On applications of generalized functions to the analysis of Euler-Bernoulli beam-columns with jump discontinuities

In this article some applications of the distribution theory of Schwarz to the analysis of beam-columns with various jump discontinuities are offered. The governing differential equation of an Euler-Bernoulli beam-column with jump discontinuities in flexural stiffness, displacement, and rotation, an d under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam-column method is introdu ced. Using this method, instead of solving the differential equation of the beam-column in the space of generalized functions, another differential eq uation can be solved in the space of classical functions. Some examples of beam-columns and columns with various jump discontinuities are solved. Defl ections of beam-columns and buckling loads for columns with jump discontinu ities are calculated using the Laplace transform method in the space of gen eralized functions. (C) 2001 Elsevier Science Ltd. All rights reserved.