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. | Vietnam Journal of Mechanics, VAST, Vol. 35, No. 1 (2013), pp. 51 – 65 A CO-ROTATIONAL BEAM ELEMENT FOR GEOMETRICALLY NONLINEAR ANALYSIS OF PLANE FRAMES Nguyen Dinh Kien1 , Trinh Thanh Huong1 , Le Thi Ha2 of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam 2 Hanoi University of Transport and Communication, Vietnam 1 Institute 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. Keywords: Plane frame, geometric nonlinearity, co-rotational beam element, critical load, equilibrium path. 1. INTRODUCTION Frame structure is widely used in civil engineering, and nonlinear analysis of this structure is of interest from both academic and practical points of views. The essential for a nonlinear analysis is to have a nonlinear element which is capable to model accurately nonlinear behavior of the structure. Development of nonlinear elements, in general, and beam elements, in particular, is an important topic in the field of structural mechanics. Many beam elements which included geometrical nonlinearity for the large displacement analysis of frames can be found in the literature, and some of them have been documented in various well-known textbooks, . [1, 2]. Depending on the choice of reference configuration, the nonlinear beam elements can be classified into three main
