Influence of end fixity on post-yield behaviors of a tubular member

Abstract

For the evaluation of the capability of a tubular member of an offshore structure to absorb the collision energy, a simple method can be employed for the collision analysis without performing the detailed analysis. The most common simple method is the rigid-plastic method. However, in this method any characteristics for horizontal movement and rotation at the ends of the corresponding tubular member are not included. In a real structural system of an offshore structure tubular members sustain a certain degree of elastic support from the adjacent structure. End fixity has influences in the behaviors of a tubular member. Three-dimensional FEM analysis can include the effect of end fixity fully, however in viewpoints of the inherent computational complexities of the 3-D approach, this is not the recommendable analysis at the initial design stage. In this paper, influence of end fixity on the behaviors of a tubular member is investigated, through a new approach and other approaches. A new analysis approach that includes the flexibility of the boundary points of the member is developed here. The flexibility at the ends of a tubular element is extracted using the rational 'reduction of the modeling characteristics. The property reduction is based on the static condensation of the related global stiffness matrix of a model to end nodal points of the tubular element. The load-displacement relation at the collision point of the tubular member with and without the end flexibility is obtained and compared. The new method lies between the rigid-plastic method and the 3-demensional analysis. It is self-evident that the rigid-plastic method gives high strengthening membrane effect of the member during global deformation, resulting in a steeper slope than the present method. On the while, full 3-D analysis gives less strengthening membrane effect on the member, resulting in a slow going load-displacement curve. Comparison of the load-displacement curves by the new approach with those by conventional methods gives the figures of the influence of end fixity on post-yielding behaviors of the relevant tubular member. One of the main contributions of this investigation is the development of an analytical rational procedure to figure out the post-yielding behaviors of a tubular member in offshore structures. The potential hazards of a collision between a ship, and any other moving object at sea and an offshore structure can be so large that an understanding of this collision problem is certainly of importance. For the evaluation of the capability of a tubular member of an offshore structure to absorb the collision energy, 3-demensional numerical model approach can be used (Dexter, 1996; Hyde, 1999; Kitamura, 1997). However, in view of the inherent computational complexities of the 3-D approach, a simple method is rather employed for the collision analysis without performing the detailed analysis. The most common simple method is the rigid-plastic method (Sorede, 1981). In this method any characteristics for horizontal movement and rotation at the ends of the corresponding tubular member are not included. In a real frame system of an offshore structure the tubular element sustains a certain degree of elastic support from the adjacent structure. Consequently, both simple method and 3-D analysis have inherent difficulties in the collision analysis. In this paper a new approach that is simple and effective, is presented. In the method, the flexibility at the ends of a tubular element is extracted using the rational reduction of the modeling characteristics. The property reduction is based on the static condensation of the related global stiffness matrix of a model to end nodal points of the tubular element (Kuy-Nam, 1989). The load-displacement relation at the collision point of the tubular member with the extracted end flexibility is obtained through the procedure described in the following sections. For the comparison of the analysis results by the new approach, the collision analysis of a typical semi-submersible rig are carried out by the simple method and 3-D numerical approach using NOAMAS program developed by Century Research Corporation (Kahaner, 1990). Thus, the influence of end fixity of a tubular member is demonstrated through the analysis.