International Congress on Computational Mechanics and Simulation (ICCMS), IIT Hyderabad, 10-12 December 2012 Page 1 of 10 Adaptive Natural Element Method for Analysis of Plates and Laminates Madhukar S  and Rajagopal A † * Project Associate, Department of Civil Engineering, IIT Hyderabad – 502205, India † Asst. Professor, Department of Civil Engineering, IIT Hyderabad – 502205, India Presenting authors email: madhukarreddy.s@gmail.com Abstract In this paper, a natural element method (NEM) is employed for the analysis of plates and laminates. The displacement field and strain field of plate are based on Reissner-Mindlin plate theory. Sibson interpolation [4] based on natural neighbor coordinates has been used for interpolation. The bending results of the isotropic and laminated composite plate based on natural neighbor method are validated with available finite element method as well analytical results taken from literature. Recovery based relative energy norm error estimator and an adaptive refinement strategy is proposed for the plates by NEM. 1. Introduction Finite element method (FEM) is being used extensively since several decades in analysis of structures and has been successfully implemented in commercial structural analysis packages. Large deformation analysis FEM poses problems such as element distortion. The element distortion affects the performance of the method. The accuracy of results in analysis of structures by finite element method depends on mesh/element shape, size and mesh density. Modeling thin structures with large deformation, material with discontinuities and crack modeling in FEM involves complexities such as adaptive mesh generation/refinement, distortion of element in coarse mesh. To overcome such problems the meshless techniques have been developed by researchers [1-2], However these meshless methods have restriction on imposition of essential and natural boundary conditions because meshless approximation do not satisfy delta Kronecker property ( ( ) I J IJ x φ δ ≠ ). The other meshless technique to overcome this problem is natural element method (NEM) was developed by Sambridge et al [3] where interpolation function is based on Sibson [4] natural neighbor coordinates. NEM was successfully applied to solid mechanics problems by Sukumar et al [5]. The analysis of plates and laminates with meshless methods is a gaining popularity in recent years. The analysis of laminated composite plates by various 2D plate theories is available in literature namely CPT, FSDT and TSDT. The CPT predicts accurate deflection and natural frequencies for thin plates but for thick plate it under predicts deflection and over predicts natural frequency as well as buckling loads because of assumption made in it. The transverse shear strains are zero in CPT but when a thick plate is being analyzed the shear deformation should be accounted. In first-order shear deformation theory (FSDT) [7] where uniform transverse shear strain is taken over the entire laminate thickness but the actual variation over the laminate thickness is not uniform, it requires an arbitrary shear correction factor. In order to overcome this limitation, higher order shear deformation theory (TSDT) [8] is proposed. Pandya and Kant [9] presented a refined higher order theory considering effect of transverse normal strains for orthotropic and laminated composite plates. Kant and Swaminathan [11] considered the effect of transverse normal strain in the buckling analysis of simply supported composite and sandwich plate. The theories [6-11] are called global displacement theories (GDT) where the transverse shear strain is continuous across the entire thickness but there is a discontinuity in the variation of the transverse shear stresses at the layer interfaces. The other improved theories which resolve the above problem are zig-zag plate theory [12-13]. There are three dimensional elasticity solutions [14-15] of the laminated plate by various researchers available in literature. The 3D elasticity solutions are computationally costly, so 2D plate theories are widely used. The 3D elasticity solutions serve as a benchmark for two dimensional plate theories for plate analysis by analytical and numerical methods. Analysis of plates and laminates by meshless methods is gaining popular in recent years because of its advantages in ease handling of large deformation problems and ease of refinement for very accurate results. Dinis et al [16] proposed an improved meshless method, natural neighbor radial point interpolation method