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Crashworthiness design draws considerable attention and interest in energy absorption systems. An optimal design of circular stepped tubes based on free inversion is presented in the current work to improve and enhance the crashworthiness characteristics under axial impact loading. Circular tubes have been known to be efficient energy absorbers per unit weight, and may be considered as the main part of energy absorbing devices even for frequently impact operation like landing gear or for sudden accidents like other vehicles. The precise choice of the circular tubes’ material, shape, and mechanism may save a person life or save a valuable equipment from damage. Adaptive Multiple-Objective Optimization (AMO) can obtain more light and efficient section. An optimization of variable parameters, which represent the shape of a stepped tube under axial impact, is performed using the platform of ANSYS-DESIGN-EXPLORATION linked with LSDYNA code. The analysis leads to 16% reducing in mass with corresponding 31% improving in energy absorption. Introduction Crashworthiness is the most important design consideration in the energy absorption applications such as car bumpers, subfloors of aircrafts, the bottom of lifts, train buffers, marine structures, and machinery and so on [1]. The crashworthiness characteristics considered include load–displacement history, total absorbed energy, and specific absorbed energy, stroke-crushing length, mean crushing force and crush force efficiency. Among of them, the specific energy absorption (SEA, energy absorption per unit mass) is one of the most extensive aspects to evaluate the efficiency of energy absorption systems [2-3] In the recent years, a type of energy absorber known as thin-walled tubes. Thin-walled tubes can be produced with different geometric shapes such as circular, conical, square, taper, octagonal, hexagonal, frusta, S-shaped and so on. Amongst them, thin -walled circular tubes are the most frequently used in energy absorbing devices due to their high strength, high stiffness, low weight, inexpensive, versatile, easy in manufacturing, excellent behaviors on energy absorption characteristics and load-carrying capacity [4]. In spite of, the thin-walled conical tubes have been considered preferable to thin-walled circular tubes as energy absorbers; therefore, it provides a desirable stable crush load–displacement curve response under axial loading and minimize the chances of collapse by global buckling which is an undesirable deformation mode since it reduces the energy absorption capacity [5]. Thin-walled tubes can be classified into different types of deformation mechanisms such as splitting, friction, extrusion, expansion, trigger, ribs, metal cutting and inversion [6-11]. This study concentrates on the inversion mechanism. The inversion process has widely used as energy absorber devices due to its constant inversion load during the process, which obtain an ideal long stable crush load–stroke curve [11]. The thin-walled tube can be inverted inside-out or outside-in. there are two basically ways to produce the inversion tube: the first one is a free inversion and the second is inversion with a die [12-13]. In this paper, a new optimal design of circular stepped tubes based on free inversion is presented to improve and enhance the crashworthiness characteristics under axial impact loading. Adaptive International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016) © 2016. The authors Published by Atlantis Press 91 Multiple-Objective Optimization (AMO), more light and efficient section can be obtained. An optimization of variable parameters, which represent the shape of a circular stepped tube under axial impact, is performed using the platform of ANSYS-DESIGN-EXPLORATION linked with LSDYNA code. Methodology Structure Configuration. Assuming an axial force F applies on a circular stepped tube with double cylinders, however, the Upper tube (T1) and the Lower tube (T2). There are four variable geometrical parameters as follow: (T1UPR) the upper radius of the upper tube T1, (T1LOR) the Lower radius of the upper tube T1, (STEPWIDTH) the horizontal step length between the two tubes and, (T2LOR) the lower radius of the lower tube T2. Moreover, the other fixed parameters are the vertical height of the both tubes (T1Height, T2Height) and the whole thickness as shown in Fig. 1. Fig. 1 The schematic drawing shows the Upper tube (T1) and the Lower tube (T2) parameters. Crashworthiness Criteria for Energy Absorber. Several authors to assess the performance and efficiency of the energy absorber [1-3], in this study the desired parameters, which used for comparison and could be obtained from load-displacement curve as follows, have presented many parameters used to judge the crushing response of structural members, these parameters: Total absorbed energy (EA). The total absorbed energy during axial crushing is calculated by the area under load–displacement curve from the following equation: (1) where, F and δ are crushing load and crushing distance, respectively. Stroke Length (SL). When an absorber is crushed to a certain crushing distance (Stroke Length SL), the structure in ‘‘densification zone’’ and the corresponding force level reaches very large and unpractical values. Finite Element Modelling Data. The explicit non-linear finite element code ANSYS-DESIGNEXPLORATION linked with LSDYNA code [14] is used to optimize the effect of shape parameter on energy absorption characteristics of aluminum circular stepped tube subjected to axial impact crushing. The sidewall of tubes is modeled with four-node shell elements with five integration points through the thickness and one integration point in the element plane. The bottom-stepped tube is fixed to a stationary rigid plane, a rigid body with an initial impact velocity of 10 m /s strikes the circular stepped tube axially and the mass of the rigid body is 100 kg as shown in Fig. 3. Assume that the friction coefficient between all surfaces in contact is 0.25. All models are made of aluminum al-loyAA6060-T4 with the following mechanical properties: Young’s Modulus E=68.2

Crashworthiness characteristics on the Optimal Design of circular stepped tube subjected to axial impact