ANALYSIS OF ORTHOTROPIC PLATES USING TWO-DIMENSIONAL MATRIX PROGRESSION WITH SPECIAL REFERENCE TO BRIDGE DECKS

Abstract

This is an attempt in the direction of obtaining a numerical solution of the orthotropic-plate-problem using the two-dimensional matrix progression technique, with a view to assess the load distribution in bridge dears. The usual Fourier series expansions have been replaced by simple algebraic power series in one variable and the resulting system of ordinary partial differential equat-ions in the other variable are solved by the said technique. Boundary conditions in the second variable have been colioc-ated. The necessity of evaluating the characteristic roots of the transcendental equation governing the boundary problem has been eliminated by suitable matrix exponentiation. The present work deals with a, centrally loaded rect-angular plate with two opposite edges simply supported and the others free. A generalisation has been indicated to tackle any other boundary conditions. Other loadings may be similarly treated breaking them into symmetrical and anti- synmaetrical equivalents using suitable particular solutions. Action-distribution-matrices for the three well-known cases of orthotropic plates (H2 a Dxy and 142 D) have been derived starting with the non-dlmensionalised version of the governing equation. Suitable computer-based scheme has been followed retaining terms upto power in the series involved but 'programmes' prepared can tackle any intended number of terms of the series.