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In SDT, what are the boundary conditions for a plate that is simply supported if ф represents the rotation of the transverse normal about an in-plane axis and w is the transverse deflection?

(a) w=0,\(\frac{\partial w}{\partial n}\)=0

(b) w=0,ф=0

(c) w=0,\(\frac{\partial w}{\partial n}\)≠0

(d) w=0, Mnn=0

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This interesting question is from Shear Deformable Plate Model in division Bending of Elastic Plates of Finite Element Method

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The correct answer is (d) w=0, Mnn=0

Easiest explanation: Plate problems are geometrically similar to the plane stress problems except that plates are also subjected to transverse loads. In SDT, a clamped plate has no deflection and rotation of the transverse normal about any in-plane axis, i.e., w=ф=0. In a simply supported end, rotation is not restricted; thusthe reactive moment is zero, i.e., w= Mnn=0. A free end does not have reactive moment and the shear force, i.e., Mnn=Qn=0.

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