Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

Abstract

Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

A Four-Variable Plate Theory for Thermoelastic Bending Analysis of Laminated Composite Plates

“…The transverse displacement is in good agreement with that of TSDT [44] for all aspect ratios. The in-plane normal stresses x ¯ y predicted by present theory are found to agree well with those of TSDT [44], whereas FSDT and CPT overestimate the same. The transverse shear stresses are obtained using equilibrium equations of elasticity to satisfy stress continuity at layer Table 2 Normalized displacements and stresses for two layered 0 /90 un-symmetric cross-ply laminated plate subjected to linear thermal load Through thickness distribution of in-plane displacement (ū), in-plane normal and shear stresses (¯ x ¯ y ¯ xy ) and transverse shear stresses (¯ xz ¯ yz ) for two layered 0 /90 un-symmetric crossply laminated composite plate with 2 / 1 = 3.…”

“…From the examination of Table 2 it is observed that the in-plane displacementsū andv predicted by present theory, TSDT of Ghugal and Kulkarni [44] and FSDT of Mindlin [13] are in close agreement with each other whereas CPT [12] underestimates the same for thick plate. The transverse displacement is in good agreement with that of TSDT [44] for all aspect ratios. The in-plane normal stresses x ¯ y predicted by present theory are found to agree well with those of TSDT [44], whereas FSDT and CPT overestimate the same.…”

“…The present results are compared with those obtained by TSDT of Ghugal and Kulkarni [44], FSDT of Mindlin [13], CPT of Kirchhoff [12], Carrera and Ciuffreda [25] and Carrera [55]. The following normalized form is used to present the numerical results.…”

“…Mechab et al [43] developed a new trigonometric shear deformation theory for the thermo-mechanical analysis of laminated composite plates. Ghugal and Kulkarni [44][45][46][47] have applied trigonometric shear deformation theory (TSDT) for the thermal analysis of cross-ply laminated plates. A higherorder shear deformation theory with Taylor series-type expansion in the thickness direction for the displacements has been developed by Kant and Khare [48] for composite and sandwich plates under thermal loading.…”

“…A closed-form solution is obtained for simply supported laminated composite plates. The numerical results for thermal displacements and stresses are compared with those of TSDT of Ghugal and Kulkarni [44]. Also, numerical results are generated using FSDT and CPT for comparison purposes.…”