On the Derivation of One and Two Dimensional Equations for Layered Elastic Beams and Plates with Interface Slips

TL;DR

This paper extends Mindlin's power series method to derive one and two dimensional equations for layered elastic beams and plates with interface slips, including slip behavior in the model.

Contribution

It introduces a step function term into the power series expansion to account for interface slips in layered beams and plates, providing a new derivation method.

Findings

Derived equations include interface slip behavior.

Applied method to a two-layer beam example.

Produced equations for extension, bending, shear, and slip.

Abstract

Mindlins systematic procedure of power series expansion for deriving one and two dimensional equations of elastic beams and plates is extended to layered beams and plates with interface slips by adding a step function term to the power series expansion. A two layer beam is used as an example. In addition to the usual one dimensional equations for extension, bending and shear deformation, an equation associated with the interface slip also results from the procedure.