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

✍ Scribed by Arash Yavari; Shahram Sarkani

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 227 KB
• Volume: 43
• Category: Article
• ISSN: 0020-7403
• DOI: 10.1016/s0020-7403(00)00041-2

✦ Synopsis

In this article some applications of the distribution theory of Schwarz to the analysis of beam}columns with various jump discontinuities are o!ered. The governing di!erential equation of an Euler}Bernoulli beam}column with jump discontinuities in #exural sti!ness, displacement, and rotation, and under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam}column method is introduced. Using this method, instead of solving the di!erential equation of the beam}column in the space of generalized functions, another di!erential equation can be solved in the space of classical functions. Some examples of beam}columns and columns with various jump discontinuities are solved. De#ections of beam}columns and buckling loads for columns with jump discontinuities are calculated using the Laplace transform method in the space of generalized functions.