Exact Method for Static Analysis of Periodic Structures

Abstract

The U‐transform method has been applied successfully to the vibration analysis of infinite periodic continuous beams and has been proven to be a very useful exact analytical method for analyzing periodic structures. In this paper it is established that this method can be applied to the rigorous analysis of some finite periodic structures under all types of static loading conditions as well. In order to demonstrate this fact, a continuous beam and a continuous plate with finite or infinite number of spans under uniformly distributed or concentrated static loading conditions are analyzed and presented as examples. The solutions obtained are rigorous analytical solutions without any restriction on the condition of loading.