No abstract

A co-rotational beam element for geometrically nonlinear analysis of plane frames is presented. On the base of the shallow arch expression for local strain, the element is formulated by using exact polynomials to interpolate the transversal displacement and rotation. Using the formulated element, the critical load and equilibrium path are computed with the aid of the bracketing procedure and the arc-length control method, respectively. Numerical examples show that the proposed element is capable to give accurate results with a smaller number of elements comparing to the elements previously used in the examples. The effect of the nonlinear term used in the local strain expression on the numerical results is also investigated and highlighted.

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.