An Analysis of the Large Deflections of Beams using the Rayleigh-Ritz Finite Element Method

Abstract

SummaryThe Rayleigh-Ritz finite element method is used to obtain an approximate solution of the exact non-linear energy functional describing the large deflection bending behaviour of a simply-supported inextensible uniform beam subjected to point loads. The solution of the non-linear algebraic equations resulting from the use of this method is effected, using three different techniques, and comparisons are made regarding the accuracy and computing effort involved in each. A description is given of an experimental investigation of the problem and comparison of the results with those of the numerical method, and of the available exact continuum analyses, indicates that the numerical method provides satisfactory predictions for the non-linear beam behaviour for deflections up to one quarter of the beam’s length.