A zigzag model for laminated composite beams

Abstract

In the present work, a zigzag model for symmetric laminated beam is developed. This model uses a sine term to represent the nonlinear displacement field across the thickness as compared to a third order polynomial term in conventional theories. Transverse shear stress and strain are represented by a cosine term as compared to parabolic term. This model satisfies displacement and transverse shear stress continuity at the interface. Zero transverse shear stress boundary condition at the top and bottom of the beam are also satisfied. The numerical results indicates that the present model predicts very accurate results for displacement and stresses for symmetric cross-ply laminated beam, even for small length to thickness ratio. The results are also compared with a simplified theory of same class.

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

“…The normalized displacement and stresses of the present approach are in excellent agreement with the exact solution [47]. It is seen for thick plate cases (a/h = 4, 10) that the ITSDT yields better results than the HSDT [6,48,49], ESDT [51] and the dTrSDTs [38,39,7] in comparison with the exact solution [47]. For thin plate case (a/h = 100), the difference between the solutions are not significant for all displacement and stresses.…”

“…For the sake of simplicity and without loss of generality, we only consider the IGA with using NURBS cubic basis functions (p = 3). Additionally, besides the proposed model, the IGA is also applied for the first time to three different trigonometric shear deformation theory models [38,39,7]. The results obtained from the present solutions have been compared with other published ones.…”

“…The exact 3D elasticity solution of this problem was given by Pagano [47]. Table 7 shows the convergence of the normalization displacement and stresses of the IGA based on the present theory and the different trigonometric shear deformation theories (dTrSDTs) [38,39,7]. The relative error percentages compared with the exact 3D elasticity solution [47] are given in a parentheses.…”

“…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.…”

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

“…Li and Liu [16] presented results of single-layered, two-layered, three-layered cross-ply laminates for cylindrical bending The theory is layer dependent and the number of degrees of freedom involved is very high and hence it is computationally complicated. Icardi [17] and Arya [18] presented zig-zag layerwise theories for the analysis of thick laminated beams.…”