A new higher order shear deformation theory for sandwich and composite laminated plates

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

“…For a comparison, the normalized displacement and stresses of a four layer simply supported square plate are computed using 17 × 17 B-spline elements. The obtained results of the IGA based on the present theory are compared with those of the several other methods based on other higher-order shear deformation theories such as the closed form solution (CSF) based on the HSDT by Reddy M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT [6], the finite strip method (FSM) based on HSDT by Akhras et al [48], the multiquadric radial basis function method (RBFs) based on a finite point formulation and HSDT by Ferreira et al [49], the closed form solution based on a trigonometric shear deformation theory (TrSDT) by Mantari et al [50], the closed form solution based on an exponential shear deformation theory (ESDT) by Karama et al [51], the IGA based on the dTrSDTs [38,39,7] and an exact 3D elasticity approach studied by Pagano [47]. Table 3 is provided the comparison between the present method and other methods.…”

“…For a comparison, we compute the normalized displacement and stresses of the sandwich square plate using 17 × 17 B-spline elements. Obtained results from the IGA based on ITSDT are compared with those of the FEM based on HSDT reported by Pandya and Kant [54], the multiquadric radial basis function method (RBFs) based on a finite point formulation and HSDT by Ferreira et al [49], the multiquadric radial basis function method (RBFs) relied on the layerwise deformation theory (LW) by Ferreira [55], the closed form solution based on IHSDT by Grover et al [37], the closed form solution based on ESDT by Mantari et al [36], exact solution by Srinivas [53] and the IGA based on dTrSDTs [38,7]. The results with respect to various values of R (R = 5, 10, 15) are given in Table 6.…”

“…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.…”

Free Vibrations Analysis of Composite Laminate Plates Used in Automotive Industry

“…Some authors have tried to solve the problem relating to correction factors by introducing shear deformation shape functions [5][6][7][8][9][10][11][12][13][14][15][16]. This paper considers the problem of free vibrations of simply supported laminate plates by applying high-order shear deformation theories (HSDT) based on selected shape functions.…”