An efficient C 0 finite element modeling of an inverse hyperbolic shear deformation theory for the flexural and stability analysis of laminated composite and sandwich plates Neeraj Grover, D.K. Maiti, B.N. Singh n Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur 721302, India article info Article history: Received 21 March 2013 Received in revised form 28 August 2013 Accepted 8 November 2013 Available online 1 December 2013 Keywords: Finite element method Composite plates Sandwich plates Static Buckling Shear deformation theory abstract A computationally efficient C 0 finite element model is developed for laminated composite and sandwich plates by implementing the inverse hyperbolic shear deformation theory recently developed by the authors. This model is used to determine responses of general laminates subjected to various combinations of boundary conditions. The present formulation has been generalized for all existing shear deformation theories involving shear strain function. An eight noded serendipity element with 56 degrees of freedom is used to discretize the plate domain. Influences of lamination sequence (cross ply and angle ply), span to thickness ratio, and boundary conditions are investigated for the flexural behavior of laminated composite and sandwich plates. Further, the stability behavior of plates subjected to in- plane loads (uni-axial and bi-axial) is investigated for a variety of examples. Effects of boundary conditions and applied loads on the critical buckling loads and buckling mode shapes are also assessed for a class of laminates in order to show the efficacy of the present mathematical technique to predict the buckling mode shapes. & 2013 Elsevier B.V. All rights reserved. 1. Introduction The use of composite material for the structure/component design has grown significantly over the last few decades because their response characteristics can be tailored to meet speci fic design requirements. Furthermore, composite structures possess high specific stiffness and high specific strength which leads to overall reduction of weight, thereby increasing the efficiency of the structure. The plates form an essential component for the structural design in aerospace, naval, civil and automobile industries. In many applications, laminated composite and sandwich plates are subjected to transverse and in-plane loads. The excessive stresses induced due to application of these loads may cause failure. In addition to excessive stresses, in-plane compressive loads may alter the equilibrium configuration of a flat plate and hence cause failure due to buckling. Therefore, a compendious and reliable treatment for the behavior of the composite plates becomes essential. Various mathematical techniques regarding the formu- lation of the plate problem, structural kinematics, and solution methodology have been developed in the past few decades. A plate problem can be formulated using the elasticity principles or energy methods. The formulation using the theory of elasticity becomes complicated for composite plates since the involvement of field variables is large as compared to monolithic plates. Structural kinematics comprises of displacement based, stress based or hybrid approaches. Exact and approximate solutions can be implemented to solve the coupled differential equations for the laminated composite plate. The significance of shear deformation [1–4] in composite plates necessitates the use of shear deformation theories instead of classical plates theories based upon Kirchoff's hypothesis. Reissner [5,6] studied the effects of transverse shear deformation on the elastic plates using the first order shear deformation theory (FSDT). The requirement of shear correction factor and its dependency on the boundary conditions, stacking sequence, and lamination sequence make FSDT less realistic [7]. Higher-order shear deformation theories (HSDTs) involving parabolic transverse shear distribution were proposed by Levinson [8], Lo et al. [9], and Reddy [10]. Over the last few decades, the rapid advancements in the use of composite struc- tures have motivated researchers to develop rigorous plate the- ories accounting for accurate structural kinematics especially shear deformation. Notably among them are due to Kant and Pandya [11], Touratier [12], Soldatos [13], Karama et al. [14], Aydogdu [15], Meiche et al. [16], Grover et al. [17], and Mantari et al. [18,19]. In recent years, researchers have focused on inter- laminar continuity (IC) and Zig-Zag (ZZ) requirement [20] in addition to shear deformation. These classes of theories are called Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/finel Finite Elements in Analysis and Design 0168-874X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finel.2013.11.003 n Corresponding author. Tel.: þ91 3222 283026; fax: þ91 3222 255303. E-mail addresses: bnsingh@aero.iitkgp.ernet.in, bnsingh9@rediffmail.com (B.N. Singh). Finite Elements in Analysis and Design 80 (2014) 11–22