# In FEM, what are the primary variables in the Shear Deformation Theory of plate deformation (w)?

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In FEM, what are the primary variables in the Shear Deformation Theory of plate deformation (w)?

(a) The transverse deflection w only

(b) The transverse deflection w and the normal derivative of w

(c) The transverse deflection w and the angles of rotation of the transverse normal about in-plane axes

(d) The angles of rotation of the transverse normal about in-plane axes only

I have been asked this question by my college director while I was bunking the class.

Asked question is from Shear Deformable Plate Model in section Bending of Elastic Plates of Finite Element Method

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The correct option is (c) The transverse deflection w and the angles of rotation of the transverse normal about in-plane axes

Explanation: An examination of the boundary terms in the weak form of Shear Deformation Theory suggests that the essential boundary conditions involve specifying the transverse deflection w and the angles of rotation of the transverse normal about in-plane axes (φx, φy), which constitute the primary variables of the problem (like in the Timoshenko beam model). Hence, the finite element interpolation of w must be such that w, (φx and φy are continuous across the inter-element boundaries in SDT elements.

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