Theoretical development of a stiffness decomposition method for calculating the displacement of complex bending structures

Abstract

It is very difficult to provide analytical displacement solutions for complex bending structures, such as beams with variable cross-sections, in structural analysis. The common methods used for such analysis—the direct integration method and the conventional graph multiplication method—have disadvantages of inefficiency and large computational costs. Therefore, a new approach called the stiffness decomposition method was proposed to overcome these shortcomings. The fundamental principle of this new approach was derived based on the unit load method. The general calculation equation of displacement was derived and provided for general n-segment complex bending structures, and an operational procedure for this method was constructed to facilitate its application. Then, the method was applied to two case studies involving classic complex bending structures. The results showed the correctness and effectiveness of the proposed method. The stiffness decomposition method was simpler and more efficient than the other two methods: the number of computations required by the stiffness decomposition method accounted for only 47.4% to 84.0% of the number of computations required by the other methods in the two case studies. The clear mathematical and mechanical derivation of the proposed method makes it easy to understand. Furthermore, the simplicity and practicality of this method make it extensively applicable.