Simulation of nonlinear bending behavior and geometric sensitivities for tubular beams with fixed supports A.O. Ayhan a , K. Genel b,n , S. Eks -i b a Yıldız Technical University, Department of Mechanical Engineering, Bes - iktas -, _ Istanbul, Turkey b Sakarya University, Department of Mechanical Engineering, 54187 Sakarya, Turkey article info Article history: Received 30 July 2011 Received in revised form 21 October 2011 Accepted 21 October 2011 Available online 25 November 2011 Keywords: Thin-walled structure Bending Plasticity Contact Finite elements abstract In this study, the bending characteristics of thin-walled (D/t ¼30) tubular beams with fixed supports are systematically investigated for different beam lengths and diameters. Bending behavior of the beam is simulated using the finite element method, in which elasto–plastic material, large-deformation and contact are included. Stress distribution is monitored by FE analyses during bending simulation. Also, load carrying and energy absorption capacities of the tubular beams having different geometrical combinations are compared with each other. The results of finite element (FE) analyses indicate that the deformation characteristics and load carrying capacities of the beam strongly depend on the diameter. From the load–displacement curve, three distinct regions were observed and the associated deformation characteristics were identified. There is a noticeable correlation between the energy absorption and transition displacements for the ranges of geometric parameters coved in this study. It is concluded that the presented simulation results can provide significant contribution to the design of side-door impact beams and passive safety research. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction It is well known that thin-walled structures are widely used in vehicle industry and other engineering applications for the purpose of increasing safety and energy absorption efficiency in an impact or collision situation. In modern vehicles, extruded thin-walled components are used in the bumpers, crash boxes, space frames as well as other safety components such as pillars. For commercial vehicles and passenger cars, rollover and side impact, respectively, are among the most crucial hazards for the safety of drivers and passengers. It is well known that the excessive deformation of the vehicle’s structure in such an event seriously threatens lives of passengers. Although improved designs of existing structural elements minimizing the deformation would be very much desired, detailed understanding of their deformation mechan- isms serves as an opportunity for further improvement. In this regard, tubular members of frame structures play an important role in maintaining the stiffness of a vehicle and keeping occupants safe from accidents. For example, the side-door tubular beams take on a task to minimize danger in a side-on crash. A number of works in both theoretical and experimental categories have been published on plastic collapse behavior and energy absorption characteristics of thin-walled tubes subjected to bending [1–8]. Poonaya et al. exam- ined the collapse mechanisms in three regimes; elastic regime, ovalisation regime and structural collapse regime, and provided a theoretical model to predict the collapse mechanism for low D/t ratios of thin-walled circular tubes subjected to pure bending [1]. In order to predict the hinge moment-rotation for square tubes, some formulas derived theoretically and experimentally were suggested for designing weight-efficient safety structures [4]. Theoretical treatment to predict the moment-rotation response of circular hollow steel tubes of varying D/t ratios under pure bending was investigated by Elchakakkani et al. [8]. Using their formulation, load deflection behavior of thin-walled tubes can be easily predicted. Also, by means of the finite element method, deformation characteristics of these structures have been inves- tigated. It was found that finite element analyses can be used successfully in predicting the load-carrying capacity for circular, square and rectangular thin-walled tubes [9–12]. From the published studies and previous experiences, it is generally agreed that the bending resistance of thin-walled tubular beams drops very significantly after reaching the ultimate load value under pure or three-point bending conditions. This is because, shortly after reaching the ultimate load, which also corresponds to maximum bending moment, local buckling deformation takes place [1,3,4]. For these types of problems, it is well known that the ends of specimens are simply supported and, thus, do not carry any bending moment. Although such investigations are useful for the comparative studies Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.10.016 n Corresponding author. Tel.: þ90 264 295 5860; fax: þ90 264 295 5601. E-mail address: kgenel@sakarya.edu.tr (K. Genel). Thin-Walled Structures 51 (2012) 1–9