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Postbuckling and postbuckled vibration characteristics of sandwich plate subjected to non-uniform in-plane loadings is investigated in this article. The core compressibility effects are considered in the model by assuming fourth and fifth order expansions for the transverse and tangential displacement of the core. The exact stress distributions within the panel are determined by panel prebuckling analysis for the applied parabolic and partial edge loadings. Multi-term Galerkin's method is employed to reduce the governing partial differential equation to a set of non-linear ordinary differential equations in the case of dynamic analysis and to a set of non-linear algebraic equations in the case of static stability analysis. Newton-Raphson method in conjunction with Riks approach is used to trace the postbuckling path. Free vibration frequencies of the sandwich plate about a static equilibrium state are obtained by solving the associated linear eigenvalue problem. From numerical study it is observed that the postbuckling path becomes more softening type with increase of aspect ratio. Moreover, unloaded fixed edge of SCSC sandwich plate gives more rigidity than unloaded simply supported edge of CSCS. The prebuckling and postbuckling frequency increases with increase in edge restraint, and in postbuckling range, frequency increases with increase of in-plane load. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, instability of a thick through-the-thickness functionally graded material (FGM) rectangular plates under the practical cases of thermal and mechanical loading conditions is analyzed. Uniform shear, uniform uni-axial or biaxial compression/tension, uniform temperature rise, heat conduction across the thickness, and combined cases are considered. For thermal buckling and combined cases in thermal field, temperature dependency of the properties is also taken into account. The four-variable refined plate theory with parabolic distribution of shear strains through-the-thickness is implemented to establish the governing equilibrium and stability equations. Only the clamped type of boundary conditions is considered after the proof of bifurcation type buckling existence. The resulted equations are uncoupled in a reasonable manner. The multi-term Galerkin method is used to derive the critical buckling loads/temperatures and buckled shapes of the plate under various loading conditions. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical study on the influence of in-plane forces on the dynamic characteristics of a plate with grooves in different sizes. A sub-structuring approach, the reverse receptance method, is applied to solve the eigenvalues of an in-plane forces loaded plate with two parallel grooves and two orthogonal grooves, respectively. On considering coupling and interaction between two orthogonally connected grooves, the point receptance arrays are employed. Accuracy is evaluated by comparing the analytical solutions with numerical results obtained from the finite element model. Parametric study reveals, the deeper the groove, the lower the natural frequencies and buckling loads of the grooved plate will be. With in-plane tensions applied and increased linearly, the grooved plate is stiffened gradually and its natural frequencies increase accordingly. With equal bi-axial tensions, the natural frequencies of the grooved plates increase twice as much as those with uni-axial tension do. With in-plane compressive forces on the plate, the situations are reversed. The lowest natural frequency of a grooved plate with sufficient tensions can be higher than that of a non-grooved unloaded plate. When the groove size and the loading condition are the same, the orthogonal grooves decrease the natural frequencies and the buckling loads of a plate more than the parallel grooves do. The in-plane forces do not affect the mode shapes of the grooved plate; but the grooves do. The analytical evaluation demonstrates the accuracy and applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: The paper presents a predictive model of the flatness defects, which appear during rolling of thin plates, the origin of which is the roll stack thermo-elastic deformation. The combination of the elastic deflection, the thermal crown and the roll grinding crown results in a non-parallel bite, and if the deformed roll transverse profile is not an affinity of the incoming strip profile, differential elongation results and induces high stresses in the outgoing strip. The latter, combined with the imposed strip tension force, result in a net post-bite stress field which may be sufficiently compressive locally to promote buckling. A variety of non-developable shapes may result, generally occurring as waviness (centre waves, wavy edges, quarter-buckles, etc.). This problem is most of the time addressed in a decoupled way, i.e. as a post-processing of the residual stresses computed by a strip rolling model; the present paper on the contrary describes a fully coupled approach of in-bite plastic deformation and post-bite buckling. For this purpose, a simple buckling criterion has been introduced in a FEM model of strip and roll deformation, Lam3/Tec3; its implementation is documented in details. The capabilities and limits of the present approach are described and discussed. Characterised by its coupled approach, it is primarily devoted to cases where on-line (under tension) manifested defects occur. It is shown that the impact of the post-bite, post-buckled stress field on the in-bite stress and strain fields is quite small in the cases investigated; however, subtle changes appear in the velocity field at bite exit, and this is sufficient to transform completely the post-bite stress field, which is found in much better agreement with measurements if such a coupled treatment is used. [Copyright &y& Elsevier]

Abstract: Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh–Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending–twisting coupling may overestimate the stiffness, thus providing higher buckling loads. [ABSTRACT FROM AUTHOR]

Abstract: A point receptance array is proposed to study behaviors of panel structures with stiffeners. Although the overall objective is intended to develop a general algorithm for large structural members with stiffeners of arbitrary arrangements, the present study focus on an analytical evaluation of the accuracy of the approximation. To simplify the formulations, a thin plate with two diagonally connected beam stiffeners is selected. By solving governing differential equations for the plate and beam, point receptances that represent the interaction and compatibility conditions at the plate–beam interfaces are analytically obtained. Buckling modes of the stiffened plate are obtained by solving an eigenvalue problem. Accuracy of the approach is verified by a comparison of the analytical solution with data obtained from a direct finite element model. A parametric study was also performed. Good agreement indicates that the point receptance is a viable approach for general applications. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin''s approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented. [Copyright &y& Elsevier]

Abstract: This paper discusses the buckling behaviour of orthotropic composite plates under uniform uniaxial compression with one free reinforced unloaded edge. A typical application example for use of such a mechanical model is the web of stiffeners and frames attached to the fuselage skin of an aircraft. The considered plates are rectangular and simply supported at the loaded transverse edges. One of the longitudinal unloaded edges is also simply supported, while the second unloaded edge is not supported at all but is reinforced by a flange of arbitrary cross-section. At first, an exact solution for the elastic buckling problem is derived from the governing differential equation by imposing the underlying boundary conditions. Thereafter, two approximate closed-form solutions for the buckling load are derived, which can be conveniently used for practical application purposes. Generic buckling curves using characteristic non-dimensional quantities are also presented. Finally, the question of the required bending stiffness of the flange is treated, to ensure that the flange withstands buckling and provides simply supported boundary conditions to the free reinforced plate edge. [Copyright &y& Elsevier]

Abstract: The buckling of thin rectangular plates with nonlinearly distributed loadings along two opposite plate edges is analyzed by using the differential quadrature (DQ) method. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem be solved. Thus, very few analytical solutions (the only one available in the literature is for rectangular plates with all edges simply supported) have been available in the literature thus far. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with a few existing analytical and/or finite element data. It has been found that a fast convergent rate can be achieved by the DQ method with non-uniform grids and very accurate results are obtained for the first time. It has also been found that the DQ results, verified by the finite element method with NASTRAN, are not quite close to the newly reported analytical solution. A possible reason is given to explain the difference. [Copyright &y& Elsevier]

Exact solutions are presented for the free vibration and buckling of rectangular plates having two opposite edges (x=0 and a) simply supported and the other two (y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress σx=−N0[1−α(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement (w) to vary as sin(mπx/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients, for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and b yields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters α=0,0.5,1,1.5,2, for which α=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for α=0,1,2 obtained by the method of integration of the differential equation (α=0) or the method of energy (α=1,2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b=0.5,1,2 subjected to three types of loadings (α=0,1,2), with load intensities N0/Ncr=0,0.5,0.8,0.95,1, where Ncr is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes are also shown. [Copyright &y& Elsevier]