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The plate displacement field under Kirchhoff hypothesis is parameterized by:
A{'text': 'Constants only', 'label': 'D'}
B{'text': 'Only u and v', 'label': 'C'}
C{'text': 'Three independent displacement fields u(x,y,z), v(x,y,z), w(x,y,z)', 'label': 'A'}
D{'text': 'The mid-surface transverse deflection w(x,y) only — in-plane displacements at any z are computed from w via u = −z·∂w/∂x, v = −z·∂w/∂y', 'label': 'B'}
Answer & Solution
Correct answer: D. {'text': 'The mid-surface transverse deflection w(x,y) only — in-plane displacements at any z are computed from w via u = −z·∂w/∂x, v = −z·∂w/∂y', 'label': 'B'}
Kirchhoff reduces the displacement field to one unknown — the mid-surface deflection w(x,y). In-plane displacements at height z from mid-plane: u(x,y,z) = −z·∂w/∂x, v(x,y,z) = −z·∂w/∂y. This makes the plate problem 2D in (x, y).
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