Question bank — Sandwich structures — face sheets, core

False — bending mein stiffer, haan, lekin strength failure modes par depend karti hai (face wrinkling, core shear, core crush) jo solid plate mein hoti hi nahi, isliye ek sandwich stiffer hone ke bawajood local defect par pehle fail ho sakta hai.

True thin-face limit mein — kyunki $(EI)\approx \frac{E_{f}b{t}_f{h}^2}{2}$ aur thin faces ke liye $h\approx c$, stiffness $h^2$ ke saath scale karti hai, toh $2\times$ depth se lagbhag $4\times$ stiffness milti hai.

False — faces bending (axial) stress carry karti hain kyunki woh neutral axis se door hain; core ka main kaam hai shear resist karna aur faces ko apart rakhna.

False — haalaanki core bending term $E_c{I}_{\text{core}}$ negligible hai, core ki shear stiffness $G_c$ aur faces ko $h$ distance par alag rakhne ki uski ability essential hai; ise air se replace karo aur faces independently slide karte hain, $h^2$ advantage collapse ho jaata hai.

False — ek point ke baad faces wrinkling ki prone ho jaati hain aur core shear ya crush ki, aur slender panels ke liye shear deflection ($\frac{VL}{G_{c}bh}$ term) aur buckling over le lete hain; ek optimum $h$ hota hai, unbounded nahi.

False — lambi panels ke liye shear-deflection term $\frac{VL}{G_{c}bh}$ significant ho jaata hai aur ise add karna padta hai, kyunki low-$G_c$ core shear mein noticeably deform karta hai.

False — yeh choose kiya jaata hai unit density par uski high $G_c$ ke liye, continuous heat-conduction path na hone ke liye (thermal insulation), aur vacuum compatibility ke liye (cells vent karte hain, koi trapped volatiles nahi); Nomex actually lower-cost option hai.

False — yeh sirf tab negligible hai jab $t_f\ll h$; thick faces ke liye (small $h/t_f$) woh term small nahi hai aur ise rakhna padta hai, isliye thin-face assumption hamesha state ki jaani chahiye.

Galat goal — denser core mass add karta hai bending mein help kiye bina; tum chahte ho sabse halka core jo enough shear stiffness aur strength supply kare aur faces ko separated rakhe. Stiffness face placement se aati hai, core density se nahi.

Galat — ${\sigma }_{\text{wr}}$ core properties $E_c$ aur $G_c$ par bhi depend karta hai. Yahan $C$ ek dimensionless constant hai (lagbhag $0.5$ se $0.82$) jo face ko elastic core par resting plate model karke, use Winkler foundation treat karke, aur wrinkle wavelength par energy minimise karke aata hai; yeh boundary conditions par depend karta hai aur sirf tab valid hai jab face wrinkle length ke relative thin ho. Soft core par stiff face tab bhi easily wrinkle hoti hai.

Category error — failure shear strength ${\tau }_{c,\text{allow}}$ se govern hoti hai (ek stress limit), jabki $G_c$ ek stiffness property hai jo shear deflection control karta hai. High modulus high strength guarantee nahi karta.

Decimal blunder — $0.005$ m 5 mm hai, das guna zyada thick; yeh face mass ko 1.92 kg se inflate karke 19.2 kg kar deta hai. Substitute karne se pehle hamesha confirm karo ki $t_f$ mm mein hai ya m mein.

Approximation ko exact bata diya gaya — true centroid distance $d=\frac{h}{2}-\frac{t_f}{2}$ hai; $d\approx h/2$ set karna sirf thin faces ke liye valid hai aur ise hamesha approximation flag karna chahiye.

Dangerous — honeycomb cores concentrated point loads ke neeche crush ho jaate hain. Point loads ko through-thickness pressure spread karne ke liye local reinforcement chahiye (solid inserts, potting).

Galat formula — simply-supported uniformly-loaded beam $\delta =\frac{5w{L}^4}{384(EI)}$ use karta hai; support conditions aur load type numerical coefficient ko puri tarah change kar dete hain.

Kyunki bending stress $\sigma =My/I$ neutral axis se distance $y$ ke saath badhta hai, toh large $y$ par material sabse zyada stress carry aur resist karta hai — strength ko jahan stress highest hai wahan rakhna capacity per unit mass maximise karta hai.

Thin faces ke liye $t_f\ll h$, toh $t_f^3\ll t_f{h}^2$; transported term $b{t}_f(h/2{)}^2$ lagbhag $(h/t_f{)}^2\gg 1$ factor se bada hai.

Kyunki $E_c{I}_{\text{core}}$ tiny hai (typically $E_c/E_f\sim 10^{-3}$) toh yeh negligible bending stiffness add karta hai, lekin shear force $V$ physically core se guzarni padti hai, aur iska low $G_c$ long panels mein shear deflection non-trivial banata hai.

Masses match karo: thickness $t_s$ ki solid plate ka mass do faces jitna hoga jab ${\rho }_{s}b{t}_s\approx 2{\rho }_{f}b{t}_f$ (halka core neglect kiya), toh $t_s\approx 2t_f$. Solid inertia hai $I_{\text{solid}}=\frac{b{t}_s^3}{12}=\frac{b(2t_f{)}^3}{12}=\frac{8b{t}_f^3}{12}$, aur sandwich inertia hai $I_{\text{sand}}\approx \frac{b{t}_f{h}^2}{2}$. Unka ratio hai $\frac{b{t}_f{h}^2/2}{8b{t}_f^3/12}=\frac{6t_f{h}^2}{8t_f^3}=\frac{3h^2}{4t_f^2}$ — $\frac{3}{4}$ exactly $6/8$ hai un do coefficients se.

Bond faces aur core ke beech shear transfer karta hai; weak ya voided bond faces ko debond aur slide karne deta hai, us composite action ko destroy karta hai jis par $h^2$ stiffness depend karti hai — dekho Adhesive Bonding.

Open honeycomb cells freely vent karte hain toh koi gas trapped nahi hoti jo outgas kare ya expand kare; sealed volumes volatiles hold kar sakte hain ya pressurise hokar vacuum mein faces delaminate kar sakte hain.

Launch cost mass ke saath scale karta hai, toh payoff stiffness per kilogram hai; ek material jo stiff lekin heavy hai woh halke, thode kam stiff material se haar jaata hai jab mass orbit cost ke against charge hota hai.

Area $A$ par shear force $V$ average shear strain $\gamma =\frac{V}{AG}$ banata hai; length $L$ par yeh strain order $\gamma L=\frac{VL}{AG}$ ki sideways displacement mein accumulate hoti hai. $A=bh$ (width times depth) aur $G=G_c$ (core shearing karta hai) rakhne par $\frac{VL}{G_{c}bh}$ milta hai.

Thin-face formula break down ho jaata hai — usne assume kiya tha $t_f\ll h$; $t_f=h/2$ par panel ek solid plate hai aur tumhe $I=\frac{b{h}^3}{12}$ use karna padega.

Tab $h\to 2t_f$ aur do faces thickness $2t_f$ ki ek solid sheet ki tarah behave karte hain; huge $h^2$ leverage khatam ho jaata hai aur tumhe sirf ek thin solid plate ki modest stiffness milti hai.

Core shear govern karta hai — panel core mein fail hoti hai, faces mein nahi, toh $h$ badhaake redesign karo (jo ${\tau }_c\approx V/(bh)$ kam karta hai) ya higher-strength core choose karo, faces kitni bhi strong hon.

Shear deflection $\frac{VL}{G_{c}bh}$ dominate karta hai aur bending deflection se zyada ho sakta hai, toh low-$G_c$ core (foam) deflection target violate kar sakta hai chahe bending stiffness adequate lage.

Local core crushing — honeycomb through-thickness compression ke neeche collapse ho jaata hai; fix hai solid insert ya potted region, stronger face sheet nahi.

Nahi — approximation $E_c\ll E_f$ fail ho jaati hai, core bending ab negligible nahi hai, aur tumhe ise composite section treat karna padega jahan sab layers contribute karti hain; yeh lightweight advantage bhi kho deta hai.