A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates

Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory

“…The normalized displacement and stresses of a square plate are defined as: Table 4 lists the results of the IGA based on present theory using 17 × 17 cubic B-Spline elements. Numerical solutions are compared to those reported in the literature such as the closed form solution based on HSDT by Reddy [6], the closed form solution based on ESDT by Karama et al [51], the closed form solution based on TrSDT by Mantari et al [50], the closed form solution based on inverse hyperbolic shear deformation theory (IHSDT) by Grover et al [52], the IGA solution based on the dTrSDTs [38,7] and an exact elasticity solution by Pagano [47]. The obtained results indicate a reasonably good agreement with other available ones for all a/h ratios.…”

“…Let Ω be the domain in R 2 occupied by the mid-plane of the plate and u 0 , v 0 , w and β = (β x , β y ) T denote the displacement components in the x, y, z directions and the rotations in the x − z and y − z planes (or the-y and the-x axes), respectively, see h − z displacement field based on higher-order shear deformation theories [7,9,36,37] are defined as follows where f (z) is shape function determining the distribution of the transverse shear strains and stresses through the thickness of plates. This distribution function is chosen so that tangential stress-free boundary conditions at the top and bottom surfaces of the plates are satisfied.…”

Finite Element Analysis of Functionally Graded Plates using Inverse Hyperbolic Shear Deformation Theory

“…The shear strain functions may be trigonometric [2][3][4], hyperbolic [5], logarithmic [6] or exponential [7]. Grover et al [1] has recently developed shear deformation theory with inverse trigonometric function and employed it for the analysis of laminated composite and sandwich plates. They have reported that the theory performs very well and can predict more accurate results than other equivalent single layer shear deformation theories.…”

“…Finite element method is a kind of numerical solution which facilitates solution of such complex problems. The present work focuses on deriving governing equations for the analysis of functionally graded plates using the inverse hyperbolic shear deformation theory developed by Grover et al [1] …”

“…Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory.…”