Analysis of Non-Prismatic Timoshenko Beams Using Basic Displacement Functions

Introducing the concept of Basic Displacement Functions (BDFs), an innovative method is presented which yields a mechanical based approach rather than a mathematical one for exact static analysis of arbitrarily tapered Timoshenko beams. Holding pure mechanical interpretations, BDFs are obtained using energy methods such as unit load method. It is shown that exact shape functions and consequently structural matrices could be derived in terms of BDFs. Unlike the most of finite element formulations which are based on prescribed displacement fields, the present finite element takes advantage of a flexibility basis which guarantees the exact interpolation of displacement field along the element and leads to fast convergence of the method in static analysis even with few elements. The method could be easily implemented into any standard displacement-based program. Carrying out numerical examples, the competency of the method in both static and free vibration is verified.