Rigorous Implementation of the Galerkin Method for Uniform and Stepped Columns

摘要

The aim of this paper is to deal with the often-occurring mistake in the implementation of the Galerkin method, and its correction. It is shown that the flexural rigidity should be represented as a discontinuous function incorporating a unit step function. This leads to occurrence of the Dirac's delta function and its derivatives when substituting the flexural rigidity into the governing differential equation.