Bending of rectangular orthotropic plates with rotationally restrained and free edges: Generalized integral transform solutions

Abstract

Generalized integral transform solutions for bending problem of orthotropic rectangular thin plates with rotationally restrained and free edges are presented in this work, including four edges rotationally restrained (RRRR), three-edges rotationally restrained and one-edge free (RRRF), and two opposite edges rotationally restrained and the other two edges free (RFRF). The dimensionless governing equation of orthotropic rectangular plate bending with RRRR, RRRF or RFRF boundary conditions are integral transformed in each spatial direction by adopting Euler–Bernoulli beam eigenfunctions with appropriate boundary conditions (RR, RF or FF). The eigenfunctions for beams with RR and RF boundary conditions in numerically stable exponential function form are presented for the first time, as well as the respective characteristic equations for the determination of the eigenvalues. Free edges of the plate are integral transformed and then incorporated into the transformed governing equations by integration by parts. Transversal deflection of the orthotropic rectangular thin plate under arbitrary transversal load distribution can be readily obtained by solving a system of linear algebraic equations. Numerical results are presented for uniform load, hydrostatic pressure, and concentrated load, with the rotational fixity parameter varying between the limiting cases of simply-supported and clamped edges. Through the comparison with available analytical solutions and finite element solutions by Abaqus, the proposed solutions show the rapid convergence and high accuracy. The effects of the rotational restraints on the deflection of orthotropic rectangular plates with the three combinations of boundary conditions are also investigated.