Question

In the Shear Deformation plate theory, what characteristic contributes to shear locking?

(a) Transverse shear strains in thick plates present computational difficulties

(b) Transverse shear strains in thin plates present computational efficiency

(c) For thick plates, the element stiffness matrix yields erroneous results for the generalized displacements

(d) For thin plates, the element stiffness matrix becomes stiff and yields erroneous results

This question was addressed to me in an interview for internship.

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

Answer 1

Right option is (d) For thin plates, the element stiffness matrix becomes stiff and yields erroneous results

Easy explanation: The transverse shear strains in the element equations of Shear Deformation Theory cause computational difficulties when the side-to-thickness ratio of the plate is large. Shear locking is observed when the transverse shear strains in thin plates are negligible, and consequently, the element stiffness matrix becomes stiff and yields erroneous results for the generalized displacements.