SP-8007 knockdown, shell axial compression, cylinder bending, ovalization collapse, curved panel stability, fuselage barrel buckling. - Skill: `ashfordeou/cylindrical-shell-buckling` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/cylindrical-shell-buckling` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/cylindrical-shell-buckling/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/cylindrical-shell-buckling --- # Cylindrical Shell Buckling (structures/fem/cylindrical-shell-buckling) Use when the task is the elastic stability of a curved, unstiffened circular cylindrical shell (fuselage barrel, pressure-vessel or tank shell, duct) under axial compression or bending. This leaf implements the NASA SP-8007 empirical knockdown method ("Buckling of Thin-Walled Circular Cylinders", 1968 original / 2023 NTRS revision 20205011530, public domain): the axial knockdown factor gamma_axial from the shell radius r and thickness t, the axial critical stress, the bending knockdown factor gamma_bending, the bending critical moment, the cross-section ovalization collapse moment, and the plasticity correction factor eta. It pairs with the flat-panel leaf structures/fem/plate-buckling, which explicitly defers the curved case here, and with structures/fem/buckling-analysis for slender straight members. The SP-8007 knockdowns are empirical fits for thin shells with r/t below about 1500; the classical stress terms are elastic, so the plasticity correction eta is reported separately and applied by the user when the material is beyond its proportional limit. ## Domain quick reference - Curvature parameter: phi = (1/16)*sqrt(r/t). It sets the knockdown sensitivity: very thin shells (large r/t) carry larger knockdowns. - Axial knockdown factor: gamma_axial = 1 - 0.901*(1 - exp(-phi)), monotonic decreasing in r/t and always in (0, 1). - Axial critical stress: sigma_cr = 0.605*gamma_axial*E*t/r, where the 0.605 coefficient is the classical value 1/sqrt(3*(1-nu^2)) at nu = 0.3. - Bending knockdown factor: gamma_bending = 1 - 0.731*(1 - exp(-phi)). - Bending critical moment: M_cr = pi*0.605*gamma_bending*E*t**2*r. The axial critical stress acts over the full wall section (area pi*r*t) at the extreme-fiber arm r, giving M = sigma_cr*(pi*r*t)*r. - Ovalization collapse moment: M_ov = 0.987*E*r*t**2/sqrt(1-nu**2), the Brazier-style collapse of the cross section under bending. - Governing verdict: "bifurcation" when M_cr < M_ov, else "ovalization". SP-8007 notes the bending bifurcation precedes collapse for shells in the validity band. - Plasticity correction: eta = sqrt(E_sec*E_tan)/E with the secant and tangent moduli at the acting stress; eta = 1 in the elastic range. - SI units throughout: m, Pa, N*m. - Validity guard: r/t must be below 1500 for the empirical knockdowns. ## Workflow 1. Fix the geometry and material: radius_m, thickness_m, e_mod_pa and the Poisson ratio (default 0.3). Confirm r/t < 1500. 2. Get the knockdown factors: knockdown_axial and knockdown_bending, or read gamma_axial and gamma_bending from shell_buckling_assessment. 3. Compute the axial critical stress with axial_critical_stress (gamma defaults to the internal axial knockdown). 4. Compute the bending critical moment with bending_critical_moment (gamma defaults to the internal bending knockdown). 5. Compute the ovalization collapse moment with ovalization_collapse_moment. 6. When the material may be beyond the proportional limit, pass the secant and tangent moduli to plasticity_correction and scale the elastic margins by eta (SP-8007 stresses are elastic). 7. Run shell_buckling_assessment for the full dict including the governing verdict between bifurcation and ovalization collapse. 8. Confirm the deterministic checks with the contract test scripts/test_cylindrical_shell_buckling.py. ## Worked example Aluminum barrel: E = 70 GPa, r = 1.5 m, t = 0.005 m (r/t = 300), nu = 0.3. Real module outputs: - curvature_parameter = 1.0825 (sqrt(300)/16). - gamma_axial = 0.4042, in the 0.35-0.45 bound. - sigma_cr_axial = 57.06 MPa, in the 50-65 MPa bound. - gamma_bending = 0.5166, in the 0.45-0.60 bound. - M_cr_bending = 2.578 MN*m, in the 2.2-3.0 MN*m bound. - M_cr_ovalization = 2.716 MN*m, in the 2.4-3.1 MN*m bound. - Governing: "bifurcation" (bending bifurcation moment below the ovalization collapse). - Check geometry r = 1.0 m, t = 0.01 m (r/t = 100): gamma_axial = 0.5813 and gamma_bending = 0.6603; the same barrel at r/t = 1600 raises ValueError on the 1500 validity guard. - eta_plasticity = 1.0 when E_sec = E_tan = E. The bending knockdown is higher than the axial one at equal r/t, so the bending critical moment sits above the axial stress level scaled by the full section; the ovalization collapse is the cross-section limit that bifurcation must beat to be governing. ## Pitfalls - Using the knockdowns outside the validity band: the SP-8007 empirical fits hold for r/t below about 1500, and every geometry-dependent function raises ValueError at r/t >= 1500 - including the exact boundary. - Reading the bending moment as a stress: M_cr scales as gamma_bending * E * t^2 * r over the full wall section while the axial case is a stress 0.605 * gamma * E * t / r; comparing the two critical quantities across units invites a wrong governing verdict. - Assuming bifurcation always governs: the verdict is "ovalization" when the Brazier collapse moment M_ov falls below the bending bifurcation moment; the worked barrel is "bifurcation", but thicker or softer shells can flip it. - Applying the plasticity correction twice: the classical stress terms are elastic and eta (sqrt(E_sec E_tan)/E, unity at E_sec = E_tan = E) is reported for the user to apply; scaling the elastic margin by eta once is the intended use. - Confusing this geometric knockdown with material knockdowns: gamma_axial and gamma_bending come from r/t geometry; the strength reduction factors of composites/cmh17-allowables are material factors for fiber-reinforced laminates. - Treating the unstiffened barrel as a stiffened fuselage: this leaf covers the curved UNSTIFFENED shell; stiffened pressurized fuselage modeling belongs to vehicle-design/structures-integration/fuselage-skin-stringer. ## Verification - Confirm curvature_parameter(1.5, 0.005) = 1.0825 and gamma_axial in the 0.35-0.45 band, sigma_cr in the 50-65 MPa band, M_cr_bending in the 2.2-3.0 MN*m band, M_cr_ovalization in the 2.4-3.1 MN*m band, and the governing verdict "bifurcation". - Confirm gamma_axial(1.0, 0.01) = 0.5813 and gamma_bending(1.0, 0.01) = 0.6603 (r/t = 100). - Confirm both knockdown factors stay in (0, 1) and decrease monotonically as r/t grows. - Confirm the identities sigma_cr = 0.605*gamma*E*t/r and M_ov = 0.987*E*r*t**2/sqrt(1-nu**2) hold exactly, and eta = 1.0 at E_sec = E_tan = E. - Confirm non-positive radius, thickness or modulus, nu outside (-1, 1), an out-of-range explicit gamma, and r/t >= 1500 all raise ValueError. - Deterministic: no RNG, identical float results run to run. - Run the contract test offline: python3 scripts/test_cylindrical_shell_buckling.py (34 tests). ## Related leaves - structures/fem/buckling-analysis: straight slender members under Euler-style compression; this leaf covers the curved shell instead. - structures/fem/plate-buckling: flat plate and skin panel buckling; it defers the curved unstiffened shell case to this leaf. - structures/thermal-structures/thermal-buckling: restrained flat panels under thermal load. - vehicle-design/structures-integration/fuselage-skin-stringer: the stiffened pressurized fuselage model; this leaf covers the unstiffened curved barrel. - structures/composites/cmh17-allowables: material strength reduction factors for fiber-reinforced laminates; the knockdown here is geometric, that leaf's is material. ## Behavior contract (gate 3) Run the deterministic contract test (stdlib unittest, offline): python3 scripts/test_cylindrical_shell_buckling.py The 34 tests cover the worked example within the spec magnitude bounds, the r/t = 100 knockdown values, unit-interval and monotonicity properties of both knockdown factors, closed-form knockdown identity, ValueError rejection of non-positive geometry/modulus, out-of-range nu, the r/t >= 1500 validity guard (including the exact boundary) on every geometry-dependent function and on the assessment dict, the explicit and default-gamma identities for the axial stress and bending moment, the exact ovalization formula, the plasticity correction (elastic and half-modulus cases plus scale invariance and ValueError), run-to-run determinism, and the assessment dict key and eta contract. ## Compliance - Standards referenced, not reproduced: NASA SP-8007 (public domain; named in the body with the pinned coefficients and the r/t validity band, paraphrased) and FAR-25 airframe loads context per standards-map.yaml. No proprietary handbook text is reproduced. - compliance: STANDARDS-REF, gated: false.