Being gradually softened approach for solving large deflection of cantilever beam subjected to distributed and tip loads

Abstract

The solutions to small deflections of uniform cantilever beams have been obtained and widely used. However, when the deflections become large, it is quite challenging to derive the solutions due to the geometric nonlinearity, especially for non-uniform beams. To handle that, in this paper, a novel and an efficient method called being gradually softened approach (BGSA) is proposed to predict the large deflections of uniform and non-uniform cantilever beams subjected to distributed and tip loads. The cantilever beam is initially regarded as a rigid beam and then is gradually softened from the free end to the fixed end to solve the deflection of the cantilever beam. As new rigid units of the cantilever beam are softened, the direction of the force load acting on the previous softened units changes. Because of that, the deflections of the previous softened units need to be updated accordingly. Experimental results show that this method can solve the large deflections of uniform and non-uniform cantilever beams that experience distributed and tip loads with high accuracy.