Availableonlineatwww.sciencedirect.com °scⅰ ence Direct Journal of Bionic Engineering 5(2008)231-238 Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo Jian-feng Ma, Wu-yi Chen, Ling Zhao, Da-hai Zhao 1. School of Mechanical Engineering and automatio Bejing 1000g Beijing University of Aeronautics and Astronautics, 2. Shenyang Aircraft Design Institute, Shenyang 110035, P. R. China Abstract High load-bearing efficiency is one of the advantages of biological structures after the evolution of billions of years iomimicking from nature may offer the potential for lightweight design. In the viewpoint of mechanics properties, the culm of bamboo comprises of two types of cells and the number of the vascular bundles takes a gradient of distribution. A three-point bending test was carried out to measure the elastic modulus. Results show that the elastic modulus of bamboo decreases adually from the periphery towards the centre. Based on the structural characteristics of bamboo, a bionic cylindrical structure as designed to mimic the gradient distribution of vascular bundles and parenchyma cells. The buckling resistance of the bionic structure was compared with that of a traditional shell of equal mass under axial pressure by finite element simulations Results show that the load-bearing capacity of bionic shell is increased by 124.8%. The buckling mode of bionic structure is global buckling while that of the conventional shell is local buckling Keywords: bionic design, bamboo culm, thin-walled cylindrical structure, buckling, load-carrying efficiency Copyright o 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. shell, supported by a compliant core, can bear a higher 1 Introduction buckling load than an equivalent hollow shell of the Material-efficient and lightweight structures are same weight and radius under uniaxial compression or critical requirements in the technical fields of aeronau- pure bending 2.1 Axial and circumferential stiffeners tics and astronautics. One of the essential objectives is to could improve the load-carrying capacity and change the improve load-carrying efficiency(the ratio of load bear- buckling mode of the cylindrical shells ng to weight) in the structure design. So the form, shape Numerical examples of cylindrical shell structures and size of structures need to be optimized to achieve the were presented to throw light on the structural analysis most appropriate configuration for special loadings. and optimization for better load-carrying efficiency. The Thin-walled cylindrical shells as efficient load-carrying buckling and post-buckling of cylindrical shells under structures are widely used in the fields of aeronautics, combined loading of external pressure and axial com- astronautics and shipbuilding. But due to high pression were investigated by Shen and ChenI.Using a length-to-radius ratio, thin-walled cylindrical shells are linear eigenvalue finite element analysis, Spagnoli prone to buckling, i.e., a cross-section flattening may studied different modes of instabil ity in stiffened conical occur which significantly reduces the resistance of the shells under axial compression sI. Sridharan and Zeg structure to bending. To avoid buckling, the thickness gane studied the interaction between local and overall and/or the radius of the hollow beam section are often buckling in stiffened plates and cylindrical shells with a increased to improve its bending stiffness. However, this novel finite elements model. The stabilization of a will reduce the load-carrying efficiency of the structures functionally graded cylindrical shell under axial har because of the increase in weight. Some studies of elas- monic loading was investigated by ng et al. 7) tic buckling suggested that a thin-walled cylindrical Nature is the largest laboratory from where many E-mail: zhiim. g author: Jian-feng Ma C un.ma@gmail.comCorresponding author: Jian-feng Ma E-mail: zhijun.ma@gmail.com Journal of Bionic Engineering 5 (2008) 231–238 Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo Jian-feng Ma1 , Wu-yi Chen1 , Ling Zhao1 , Da-hai Zhao2 1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China 2. Shenyang Aircraft Design Institute, Shenyang 110035, P. R. China Abstract High load-bearing efficiency is one of the advantages of biological structures after the evolution of billions of years. Biomimicking from nature may offer the potential for lightweight design. In the viewpoint of mechanics properties, the culm of bamboo comprises of two types of cells and the number of the vascular bundles takes a gradient of distribution. A three-point bending test was carried out to measure the elastic modulus. Results show that the elastic modulus of bamboo decreases gradually from the periphery towards the centre. Based on the structural characteristics of bamboo, a bionic cylindrical structure was designed to mimic the gradient distribution of vascular bundles and parenchyma cells. The buckling resistance of the bionic structure was compared with that of a traditional shell of equal mass under axial pressure by finite element simulations. Results show that the load-bearing capacity of bionic shell is increased by 124.8%. The buckling mode of bionic structure is global buckling while that of the conventional shell is local buckling. Keywords: bionic design, bamboo culm, thin-walled cylindrical structure, buckling, load-carrying efficiency Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. 1 Introduction Material-efficient and lightweight structures are critical requirements in the technical fields of aeronau￾tics and astronautics. One of the essential objectives is to improve load-carrying efficiency (the ratio of load bear￾ing to weight) in the structure design. So the form, shape and size of structures need to be optimized to achieve the most appropriate configuration for special loadings. Thin-walled cylindrical shells as efficient load-carrying structures are widely used in the fields of aeronautics, astronautics and shipbuilding. But due to high length-to-radius ratio, thin-walled cylindrical shells are prone to buckling, i.e., a cross-section flattening may occur which significantly reduces the resistance of the structure to bending[1]. To avoid buckling, the thickness and/or the radius of the hollow beam section are often increased to improve its bending stiffness. However, this will reduce the load-carrying efficiency of the structures because of the increase in weight. Some studies of elas￾tic buckling suggested that a thin-walled cylindrical shell, supported by a compliant core, can bear a higher buckling load than an equivalent hollow shell of the same weight and radius under uniaxial compression or pure bending[2,3]. Axial and circumferential stiffeners could improve the load-carrying capacity and change the buckling mode of the cylindrical shells. Numerical examples of cylindrical shell structures were presented to throw light on the structural analysis and optimization for better load-carrying efficiency. The buckling and post-buckling of cylindrical shells under combined loading of external pressure and axial com￾pression were investigated by Shen and Chen[4]. Using a linear eigenvalue finite element analysis, Spagnoli studied different modes of instability in stiffened conical shells under axial compression[5]. Sridharan and Zeg￾gane[6] studied the interaction between local and overall buckling in stiffened plates and cylindrical shells with a novel finite elements model. The stabilization of a functionally graded cylindrical shell under axial har￾monic loading was investigated by Ng et al. [7]. Nature is the largest laboratory from where many