This review, overviews the development and applications of shear deformation (SD) laminated composite plate theories. The present overview mainly focuses on theoretical models based on SD theories of laminated composite plates. This comprehensive review has been categorized with an equivalent single-layer laminate and layerwise laminate theories. An equivalent single-layer laminate theory includes classical laminated plate theory, first-order shear deformation laminated theory, second-order shear deformation laminated theory, third-order shear deformation laminated theory, parabolic shear deformation laminated theory, trigonometric shear deformation laminated theory, hyperbolic shear deformation laminated theory, and higher order shear deformation laminated theory. The layerwise laminate theories include discrete-layer theories and zig-zag theories. In addition, the 3D elasticity solutions theory, the mixed (hybrid) plate theories, unified theories, advanced shear deformation theories, and the recently developed smart composite are also reviewed.

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This paper developed the buckling analysis of nonlinear behavior of firstorder shear deformation laminated composite plates. The first-order displacement functions are used based on some simplifying assumptions. This article further simplifies the transverse displacement into bending and shear components at the midplane have reduced the number of variables and governing differential equations. The von Karman assumptions are used to derive the nonlinear strains based on the displacement functions. Hamilton's principle is used to derive the equation of motion and boundary conditions. The analytical solutions are developed from the present theory and compared the results of the critical buckling loads with exact and three-dimensional solutions. Result shows that the present theory has closely associated with the exact and three-dimensional theory.

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