sandwich-panel

name	sandwich-panel
description	Sandwich panel structural analysis — face sheet design (Euler buckling, wrinkling), core shear (Vinson formula), bending stiffness D = E_f×t_f×d²/2, deflection with transverse shear, face dimpling, core types (honeycomb, foam, balsa), materials (CFRP/aluminum face + Nomex/Rohacell/aluminum honeycomb), bonding (film adhesive, co-cure), edge closeout details, ASTM C393/C365 tests, and aerospace/marine applications.
metadata	{"priority":7,"promptSignals":{"phrases":["sandwich panel","sandwich structure","honeycomb panel","foam core panel","face sheet wrinkling","sandwich composite"],"minScore":3}}

Sandwich Panel Structural Analysis — Complete Skill

Sandwich Panel Theory

Basic Geometry and Assumptions

Sandwich panel geometry:

• Face sheets (skins): thickness t_f each; material elastic modulus E_f, yield/strength σ_f
• Core: thickness t_c; shear modulus G_c; compressive modulus E_c
• Total panel thickness: h = t_c + 2t_f ≈ t_c (when t_c >> t_f)
• Distance between face sheet centroids: d = t_c + t_f

Key assumption: Faces carry in-plane loads (bending moments → axial forces); core carries shear only (no bending stiffness)

Bending stiffness (EI equivalent): D = E_f × t_f × d² / 2 [per unit width; Nm; assumes t_f << t_c] Full expression: D = E_f/(1-ν_f²) × [t_f × d²/2 + t_f³/6] + E_c × t_c³/12 For practical sandwich: D ≈ E_f × t_f × d² / 2 (face bending dominates when E_f × t_f >> E_c × t_c)

Shear stiffness: AG = G_c × d² / t_c [shear stiffness per unit width; N — for uniform core; wide beam] (Also written: S = G_c × d²/t_c per unit width)

Bending Analysis (Beam/Plate)

Deflection with Transverse Shear

Simply supported beam under uniform load q: δ_total = δ_bending + δ_shear = 5×q×L⁴/(384×D) + q×L²/(8×AG) [shear deflection term can dominate for low-density cores!]

Relative importance (shear vs. bending deflection): δ_shear/δ_bending = 48/(5 × L² × G_c × d²/(t_c × D)) × (5/1) If L/(t_c)² is small → shear dominant; typical aerospace sandwich: shear = 10–30% of total

Face sheet stresses from bending: σ_face = M_max / (t_f × d) [at mid-span; maximum bending moment M_max] Verify: σ_face ≤ σ_allow (tensile/compressive)

Core shear stress: τ_core = V_max / d [V = transverse shear force; maximum at supports for uniform load V = qL/2] Verify: τ_core ≤ τ_core_allow (from test or datasheets)

Example: Panel: L = 1.0 m, E_f = 70 GPa (Al 5052), t_f = 1.0 mm, G_c = 200 MPa (Nomex honeycomb), t_c = 25 mm, q = 10 kN/m² d ≈ 26 mm = 0.026 m D = 70,000 × 1 × 0.026²/2 = 23.66 Nm (per mm → 23,660 N·mm²/mm) AG = 200 × 0.026²/0.025 = 5.408 kN/mm → 5.408×10⁶ N/m per unit width δ_bending = 5×10×1⁴/(384×23,660×10⁻³ [adjust units]) → work consistently in N, m δ_shear = qL²/(8×AG) = 10,000×1²/(8×5.408×10⁶) = 2.31×10⁻⁴ m = 0.23 mm (Full calculation requires consistent unit tracking)

Face Sheet Failure Modes

1. Facing Failure (Tensile or Compressive Overstress)

σ_face = M / (d × t_f) ≤ F_tu (tensile) or F_cu (compressive) For CFRP: F_cu = 500–800 MPa (laminate compressive strength, layup-dependent) For Al 5052-H39: F_cu = 255 MPa; F_tu = 290 MPa

2. Face Sheet Wrinkling (Symmetric — Inward Mode)

Critical wrinkling stress (symmetric, inward): σ_cr_wr = k_w × (E_f × E_c × G_c)^(1/3) [per Hoff-Mautner/Wierzbicki; k_w ≈ 0.5–0.82] Conservative: σ_cr_wr = 0.5 × (E_f × E_c × G_c)^(1/3)

Example: E_f = 70 GPa, E_c = 200 MPa (T-direction: E_c compression for Nomex core), G_c = 75 MPa σ_cr_wr = 0.5 × (70,000 × 200 × 75)^(1/3) [MPa] = 0.5 × (1.05×10⁹)^(1/3) = 0.5 × 1,016 = 508 MPa → Wrinkling > face yield for this case (aluminum skin won't wrinkle; CFRP is critical at high stiffness)

3. Face Sheet Dimpling (Hexagonal Honeycomb — Local Buckling)

Face dimpling into honeycomb cells: σ_cr_dim = 2 × E_f × (t_f/s)² [s = cell size; for hexagonal honeycomb s ≈ cell diameter] For Al face 1 mm, s = 6.35 mm cell: σ_cr_dim = 2 × 70,000 × (1/6.35)² = 3,470 MPa >> yield → no dimpling risk Risk: t_f/s < 1/30 → dimpling can occur before yield (thin faces on large cell core)

4. Overall Panel Buckling (Face Sheet + Core Combination)

Critical compressive load for simply supported panel: N_cr = π² × D / L² × 1 / (1 + π²×D/(L²×AG)) [buckling with shear correction; N_cr [N/m width]] Compare with applied N = σ_face × t_f × 2; verify N < N_cr

Core Materials

Honeycomb Core

Core Type	Density [kg/m³]	σ_c [MPa]	τ_L [MPa]	G_L [MPa]	G_W [MPa]	T_max [°C]
Nomex 1/8"-3.0#	48	1.03	0.69	37	21	180
Nomex 1/8"-4.0#	64	2.07	1.17	55	32	180
Al 5052 1/8"-3.1#	50	1.72	1.10	110	52	150
Al 5052 3/16"-4.4#	70	3.10	1.72	165	78	150
Al 5056 1/8"-5.7#	91	3.45	2.41	207	104	150

[L = ribbon direction (stronger); W = transverse direction] Note: lb/ft³ → kg/m³: multiply by 16.02

Foam Core

Foam	Density [kg/m³]	σ_c [MPa]	τ [MPa]	G [MPa]	T_max [°C]
Rohacell 31 (PMI)	32	0.36	0.30	13	200
Rohacell 51	52	0.80	0.60	19	200
Rohacell 110	110	2.80	1.80	50	200
PVC Divinycell H60	60	0.55	0.60	22	80
PVC H80	80	1.00	0.90	31	80
Balsa (end-grain)	150	5.50	3.80	300	60

Face Sheet Materials

CFRP (unidirectional laminate, quasi-isotropic): E_x = E_y ≈ 55 GPa; F_tu ≈ 600 MPa; F_cu ≈ 500 MPa; ρ = 1,550 kg/m³; t_ply = 0.125 mm

Aluminum 2024-T3: E = 72 GPa; F_ty = 345 MPa; F_tu = 483 MPa; ρ = 2,780 kg/m³

GFRP (woven): E ≈ 20–25 GPa; F_tu ≈ 250–350 MPa; lower cost; marine applications

Manufacturing and Bonding

Bonding Methods

Film adhesive (Redux 312, FM-73, Cytec FM-300): Shear strength τ_adh = 15–35 MPa (at room temp); T-peel ≥ 4 N/mm Applied as film between face and core; co-cured or secondary bond Honeycomb bond: adhesive fillet forms around cell walls → "fillet bond"

Co-cure (CFRP prepreg + adhesive film + core): Single cure cycle; eliminates secondary bond; best mechanical performance Risk: core crush during cure (pressure control critical); low-porosity requirement

Potted edge closeout: Honeycomb edges: foam or potting compound fills cells to solid zone before machining/drilling Insert design: threaded inserts potted into core; pull-out force per insert: P = π × D × t_c × τ_adh

Testing (ASTM)

Test	Standard	Measures
Flatwise tensile	ASTM C297	Core-face bond; core tensile strength
Core shear	ASTM C273	G_c; τ_core
Edgewise compression	ASTM C364	Panel compressive strength
Flatwise compression	ASTM C365	Core compressive strength σ_c
Flexure (3 or 4 pt)	ASTM C393	Bending stiffness D; core shear strength
Climbing drum peel	ASTM D1781	Adhesive peel; face-to-core bond

Standards and References

Standard	Scope
ASTM C393	Flexural properties of sandwich constructions
MIL-HDBK-23	Design of sandwich panels for aerospace
Vinson "The Behavior of Sandwich Structures"	Core reference
ESA PSS-03-203	Spacecraft sandwich panels
DNV C401	Marine composite sandwich structures

Output

Provide: panel geometry (L × W [m]; face thickness t_f [mm]; core thickness t_c [mm]; material: face type/grade, core type/density), loading (distributed q [kPa]; point load P [kN]; in-plane N [kN/m]; load combination), bending stiffness D [N·m] and shear stiffness AG [kN/m] per unit width, deflection (δ_bend + δ_shear [mm]; δ_total vs. limit L/250 or specified), face stress σ_face [MPa] vs. allowable (tensile/compressive; margin of safety = allow/actual - 1), core shear τ_core [MPa] vs. τ_core_allow [MPa] (margin), face sheet wrinkling σ_cr_wr [MPa] (k_w = 0.5 used; compare with face compressive stress), face dimpling check (σ_cr_dim [MPa] vs. face compressive stress; only for honeycomb), global buckling N_cr [kN/m] (with shear correction; margin vs. applied N), adhesive bond (τ_adh_allow [MPa]; bond area; peel check), insert pull-out (if applicable; P_allow [kN] per insert), and applicable standard (ASTM C393/C273/C297; MIL-HDBK-23; face wrinkling ref.).