An improved C 0 FE model for the analysis of laminated sandwich plate with soft core H.D. Chalak a,n , Anupam Chakrabarti a , Mohd. Ashraf Iqbal a , Abdul Hamid Sheikh b a Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India b School of Civil, Environment and Mining Engineering, University of Adelaide, North Terrace, Adelaide, SA 5005, Australia article info Article history: Received 16 September 2011 Received in revised form 13 February 2012 Accepted 18 February 2012 Available online 22 March 2012 Keywords: Sandwich plate Soft core Zigzag theory Finite element Stress continuity abstract An improved C 0 two dimensional finite element model based on higher order zigzag plate theory (HOZT) is developed and applied to the analysis of laminated composite and sandwich plates under different situations to study the performance of the model. In the proposed model, the in-plane displacements variation is considered to be cubic for both the face sheets and the core, while the transverse displacement is assumed to vary quadratically within the core and remains constant in the faces beyond the core. It satisfies the conditions of transverse shear stress continuity at the layer interfaces as well as satisfies the zero transverse shear stress condition at the top and bottom of the plate. The well-known problem of continuity requirement of the derivatives of transverse displace- ments is overcome by choosing the nodal field variables in an efficient manner. A nine-node C 0 quadratic plate finite element is implemented to model the HOZT for the present analysis. Numerical examples covering different features of laminated composite and sandwich plates are presented to illustrate the accuracy of the present model. & 2012 Elsevier B.V. All rights reserved. 1. Introduction A laminated composite/sandwich structure has a layered construction, which consists of a number of lamina or ply of orthotropic materials stacked one over the other and bonded together to act as an integral structural element. The individual layers of the laminate may have different orientations which enables the structural designer to achieve required strength in the preferred direction. It also shows superior properties such as high strength/stiffness to weight ratio and greater resistance to envir- onmental degradation compared to conventional metallic materi- als. Due to all these merits, the fiber reinforced laminated composite/sandwich is gaining wide acceptance in various struc- tural applications. In order to fulfill the requirement of weight minimization in a more efficient manner, a sandwich construction having low strength core and high strength face sheets is used. The role of transverse shear deformation is very important in laminated composites, as the material is weak in shear due to its low shear modulus to extensional rigidity. Due to the large variation of material properties across the thickness, the behavior of laminated sandwich plates becomes very complex. A proper understating on the response of these structures under different loading conditions is extremely important for their safe design. In this context a number of plate theories have been developed where the major emphasis is to model the shear deformation in refined manner. These plate theories can be broadly divided into two categories based on their assumed displacement fields: (1) Single layer theory and (2) Layer-wise theory. In single layer theory, the deformation of plate is expressed in terms of unknown parameters of the reference plane, i.e. middle plane. In this theory the transverse shear strain is assumed to be uniform over the entire plate thickness and it is known as Reissner–Mindlin’s plate theory which is also known as the first order shear deformation theory (FSDT). Goyal and Kapania [1] developed a five node beam FE model based on FSDT. Moderately thick rectangular laminated composite plate was analyzed by Ferreira [2] using multiquadric radial basis function method (i.e. mesh free collocation method) based on FSDT. However, this theory (FSDT) requires a shear correction factor to compensate for the actual parabolic variation of the shear stress. The higher order shear deformation theories (HSDT) have been developed with the aim to avoid the use of shear correction factors by including the actual cross sectional warping and to get the realistic variation of the transverse shear strains and stresses throughout the plate thickness [3]. Kant [4] derived the complete set of equations for the analysis of thick elastic plates with the help of third order refined shear deformation theory (HSDT). The three-dimensional Hooke’s laws was also used for plate material Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/finel Finite Elements in Analysis and Design 0168-874X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.finel.2012.02.005 n Corresponding author. Tel.: þ91 1332 285844; fax: þ91 1332 275568. E-mail address: chalakhd@yahoo.co.in (H.D. Chalak). Finite Elements in Analysis and Design 56 (2012) 20–31