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For an ANISOTROPIC plate (e.g., laminate), the governing equation involves which sub-matrix of ABD?
A{'text': 'D (bending) — the laminate plate equation is essentially the isotropic biharmonic with D replaced by the orthotropic 3×3 bending matrix', 'label': 'C'}
B{'text': 'Only A (extension)', 'label': 'A'}
C{'text': 'Only B (coupling)', 'label': 'B'}
D{'text': 'Identity matrix', 'label': 'D'}
Answer & Solution
Correct answer: A. {'text': 'D (bending) — the laminate plate equation is essentially the isotropic biharmonic with D replaced by the orthotropic 3×3 bending matrix', 'label': 'C'}
The orthotropic plate equation is $D_{11} w_{xxxx} + 4 D_{16} w_{xxxy} + 2(D_{12}+2D_{66}) w_{xxyy} + 4 D_{26} w_{xyyy} + D_{22} w_{yyyy} = q$. For "specially orthotropic" plates D_{16} = D_{26} = 0, giving a simpler form.
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