抄録
This paper presents consistent new shape functions for a linearly tapered Timoshenko beam element. The formulated shape functions can be used in the energy method based finite element context. The shape functions formulated in this report are derived for a solid rectangular beam with a linear change in its width and/or height. With the consistent shape functions, highly accurate solutions for structural problems can be obtained by using the least element per member in the finite element calculation. Comparison studies with reference works with respect to the accuracy and computational efficiency for various linearly tapered Timoshenko beam structures are highlighted. Concise formulations of the shape functions in the series of matrix forms are provided in the appendix.
