Abstract
A refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter Pasternak’s foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces.Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories.It is assumed that the warping of the cross sections generated by transverse shear is presented by a hyperbolic function. The stability equations are determined using the present theory and based on the existence of material symmetry with respect to the median plane.The nonlinear strain-displacement of Von Karman relations are also taken into consideration. .The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical load of mecanical buckling, which are useful for engineers in design. The effects of the foundation parameters,side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are considered in this analysis.are presented comprehensively for the mechanical buckling of rectangular composite plates.
Highlights
Composite materials have important advantages over traditional materials
In order to overcome this limitation, the shear deformable theory which takes account of transverse shear effects is recommended
The Reissner [13] and Mindlin [14] theories are known as the first-order shear deformation theory (FSDT), and account for the transverse shear effects by the way of linear variation of in-plane displacements through the thickness
Summary
Composite materials have important advantages over traditional materials. They bring many functional advantages: lightness, mechanical and chemical resistance, reduced maintenance, freedom of forms. The Reissner [13] and Mindlin [14] theories are known as the first-order shear deformation theory (FSDT), and account for the transverse shear effects by the way of linear variation of in-plane displacements through the thickness These models do not satisfy the zero traction boundary conditions on the top and bottom faces of the plate, and need to use the shear correction factor to satisfy the constitutive relations for transverse shear stresses and shear strains. The most interesting feature of this theory is that it does not require shear correction factor, and has strong similarities with the CPT in some aspects such as governing equation, boundary conditions and moment expressions The accuracy of this theory has been demonstrated for static bending and free vibration behaviors of plates by Shimpi and Patel [17], it seems to be important to extend this theory to the static buckling behavior. Qij are the elements of the reduced stiffness matrix that are defined as follows: Q11
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