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Grid structures are extensively used in many engineering structures as an orthotropic layer with at most in-plane anisotropy. In this study, the laminated grids structures are considered. These structures are composed of various numbers of thin composite grid layers. This concept yields to numerous laminated grid configurations with disparate coupling effects, which can be used to tailor the stiffness, compare to conventional grids. In the present study, four known grid patterns with equal weight and thickness constitute the laminated grids. The genetic algorithm (GA) is employed to optimize the stacking sequence and pattern composition of the laminated grid. The buckling load is taken as a fitness function and the pattern and orientation of the grid layer are considered as the design variables. The first-order shear deformation and classical laminated plate theories are considered along with Ritz method to obtain the elastic buckling loads. The optimization results are presented for various boundary conditions and aspect ratios. The results show, using the laminated grid considerably improves the axial buckling load of the plates. Moreover, the plate boundary conditions and aspect ratios play an imperative role in the optimum pattern and stacking sequence of the laminated grid plates. [ABSTRACT FROM AUTHOR]

Buckling of anisotropic piezoelectric cylindrical shells subjected to axial compression and lateral pressure is investigated based on the new modified couple stress theory and using the shear deformation theory with the von Kármán geometrical nonlinearity. By applying the principle of minimum potential energy, the governing equations and boundary conditions are derived. Unlike the classical continuum model, the present model is size-dependent, and the size effects are captured using the new modified couple stress theory. The critical buckling load is obtained for simply supported, clamped-simply supported and clamped piezoelectric cylindrical shells. A detailed numerical study is carried out to discuss the effects of different parameters, such as material length scale parameter, thickness ratio, length ratio, load interaction parameter and the external electric voltage on the critical buckling load. The critical buckling load is found to be significantly size-dependent, especially for large values of thickness and small values of length ratio. Besides, the influence of load interaction parameter is found to be negligible for large values of length and small values of thickness ratio. [ABSTRACT FROM AUTHOR]

In this article, buckling response of functionally graded nano-plate based on exponential shear deformation theory is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, refined shear deformation theory, an exponential functions are used in terms of thickness co-ordinate to include the effect of transverse shear deformation and rotary inertia. The number of unknown displacement variables in the proposed theory are same as that in first order shear deformation theory. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the functionally graded rectangular nano-plate. The material properties of the plate are assumed to vary according to the Power Law form in the thickness direction. The governing equations and corresponding boundary conditions are derived by implementing Hamilton's principle. To show the accuracy of the formulations, our research results in specific cases are compared with available results in the literature and a good agreement will be observed. Finally, the effect of various parameters such as nonlocal parameter, Power Law indexes, aspect ratio, and the thickness ratio on the non-dimensional critical buckling load of rectangular FG nano-plates are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

A new accurate four-variable shear deformation plate theory is introduced in this paper to illustrate the hygrothermal vibration and buckling of FGM sandwich plates resting on Winkler–Pasternak elastic foundations. Based on the suggested theory, the equations of motion are derived from Hamilton׳s principle containing the hygrothermal effects. This theory involves only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the sandwich plate. A power law distribution is used to govern the gradation of material properties through the plate thickness. Various types of FGM sandwich plates are considered. To check the validity of the theory and formulations, the obtained results are compared with the previous results. Comparison studies reveal that the results of the proposed theory are more accurate than those of other shear deformation plate theories. Parametric study is performed to show the influences of moisture condition, temperature rise, elastic foundation coefficients and power law index on the buckling and natural frequency of FGM sandwich plates. [ABSTRACT FROM AUTHOR]

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle. [ABSTRACT FROM AUTHOR]

In this work a finite element model is presented for buckling and nonlinear analysis of multilayer sandwich plates and shells, with a soft core sandwiched between stiff elastic layers. The finite element is obtained by assembling all element-layers through the thickness using specific assumptions on the displacement continuity at the interfaces between layers, but allowing for different behaviors of the layers. The stiff elastic layers are modelled using the classic plate theory and the core is modelled using Reddy׳s third order shear deformation theory. The present finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements. This model is applied in the solution of illustrative examples and the results are presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the large amplitude vibration, nonlinear bending and thermal postbuckling of functionally graded material (FGM) beams resting on an elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The motion equations are based on a higher order shear deformation beam theory that includes beam–foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The numerical illustrations concern the nonlinear vibration, nonlinear bending and thermal postbuckling of FGM beams resting on Pasternak elastic foundations under different thermal environmental conditions. It is found that the FGM beam with intermediate material properties does not necessarily have intermediate nonlinear frequencies. The thermal postbuckling path of simply supported FGM beams is no longer of the bifurcation type for both uniform and non-uniform temperature fields. [Copyright &y& Elsevier]

Abstract: A simple refined shear deformation theory is proposed for bending, buckling, and vibration of thick plates resting on elastic foundation. The theory accounts for parabolic distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The number of unknowns of present theory is two as against three in the case of other shear deformation theories. The elastic foundation is modeled as two-parameter Pasternak foundation. Equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of thick plates resting on elastic foundation. [Copyright &y& Elsevier]

Abstract: This paper is a theoretical and numerical study of the uniform growth of a repeating sinusoidal imperfection in the line of a strut on a nonlinear elastic Winkler-type foundation. The imperfection is introduced by considering an initially deformed shape which is a sine function with an half wavelength. The restoring force is either a bi-linear or an exponential profile. Periodic solutions of the equilibrium problem are found using three different approaches: a semi-analytical method, an explicit solution of a Galerkin method and a direct numerical resolution. These methods are found in very good agreement and show the existence of a maximum imperfection size which leads to a limit point in the equilibrium curve of the system. The existence of this limit point is very important since it governs the appearance of localization phenomena. Using the Galerkin method, we then establish an exact formula for this maximum imperfection size and we show that it does not depend on the choice of the restoring force. We also show that this method provides a better estimate with respect to previous publications. The decrease in the maximum compressive force supported by the beam as a function of the imperfection magnitude is also determined. We show that the leading term of the development has a different exponent than in subcritical buckling of elastic systems, and that the exponent values depend on the choice of the restoring force. [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: A new hyperbolic shear deformation theory taking into account transverse shear deformation effects is presented for the buckling and free vibration analysis of thick functionally graded sandwich plates. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from Hamilton''s principle. The closed-form solutions of functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions. [Copyright &y& Elsevier]

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: Analytical and experimental investigations of typical hydraulic cylinders have indicated that their load capacities are significantly different from those obtained from simple buckling analysis of idealized systems. In any case, an increase in the friction coefficient at the restrained ends changes the actuator''s limit load, while an increase in the initial maximum deflection (initial misalignment) decreases the limit load. A common practice of most cylinder manufacturers is to use a safety factor (between 2.5 and 4) to determine the service load after the critical load (buckling) is obtained by simple analytical procedures treating the cylinder as a perfect stepped column. The intricate aspects of friction effects have been deliberately left aside in this present work. Nevertheless, friction and interaction between mechanism and actuator in the buckling characteristics will be presented in the ongoing paper, which will follow this work. Authors know that, in a real system, the cylinder tube–rod interface is not rigid. Due to the flexibility of guide rings and clearances between components, misalignment (an angular deflection which increases with increasing axial load) exits at the interface. When initial imperfection angle exists, there is no sudden buckling. Then, stresses and deflections increase with increasing load. After repetitive use, the tolerance between the parts will become larger, consequently increasing the initial deflection, which has been proved to considerably decrease the load capacities of the power cylinders. From this analysis, a theoretical and experimental work has been carried out in order to show the advantages and disadvantages of the current design methods, characterizing the critical factors that cause the collapse and proposing useful design criterions. The present work aims to describe the behaviour of actuators under load capacity with experimental validation. [Copyright &y& Elsevier]

Abstract: The present paper investigates the structural stability of thin-walled steel cylinders surrounded by an elastic medium, subjected to uniform external pressure. A two-dimensional model is developed, assuming no variation of load and deformation along the cylinder axis. The cylinder and the surrounding medium are simulated with nonlinear finite elements that account for both geometric and material nonlinearities. Cylinders of elastic material within a rigid boundary are considered first, and the numerical results are compared successfully with available closed-form analytical predictions. Subsequently, the external pressure response of confined thin-walled steel cylinders is examined, in terms of the initial out-of-roundness of the cylinder, the initial gap between the cylinder and the medium, and the stiffness of the surrounding medium. Numerical results are presented in the form of pressure-deformation equilibrium paths, and show a rapid drop of pressure after reaching the maximum pressure level, as well as a significant imperfection sensitivity. A plastic-hinge mechanism is developed that results in a closed-form expression and illustrates the post-buckling response of the cylinder in an approximate manner. The distributions of plastic deformation, as well as the variation of cylinder-medium contact pressure around the cylinder cross-section are also depicted and discussed. Furthermore, the effects of uniform vertical preloading on the maximum pressure sustained by the cylinder are examined. Finally, the numerical results show good comparison with a simplified closed-form expression, proposed elsewhere, which could be used for design purposes. [Copyright &y& Elsevier]

Abstract: The paper presents finite element free vibration and buckling analysis of laminated hat-stiffened shallow and deep shells using arbitrarily oriented stiffener formulation. Modified approach for modelling the curved stiffener is implemented using necessary transformations. A simplified stiffener formulation is presented to accommodate various shapes of stiffener shapes in developing the rigidity matrix for the finite element formulation. Investigation has been carried out on free vibration and buckling analyses of laminated composite stiffened shell structures with laminated open section (rectangular or ‘T’ shaped) and closed section (‘hat’ shaped) stiffeners. Parametric study on the hat-stiffened panels for the free vibration and buckling analyses confirms that the closed section stiffener being torsionally rigid is found to show better performance over open section stiffeners. [Copyright &y& Elsevier]

Abstract: In this research, mechanical buckling of circular plates composed of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM circular plate under uniform radial compression are derived, based on the higher order shear deformation plate theory (HSDT). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations are established. A buckling analysis of a functionally graded circular plate (FGCP) under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for FGCP based on the first order shear deformation plate theory (FSDT) and classical plate theory (CPT) given in the literature. The study concludes that HSDT accurately predicts the behavior of FGCP, whereas the FSDT and CPT overestimates buckling loads. [Copyright &y& Elsevier]

Abstract: In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure. [Copyright &y& Elsevier]

Abstract: The main objective of this study is to give a numerical solution of three-dimensional analysis of thick rectangular plates. The analysis uses discrete singular convolution (DSC) method. Free vibration, bending and buckling of rectangular plates have been studied in this paper. Regularized Shannon''s delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtanied results are compared with those of other numerical methods. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers. [Copyright &y& Elsevier]

Abstract: The mechanical buckling of curved beams made of functionally graded materials is studies in this paper. The equilibrium and stability equations of curved beams under mechanical loads are derived. Using proper approximate functions for the displacement components, the stability equations are employed to obtain the related eigenvalues associated with the buckling load of the curved beam. Closed-form solutions are obtained for mechanical buckling of curved beams with doubly symmetric cross section subjected to uniform distributed radial load and pure bending moment. The results are validated with the known data in the literature for beams with isotropic materials. [Copyright &y& Elsevier]

Abstract: A generalized layer-wise stochastic finite element formulation is developed for the buckling analysis of both homogeneous and laminated plates with random material properties. The pre-buckled stresses are considered in the derivation of geometric stiffness matrix and the effect of variation in these stresses on the mean and coefficient of variation of buckling strength is studied. The mean buckling strength of plates under uniform stress assumption exactly matches with those reported in the literature. However, it is shown that the actual mean buckling strength of plates can be significantly different based on the pre-buckled stress analysis which depends on boundary constraints, principal material directions, aspect and thickness ratios of plates. The statistics of buckling strength is determined using a Taylor series expansion based mean centered first order perturbation technique. The stochastic finite element solutions obtained using layer-wise plate theory is also validated with analytical solutions presented in this paper. Parametric studies are conducted for different aspect ratios, ply orientations and boundary conditions. [Copyright &y& Elsevier]

Abstract: The buckling characteristics of sandwich plates having laminated stiff layers are studied for different types of partial edge loadings using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piecewise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. It is quite interesting to note that this plate model having all these refined features requires unknown parameters only at the reference plane. To have a generality in the present analysis, finite element technique is adopted and it is carried out with newly developed triangular element, as existing finite elements cannot accommodate this plate model. So far, no solution exists in the literature for the problem of sandwich plate subjected to partial edge loading. The present analysis is first validated for the case of an isotropic plate subjected to partial edge compression and then it is extended to analyze sandwich plates. Few results are presented. [Copyright &y& Elsevier]

The large deflection equation of a shallow spherical shell under uniformly distributed transverse loads is established in this paper with consideration of effects of transverse shear deformation on flexural deformation. Using an updated iteration method, an analytical solution for nonlinear stability of a shallow spherical shell is obtained. Formulae for estimating the critical buckling loads are presented for two types of boundary conditions. Discussions on the influences of the geometric and physical parameters on the critical buckling loads are given. [Copyright &y& Elsevier]

This paper investigates the buckling behavior of a symmetrically laminated composite rectangular plate composed of AS4 graphite fibers and 3501-6 epoxy resin under parabolic variation of axial loads. The plate is assumed to be general anisotropy and symmetric about its mid-plane. Two loading conditions are considered. They are (a) an axial load that varies parabolically with respect to the plate longitudinal direction, and (b) an axial load that varies parabolically with respect to the plate transverse direction. Analytical solutions of buckling load and mode shape are obtained based on classical laminated plate theory and the Rayleigh–Ritz method. The influences of plate aspect ratio and fiber orientations have been investigated. Some numerical results from the present study are compared with published results and good agreement is found. [Copyright &y& Elsevier]

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates. [Copyright &y& Elsevier]

The process of rotational symmetric tube bulging with inside pressure and axial compression enables the standard tubes to be formed into different rotational symmetric hollow parts in such a way that their central part is expanded into a desired shape while the ends remain unchanged. The superposition of axial compression contributes to a more favorable forming stress state, which is reflected in larger forming limits and smaller wall thinning in the widened area. The problems characterizing the process are a limited range of compression stability and difficulties met when establishing and optimizing the technological parameters of the process whose course cannot be defined in an analytical way. Based on a physical model of the forming process a numerical model was built. Using ABAQUS code the model was simulated over the entire stress/forming region. The comparison of the computer simulated forming process with the experimentally obtained results showed that the model was highly accurate. Finally, the paper studies the influences of particular parameters on the stability of the process, showing on a practical example how it is possible to achieve tube bulging without wall thinning. [Copyright &y& Elsevier]