A Correction for the Rigid Constraint of Elastic Plate Theory

Research Category: Engineering and Technology
Presenter: Dan Hu
PI: George Adams

Elastic plate theory is used by mechanical and civil engineers to model a variety of structures which are flat in two dimensions and thin in the other direction.  If the plate is fixed at an end by being sandwiched between two rigid surfaces it is customary to model this constraint (i.e. boundary condition) as a rigid clamp which does not permit either displacements or rotations at that edge.  Here we show that an elastic plate, with an end perfectly bonded at its top and bottom surfaces to rigid constraints, deflects an additional amount due to elastic rotation effects within the support.

This finite rotational stiffness within the support is determined by applying a distributed load (statically equivalent to a couple moment) to such a constrained elastic strip.  The displacement profile is determined analytically and approximated by a straight line.  The ratio of the moment to the slope of this line provides the rotational stiffness.  Examples are given both for a cantilever and a fixed-fixed beam. For both of these cases the correction due to the effect of rotational compliance is often greater than the correction due to shear deformation.  Two-dimensional finite element analyzes of these configurations show good agreement with the analytical results.