# Which option specifies an assumption made in Shear Deformation Theory for a plate lying in the plane XY?

Which option specifies an assumption made in Shear Deformation Theory for a plate lying in the plane XY?

(a) εzz≠0

(b) εxz=0

(c) εyz≠0

(d) εxy=0

The question was posed to me in unit test.

This is a very interesting question from Shear Deformable Plate Model topic in chapter Bending of Elastic Plates of Finite Element Method

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The correct choice is (c) εyz≠0

To explain: The Classical Plate Theory is based on the assumption that a straight line perpendicular to the plane of the plate is (1) inextensible, (2) remains straight, and (3) rotates such that it remains perpendicular to the tangent to the deformed surface, but In the SDT, we relax the normality assumption of CPT, i.e., transverse normal may rotate without remaining normal to the mid-plane. Thus, for a plate in the XY plane, the assumptions are equivalent to specifying εzz=0 only whereas εyz and εxz are non-zero.

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