Ma et al.: Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo 35 42.2 Graded elastic modulus of bamboo gion and sparse in the inner surface region(Fig. 7a) A three-point flexural test of the bamboo specimens Actually, the strength distribution in the cross-section of was carried out on an Instron 5565 at 5 mm min using culm is proportional to the volume fraction of fibers, and a 5 kN load cell. An extensometer was used to precisely the culm has a higher strength in the outer surface region monitor the deformation of the specimens(shown in Fig. than in the inner region[ 2 9). The initial linear portion of the load-displacement curve was used to calculate the elastic modulus. as 5 Bionic design of cylindrical shell shown in Fig. 10, the graded elastic moduli displayed a 5.1 Bionic design trend of decrease with the increase in location parameter To a great extent, the structures of organisms de- p. Each value reported is the average of four specimens pend on the environmental loads, so it is necessary to at the same radial location from different fan-shaped analyze the growth environment in order to understand block. the mechanical advantage of the structures of organisms The similarities between the biological and engi neering structures, including structural, functional and loading comparabilities, should be studied extensively Then the structural superiority of the selected organism could be applied in the engineering structural optimiza- tion. Biological structures are often more complicated than the engineering ones, so the manufacturability of the designed bionic structures must be taken into ac count. After full research on the structures of organisms, the bionic structure would be modeled with 3D model- ing software and a structural analysis would be run with FEA software to verify the effect of the optimization. If this approach fails, repeating the similarity analysis and structural characteristics to further the design criteria Fig 9 Test set-up for testing bamboo specimens and methods until the bionic structure obtains excellent mechanical properties, as shown in Fig. 1 Based on the relationship between ture and the mechanical properties of bamboo, a bio cylindrical shell structure was designed(shown in Fi 14 12), where the pipes and the ribs have the same function as the parenchyma cells, and the thin-walled cylindrical shells have the same function as the vascular bundles aggregated at the same radial location of the bamboo The graded thickness of the shells, the variational pipes and the ribs show that the bionic cylindrical shell is functionally graded structure In order to show the superiority of the bionic 0.5 Location parameter ructure,an equal-mass conventional shell witl Fig 10 Elastic modulus of bamboo specimens Fig 5b)was compare the load-carrying efficiency. Both of the The fiber distribution of sclerenchyma tissue in the structures have the same outer diameter D of 200 mm cross-section of bamboo culm is dense in the outer re- and the same length H of 1000 mmMa et al.: Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo 235 4.2.2 Graded elastic modulus of bamboo A three-point flexural test of the bamboo specimens was carried out on an Instron 5565 at 5 mm·min−1 using a 5 kN load cell. An extensometer was used to precisely monitor the deformation of the specimens (shown in Fig. 9). The initial linear portion of the load-displacement curve was used to calculate the elastic modulus. As shown in Fig. 10, the graded elastic moduli displayed a trend of decrease with the increase in location parameter ρ. Each value reported is the average of four specimens at the same radial location from different fan-shaped blocks. Fig. 9 Test set-up for testing bamboo specimens. Fig. 10 Elastic modulus of bamboo specimens. The fiber distribution of sclerenchyma tissue in the cross-section of bamboo culm is dense in the outer re￾gion and sparse in the inner surface region (Fig. 7a). Actually, the strength distribution in the cross-section of culm is proportional to the volume fraction of fibers, and the culm has a higher strength in the outer surface region than in the inner region[12]. 5 Bionic design of cylindrical shell 5.1 Bionic design To a great extent, the structures of organisms de￾pend on the environmental loads, so it is necessary to analyze the growth environment in order to understand the mechanical advantage of the structures of organisms. The similarities between the biological and engi￾neering structures, including structural, functional and loading comparabilities, should be studied extensively. Then the structural superiority of the selected organisms could be applied in the engineering structural optimiza￾tion. Biological structures are often more complicated than the engineering ones, so the manufacturability of the designed bionic structures must be taken into ac￾count. After full research on the structures of organisms, the bionic structure would be modeled with 3D model￾ing software and a structural analysis would be run with FEA software to verify the effect of the optimization. If this approach fails, repeating the similarity analysis and structural characteristics to further the design criteria and methods until the bionic structure obtains excellent mechanical properties, as shown in Fig. 11. Based on the relationship between the microstruc￾ture and the mechanical properties of bamboo, a bionic cylindrical shell structure was designed (shown in Fig. 12), where the pipes and the ribs have the same function as the parenchyma cells, and the thin-walled cylindrical shells have the same function as the vascular bundles aggregated at the same radial location of the bamboo. The graded thickness of the shells, the variational pipes and the ribs show that the bionic cylindrical shell is a functionally graded structure. In order to show the superiority of the bionic structure, an equal-mass conventional shell with hat-stiffened plates (shown in Fig. 5b) was used to compare the load-carrying efficiency. Both of the structures have the same outer diameter D of 200 mm and the same length H of 1000 mm