In classical laminated plate theory (CLPT), if a composite airframe laminate has a ply stacking sequence that is symmetric about its midplane ($z = 0$), which coupling stiffness matrix identically vanishes?

(A) The extension-bending coupling matrix [B] ($B_{ij} = 0$)

(B) The in-plane extensional stiffness matrix [A]

(C) The bending stiffness matrix [D]

(D) The transverse shear matrix [A_{shear}]

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Coupling Matrix Definition:** $B_{ij} = \int_{-h/2}^{h/2} \bar{Q}_{ij} z dz$. 2. **Stage 2: Symmetry Condition:** If $\bar{Q}_{ij}(z) = \bar{Q}_{ij}(-z)$, the integrand $\bar{Q}_{ij} z$ is an odd function of $z$. 3. **Stage 3: Integration:** The integral of an odd function over symmetric bounds $[-h/2, h/2]$ is identically zero ($B_{ij} = 0$). 4. **Stage 4: Selection:** Option A is correct.

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