Abstract
Optimization of parameters of the corrugated shell aims to achieve its minimum weight while keeping maximum stiffness ability. How an introduction of functionally graded corrugations resulted in improved efficiency of this thin-walled structure is demonstrated. The corrugations are graded varying their pitch. The effect of variation in pitch is studied. Homogenization approach gives explicit expressions to calculate the equivalent shell properties. Then well-elaborate methods of optimal design theory are used. The illustrative examples for hydrostatic load demonstrate a high efficiency of the used method.
Acknowledgments
The authors thank the anonymous referees whose valuable comments and suggestions favored improvement of the paper.
References
[1] I. Dayyani, A. D. Shaw, E. I. Saavedra Flores and M. I. Friswell, The mechanics of composite corrugated structures: A review with applications in morphing aircraft, Comp. Struct. 133 (2015), 358–380.10.1016/j.compstruct.2015.07.099Search in Google Scholar
[2] S. Rawat, A. Narayanan, T. Nagendiran and A. K. Upadhyay, Collapse behavior and energy absorption in elliptical tubes with functionally graded corrugations, Proc. Eng. 173 (2017), 1374–1381.10.1016/j.proeng.2016.12.194Search in Google Scholar
[3] F. Guinea, M. I. Katsnelson and M. A. H. Vozmediano, Midgap states and charge inhomogeneities in corrugated graphene, Phys. Rev. B 77 (7) (2008), 075422.10.1103/PhysRevB.77.075422Search in Google Scholar
[4] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Sensitivity analysis in design of constructions made of functionally graded materials, Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sc. 227 (1) (2013), 19–28.10.1177/0954406212445139Search in Google Scholar
[5] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated rods subjected to longitudinal deformation, Arch. Appl. Mech. 85 (2015), 303–314.10.1007/s00419-014-0914-2Search in Google Scholar
[6] I. V. Andrianov, A. A. Diskovsky and E. Syerko, Optimal design of a circular diaphragm using the homogenization approach, Math. Mech. Sol. 22 (3) (2017), 283–303.10.1177/1081286515586278Search in Google Scholar
[7] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading, Arch. Appl. Mech. 88 (2018), 1027–1039.10.1007/s00419-018-1356-zSearch in Google Scholar
[8] A. G. Kolpakov, Design of corrugated plates with extreme stiffnesses, J. Appl. Mech. Tech. Phys. 58 (3) (2017), 495–502.10.1134/S0021894417030142Search in Google Scholar
[9] Y. S. Tian and T. J. Lu, Optimal design of compression corrugated panels, Thin-Wall. Struct. 43 (1) (2005), 477–498.10.1016/j.tws.2004.07.014Search in Google Scholar
[10] T. Flatscher, T. Daxner, D. H. Pahr and F. G. Rammerstorfer, Optimization of corrugated paperboard under local and global buckling constraints, Lect. Notes Appl. Comput. Mech. 55 (2011), 329–346.10.1007/978-90-481-9809-2_17Search in Google Scholar
[11] N. V. Banichuk and B. L. Karihaloo, On the solution of optimization problems with non-smooth extremals, Int. J. Sol. Struct. 13 (8) (1977), 725–733.10.1016/0020-7683(77)90109-3Search in Google Scholar
[12] A. F. Arkhangelskii and V. I. Gorbachev, Effective characteristics of corrugated plates, Mech. Sol. 42 (2007), 447–462.10.3103/S0025654407030132Search in Google Scholar
[13] A. G. Kolpakov and S. I. Rakin, Calculation of the effective stiffness of the corrugated plate by solving the problem on the plate cross-section, J. Appl. Mech. Tech. Phys. 57 (4) (2016), 757–767.10.1134/S0021894416040209Search in Google Scholar
[14] E. Syerko, A. A. Diskovsky, I. V. Andrianov, S. Comas-Cardona and C. Binetruy, Corrugated beams mechanical behavior modeling by the homogenization method, Int. J. Sol. Struct. 50 (2013), 928–936.10.1016/j.ijsolstr.2012.11.013Search in Google Scholar
[15] Y. Zheng, V. L. Berdichevsky and W. Yu, An equivalent classical plate model of corrugated structures, Int. J. Sol. Struct. 51 (11) (2014), 2073–2083.10.1016/j.ijsolstr.2014.02.025Search in Google Scholar
[16] D. Briassoulis, Equivalent orthotropic properties of corrugated sheets, Comput. Struct. 23 (1986), 129–138.10.1016/0045-7949(86)90207-5Search in Google Scholar
[17] Y. Xia, M. I. Friswell and E. I. Saavedra Flores, Equivalent models of corrugated panels, Int. J. Sol. Struct. 49 (13) (2012), 1453–1462.10.1016/j.ijsolstr.2012.02.023Search in Google Scholar
[18] I. V. Andrianov, A. A. Diskovsky and E.G. Kholod, Homogenization method in the theory of corrugated plates, Tech. Mech. 18 (1998), 123–133.Search in Google Scholar
[19] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1959.Search in Google Scholar
[20] M. V. Pryjmak, Periodic functions with variable period, arXiv:1006.2792v1 [math.GM].Search in Google Scholar
[21] A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
