A note on an orthotropic plate model describing the deck of a bridge

TL;DR

This paper develops a mathematical model for orthotropic rectangular plates, such as bridge decks, capturing directional differences in rigidity to improve structural analysis accuracy.

Contribution

It introduces a novel orthotropic plate model based on the Kirchhoff-Love theory, accounting for anisotropic elastic properties and deriving the equilibrium equations under vertical loads.

Findings

The model accurately describes directional stiffness differences.

Derivation of equilibrium equations for orthotropic plates.

Application potential for bridge deck analysis.

Abstract

The purpose of this work is to develop a model for a rectangular plate made of an orthotropic material. If compared with the classical model of the isotropic plate, the relaxed condition of orthotropy increases the degrees of freedom as a consequence of the larger number of elastic parameters, thus allowing to better describe rectangular plates having different behaviors in the two directions parallel to the edges of the rectangle. We have in mind structures like decks of bridges where the rigidity in the direction of their length does not necessarily coincide with the one in the direction of its width. We introduce some basic notions from the theory of linear elasticity, having a special attention for the theory of orthotropic materials. In particular we recall the Hooke's law in its general setting and we explain how it can be simplified under the orthotropy assumption. Following the approach of the Kirchhoff-Love model, we obtain the bending energy of an orthotropic plate and from it the corresponding equilibrium equation when the plate is subject to the action of a vertical load. Accordingly, we write the kinetic energy of the plate which combined with the bending energy gives the complete Lagrangian; classical variational methods then produces the equation of motion.