Question

In SDT, what are the boundary conditions for a plate that is clamped 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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Query is from Shear Deformable Plate Model in portion Bending of Elastic Plates of Finite Element Method

Answer 1

Correct answer is (b) w=0,ф=0

Easiest explanation: Geometrically, plate problems are similar to the plane stress problems except that plates are also subjected to transverse loads that cause bending about axes in the plane of the plate. In SDT, the boundary condition for a clamped plate is the absence of deflection and rotation of the transverse normal about any in-plane axis, i.e., w=ф=0. Because a simply supported end does not restrict rotation, the reactive moment is zero, i.e., w=Mnn=0. For a free end, both, the reactive moment and the shear force are absent, i.e., Mnn=Qn=0.