Generation of beam elements using the finite difference method

Abstract

This paper is a part of a larger study trying to build a bridge between the finite element and finite difference methods. The classic finite difference method is used to generate accurate macro-elements for beams with varying cross-sectional properties. The material of the beam is assumed to be linearly elastic. The geometric nonlinearity is taken into account. The accuracy of the method is tested by comparing the results obtained with the analytical ones by hand calculation utilizing Berry's functions. A planar frame is used as a numerical example. The iterative stiffness method employed is quite similar to the one using Berry's functions.