Macroapproach Closed-Form Series Solution for Orthotropic Plates

Abstract

The objective of this study is to present the derivations in closed-form series for moments and deflections of thin orthotropic plates with general edge beams (boundaries) under arbitrary out-of-plane loading. The displacement solutions for the major components of the system (plate and beam) or macroelements are obtained by first solving for the unknown interactive forces and moments at the beam or nodal line locations after satisfying displacement compatibility along nodal lines. Such an approach is referred to herein as the macroapproach. The displacement functions for the macroelements are proposed in Fourier cum polynomial series after making sure that the series satisfies the boundary conditions. Using known solution forms of summation equations, solutions of systems of equations in open form has been avoided. The proposed series solution can be applied to all types of orthotropic decks with bridge boundaries. Numerical examples involving orthotropic plates with various aspect ratios, loading cases, and bridge-type boundary conditions are presented to demonstrate the accuracy of the approach for predicting deflections and moments. The major advantage of this technique is the development of a solution algorithm in the form of summation equations, leading to fast converging closed-form series solutions.