Nonlinear flexural response of laminated composite plates under hygro-thermo-mechanical loading A.K. Upadhyay a , Ramesh Pandey a , K.K. Shukla b, * a Department of Applied Mechanics, MNNIT Allahabad, UP 211004, India b Civil Engineering Department, MNNIT Allahabad, UP 211004, India article info Article history: Received 1 July 2009 Received in revised form 7 August 2009 Accepted 20 August 2009 Available online 11 November 2009 Keywords: Analytical Composite plate Nonlinear Hygro-thermo-mechanical Elastic foundation abstract The paper deals with Chebyshev series based analytical solution for the nonlinear flex- ural response of the elastically supported moderately thick laminated composite rect- angular plates subjected to hygro-thermo-mechanical loading. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Kar- man nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The elastic and hygrothermal properties of the fiber reinforced com- posite material are considered to be dependent on temperature and moisture concen- tration and have been evaluated utilizing micromechanics model. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of Winkler and Pasternak foundation parameters, tempera- ture and moisture concentration on nonlinear flexural response of the laminated com- posite rectangular plate with different lamination scheme and boundary conditions are presented. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction The plates/panels made up of the polymer based fibre reinforced composite materials, primarily used as one of the major structural elements in aerospace, naval, automobile, etc. are often subjected to hostile environmental conditions during their operational life. The development of solid propellant rocket motors and increased use of soft filaments in aerospace struc- tures etc. have intensified the need for the solutions of various plate/panel problems supported by elastic medium. Also, the sandwich plates/panels may be viewed as problem of plates/panels supported with elastic medium. In addition to mechan- ical loading, these structures are often subjected to hygroscopic as well as destabilizing thermal loadings also. The structural components of high-speed aircrafts, spacecrafts and re-entry space vehicle encounter hygrothermal loading conditions. The adsorbed moisture and induced temperature adversely affects the material properties, which in turn reduces the stiffness and strength of the structure thus affecting the performance of the structure. Hence, the degradation in performance of the structure due to moisture concentration and high temperature has become increasingly more important with the pro- longed use of fiber-reinforced polymer composite material in many structural applications. The deformation and stress analysis of the laminated composite plates subjected to moisture and temperature has been the subject of research interest of many investigators. Adams and Miller [1], Ishikawa et al. [2] and Strife and Prewo [3] studied the effect of environment on the material properties of composite materials and observed that it has significant effect on strength and stiffness of the composites. Therefore, there is a need to understand the behavior of composite 1007-5704/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2009.08.026 * Corresponding author. Tel.: +91 532 2271206; fax: +91 532 2445101. E-mail addresses: ashu157@gmail.com (A.K. Upadhyay), ramesh@mnnit.ac.in (R. Pandey), kkshukla@mnnit.ac.in, shuklakk@hotmail.com (K.K. Shukla). Commun Nonlinear Sci Numer Simulat 15 (2010) 2634–2650 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns