In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.<\/p>\r\n","references":"[1]\tL. Guo, S. Yang, H. Jiao, \u201cBehavior of thin-walled circular hollow section tubes subjected to bending,\u201d Thin-Walled Structures, vol. 73, pp. 281-289, 2013. \r\n[2]\tD. Karagiozova, T. X. Yu, G. Lu, X. Xiang, \u201cResponse of a circular metallic hollow beam to an impulsive loading,\u201d Thin-Walled Structures, vol. 80, pp. 80-90, 2014. \r\n[3]\tD. Karagiozova, T. X. Yu, G. Lu, \u201cTransverse blast loading of hollow beams with square cross-sections,\u201d Thin-Walled Structures, vol. 62, pp. 169-178, 2013. \r\n[4]\tB. Zheng, G. Shu, L. Xin, R. Yang, Q. Jiang, \u201cStudy on the Bending Capacity of Cold-formed Stainless Steel Hollow Sections,\u201d Structures, vol. 8, pp. 63-74, 2016. \r\n[5]\tZ. Li, D. Yang, \u201cThermal post buckling analysis of anisotropic laminated beams with tubular cross-section based on higher-order theory,\u201d Ocean Engineering, vol. 115, pp. 93-106, 2016. \r\n[6]\tH. Asadi, M. M. Aghdam, \u201cLarge amplitude vibration and post-buckling analysis of variable cross-section composite beams on nonlinear elastic foundation,\u201d International Journal of Mechanical Sciences, vol. 79, pp. 47-55, 2014. \r\n[7]\tY. Zhao, Y. Huang, M. Guo, \u201cA novel approach for free vibration of axially functionally graded beams with non-uniform cross-section based on Chebyshev polynomials theory\u201d Composite Structures, vol. 168, pp. 277-284, 2017. \r\n[8]\tE. Ghafari, J. Rezaeepazhand, \u201cIsogeometric analysis of composite beams with arbitrary cross-section using dimensional reduction method\u201d Computer Methods in Applied Mechanics and Engineering, vol. 318, pp. 594-618, 2017. \r\n[9]\tP. Jiao, W. Borchani, H. Hasni, A. Alavi, N. Lajnef, \u201cPost-buckling response of non-uniform cross-section bilaterally constrained beams\u201d Mechanics Research Communications, vol. 78, pp. 42-50, 2016. \r\n[10]\tK. H. Law, L. Gardner, \u201cLateral instability of elliptical hollow section beams\u201d Engineering Structures, vol. 37, pp. 152-166, 2012. \r\n[11]\tJ. Murin, V. Goga, M. Aminbaghai, J. Hrabovsky, T. Sedlar, H. A. Mang, \u201cMeasurement and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections\u201d Engineering Structures, vol. 136, pp. 68-76, 2017. \r\n[12]\tJ. N. Reddy, \u201cGeometrically Nonlinear Transient Analysis of Laminated Composite Plates\u201d AIAA Journal, vol. 21(4), pp. 621-628, 1983. \r\n[13]\tG. R. Cowper, \u201cThe Shear Coefficient in Timoshenko's Beam Theory\u201d Journal of Applied Mechanics, vol. 33(2), pp. 335-340, 1966. \r\n[14]\tM, Hajianmaleki, M. S. Qatu. \u201cStatic and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions\u201d Composite Part B: Eng, vol. 43, pp. 1767\u201375, 2012.\r\n[15]\tG. She, F. Yuan, Y. Ren, \u201cNonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory\u201d Composite Structures, vol. 165, pp. 74-82, 2017.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 128, 2017"}