Question

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

(a) The transverse deflection w only

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

(c) The normal derivative of w only

(d) The normal and the time derivative of w

I have been asked this question in homework.

I'm obligated to ask this question of Classical Plate Model in section Bending of Elastic Plates of Finite Element Method

Answer 1

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

The best I can explain: An examination of the boundary terms in the weak form of Classical Plate Theory suggests that the essential boundary conditions involve specifying the transverse deflection w and the normal derivative of w, which constitute the primary variables of the problem (like in the Euler-Bernoulli beam model). Hence, the finite element interpolation of w must be such that w and \(\frac{dw}{dn}\) are continuous across the inter-element boundaries in CPT elements.