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Why is the IN-PLANE behavior of a symmetric laminate the SAME REGARDLESS of stacking order, while BENDING behavior is NOT?
A{'text': 'Random reason', 'label': 'A'}
B{'text': 'A depends only on ply ORIENTATIONS and THICKNESSES (not z-position), but D depends on z³ — the further from the mid-plane, the more a ply contributes to bending stiffness', 'label': 'B'}
C{'text': 'In-plane behavior is undefined', 'label': 'C'}
D{'text': 'D is always zero', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': 'A depends only on ply ORIENTATIONS and THICKNESSES (not z-position), but D depends on z³ — the further from the mid-plane, the more a ply contributes to bending stiffness', 'label': 'B'}
A_ij = sum of Q_ij·(z_k − z_{k-1}) — linear in z. D_ij = sum of Q_ij·(z_k³ − z_{k-1}³)/3 — cubic in z. Plies far from the mid-plane contribute much more to D. So [0/90/90/0] and [90/0/0/90] have same A but different D.
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