Abstract
Stiffened panels buckle under compressive loads which would degrade load-bearing capabilities of the structures. Fast yet accurate estimations of buckling loads and associated mode shapes are critical in the early stages of design and optimization. This paper presents a method based on the mechanics of structure genome (MSG) for the global buckling analysis of stiffened composite panels. The original geometrically nonlinear problem is mathematically reduced to a geometrically linear constitutive modeling of the structure genome and a geometrically nonlinear formulation of the macroscopic plate analysis. Validation case studies show that MSG is highly accurate and efficient as compared to the detailed finite element analysis. The buckling behaviors of stiffened panels under various boundary conditions and loadings are investigated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Zheng, Q., Jiang, D., Huang, C., Shang, X., Ju, S.: Analysis of failure loads and optimal design of composite lattice cylinder under axial compression. Compos. Struct. 131, 885 (2015)
Lopatin, A., Morozov, E.: Buckling of the composite sandwich cylindrical shell with clamped ends under uniform external pressure. Compos. Struct. 122, 209 (2015)
Wodesenbet, E., Kidane, S., Pang, S.S.: Optimization for buckling loads of grid stiffened composite panels. Compos. Struct. 60(2), 159 (2003)
Fenner, P.E.: Finite element buckling analysis of stiffened plates with filleted junctions. Thin-Walled Struct. 59, 171 (2012)
Bisagni, C., Vescovini, R.: Analytical formulation for local buckling and post-buckling analysis of stiffened laminated panels. Thin-Walled Struct. 47(3), 318 (2009)
Stamatelos, D., Labeas, G., Tserpes, K.: Analytical calculation of local buckling and post-buckling behavior of isotropic and orthotropic stiffened panels. Thin-Walled Struct. 49(3), 422 (2011)
Szilard, R.: Theories and Applications of Plate Analysis: Classical Numerical and Engineering Methods. Wiley, Hoboken (2004)
Chen, H.J., Tsai, S.W.: Analysis and optimum design of composite grid structures. J. Compos. Mater. 30(4), 503 (1996)
Sadeghifar, M.: Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity. Arch. Appl. Mech. 81(7), 875 (2011)
Jaunky, N., Knight, N.F., Ambur, D.R.: Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels. Compos. Part B 27(5), 519 (1996)
Byklum, E., Steen, E., Amdahl, J.: A semi-analytical model for global buckling and postbuckling analysis of stiffened panels. Thin-Walled Struct. 42(5), 701 (2004)
Kidane, S., Li, G., Helms, J., Pang, S.S., Woldesenbet, E.: Buckling load analysis of grid stiffened composite cylinders. Compos. Part B 34(1), 1 (2003)
Xu, Y., Tong, Y., Liu, M., Suman, B.: A new effective smeared stiffener method for global buckling analysis of grid stiffened composite panels. Compos. Struct. 158, 83 (2016)
Ren, M., Li, T., Huang, Q., Wang, B.: Numerical investigation into the buckling behavior of advanced grid stiffened composite cylindrical shell. J. Reinf. Plast. Compos. 33(16), 1508 (2014)
Wang, B., Tian, K., Hao, P., Zheng, Y., Ma, Y., Wang, J.: Numerical-based smeared stiffener method for global buckling analysis of grid-stiffened composite cylindrical shells. Compos. Struct. 152, 807 (2016)
Ninh, D.G., Bich, D.H., Kien, B.H.: Torsional buckling and post-buckling behavior of eccentrically stiffened functionally graded toroidal shell segments surrounded by an elastic medium. Acta Mech. 226(10), 3501 (2015)
Bich, D.H., Ninh, D.G.: Research on dynamical buckling of imperfect stiffened three-layered toroidal shell segments containing fluid under mechanical loads. Acta Mech. 228(2), 711 (2017)
Dung, D., Nga, N.: Buckling and postbuckling nonlinear analysis of imperfect FGM plates reinforced by FGM stiffeners with temperature-dependent properties based on TSDT. Acta Mech. 227(8), 2377 (2016)
Dung, D., Hoai, B., Hoa, L.: Postbuckling nonlinear analysis of FGM truncated conical shells reinforced by orthogonal stiffeners resting on elastic foundations. Acta Mech. 228(4), 1457 (2017)
Chan, D., Dung, D., Hoa, L.: Thermal buckling analysis of stiffened FGM truncated conical shells resting on elastic foundations using FSDT. Acta Mech. 229(5), 2221 (2018)
Hassani, B., Hinton, E.: A review of homogenization and topology optimization I: homogenization theory for media with periodic structure. Comput. Struct. 69(6), 707 (1998)
Kwon, Y.W., Allen, D.H., Talreja, R.: Multiscale Modeling and Simulation of Composite Materials and Structures. Springer, New York (2008)
Kalamkarov, A.L., Andrianov, I.V., Danishevs’kyy, V.V.: Asymptotic homogenization of composite materials and structures. Appl. Mech. Rev. 62(3), 030802 (2009)
Challagulla, K., Georgiades, A., Kalamkarov, A.: Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: part I theory. Eur. J. Mech. A Solids 29(4), 530 (2010)
Wang, D., Abdalla, M.M.: Global and local buckling analysis of grid-stiffened composite panels. Compos. Struct. 119, 767 (2015)
Yu, W.: A unified theory for constitutive modeling of composites. J. Mech. Mater. Struct. 11(4), 379 (2016)
Liu, X., Yu, W.: A novel approach to analyze beam-like composite structures using mechanics of structure genome. Adv. Eng. Softw. 100, 238 (2016)
Peng, B., Goodsell, J., Pipes, R.B., Yu, W.: Generalized free-edge stress analysis using mechanics of structure genome. J. Appl. Mech. 83(10), 101013 (2016)
Liu, N., Yu, W.: Evaluation of smeared properties approaches and mechanics of structure genome for analyzing composite beams. Mech. Adv. Mater. Struct. 25, 1–15 (2017)
Rouf, K., Liu, X., Yu, W.: Multiscale structural analysis of textile composites using mechanics of structure genome. Int. J. Solids Struct. 89, 136–137 (2018)
Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11, 357 (1963)
Zhang, D., Waas, A.M.: A micromechanics based multiscale model for nonlinear composites. Acta Mech. 225(4–5), 1391 (2014)
Allaire, G., Brizzi, R.: A multiscale finite element method for numerical homogenization. Multiscale Model. Simul. 4(3), 790 (2005)
Yang, D., Zhang, H., Zhang, S., Lu, M.: A multiscale strategy for thermo-elastic plastic stress analysis of heterogeneous multiphase materials. Acta Mech. 226(5), 1549 (2015)
Efendiev, Y., Hou, T.Y.: Multiscale Finite Element Methods Theory and Applications. Springer, Berlin (2009)
Hou, T., Wu, X.H.: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134(1), 169 (1997)
Yu, W., Hodges, D.H., Volovoi, V.V.: Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery. Int. J. Solids Struct. 39(20), 5185 (2002)
Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications. AMS Chelsea Publishing, Providence (1978)
Danielson, D.A., Hodges, D.H.: Nonlinear beam kinematics by decomposition of the rotation tensor. J. Appl. Mech. 54(2), 258 (1987)
Yu, W., Hodges, D.H., Ho, J.C.: Variational asymptotic beam sectional analysis: an updated version. Int. J. Eng. Sci. 59, 40 (2012)
Yu, W., Hodges, D.H.: A geometrically nonlinear shear deformation theory for composite shells. J. Appl. Mech. 71(1), 1 (2004)
Pietraszkiewicz, W., Eremeyev, V.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3), 774 (2009)
Cosserat, E., Cosserat, F., et al.: Théorie des corps déformables (1909)
Yu, W., Hodges, D.H., Volovoi, V.V.: Asymptotic generalization of Reissner–Mindlin theory: accurate three-dimensional recovery for composite shells. Comput. Methods Appl. Mech. Eng. 191(44), 5087 (2002)
Lopatin, A., Morozov, E.: Buckling of the SSCF rectangular orthotropic plate subjected to linearly varying in-plane loading. Compos. Struct. 93(7), 1900 (2011)
Shufrin, I., Rabinovitch, O., Eisenberger, M.: Buckling of symmetrically laminated rectangular plates with general boundary conditions: a semi-analytical approach. Compos. Struct. 82(4), 521 (2008)
Meziane, M.A.A., Abdelaziz, H.H., Tounsi, A.: An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. J. Sandw. Struct. Mater. 16(3), 293 (2014)
Panda, S.K., Ramachandra, L.: Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads. Int. J. Mech. Sci. 52(6), 819 (2010)
Hamedani, S.J., Ranji, A.R.: Buckling analysis of stiffened plates subjected to non-uniform biaxial compressive loads using conventional and super finite elements. Thin-Walled Struct. 64, 41 (2013)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)
Riks, E.: The application of Newton’s method to the problem of elastic stability. J. Appl. Mech. 39(4), 1060 (1972)
Riks, E.: Some computational aspects of the stability analysis of nonlinear structures. Comput. Methods Appl. Mech. Eng. 47(3), 219 (1984)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, N., Yu, W. & Hodges, D.H. Mechanics of structure genome-based global buckling analysis of stiffened composite panels. Acta Mech 230, 4109–4124 (2019). https://doi.org/10.1007/s00707-018-2339-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-018-2339-4