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Abstract The paper investigates the possibility of bifurcation buckling from axisymmetrical equilibrium states of a heated circular plate with immovable edge. The plate is composed of a functionally graded material whose mechanical and physical properties are varied in the thickness direction according to the power law. Because of high compressive circumferential stresses that develop near the edge, the symmetrically deformed plate can buckle into asymmetric equilibrium configurations characterized by local circumferential waves (wrinkles). The problem of determining wrinkling thermal loads is formulated using the von Karman nonlinear plate theory based on the concept of physically neutral surface and solved by the power series method. The existence of wrinkling loads is examined for various pressure levels and boundary conditions. The calculation results are compared to the finite-element solution obtained by a general-purpose shell element. Highlights • Existence of wrinkling phenomenon of pressurized and heated circular FGM plates is examined. • The critical thermal loads that causes the plate to wrinkle are determined by the power series method. • Clamped plates exhibit wrinkling upon heating, whereas simply supported plates do not. • Findings on the wrinkling loads and modes agree with the finite-element simulations. [ABSTRACT FROM AUTHOR]

Elastoplastic buckling behaviors of rectangular plates made from functionally graded materials (FGMs) are investigated in this paper. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plates. The three dimensional material constitutive relation of FGMs is found by introducing the material homogenization method, named Tamura-Tomota-Ozawa(TTO) model, into J 2 deformation theory or J 2 flow theory. The uniform strain hypothesis helps to simplify the prebuckling state and derive the analytical expression of the position of the material elastoplastic interface. The buckling governing equations and the buckling critical condition of the structures are formulated under the framework of the classical plate theory. An iterative algorithm is designed to obtain the elastoplastic buckling critical load, a converging result between the prebuckling and the buckling critical internal forces. ABAQUS simulation well verifies the present theoretical predictions from J 2 flow theory, and is resorted to investigate the postbuckling behaviors of FGM plates. Discussions are addressed for the effects of the constituent distribution, the material plastic flow, the preloaded states of the plates, and the regions of buckling types are plotted as well. [ABSTRACT FROM AUTHOR]

There are considered thin periodic plates with moderately large deflections. To take into account the effect of the microstructure on behaviour of these plates the tolerance modelling method is applied, cf. Domagalski and Jędrysiak [2] , Meccanica, 2012. This method makes it possible to derive model equations with constant coefficients involving terms dependent of the microstructure size. The paper contains an computational example of critical load calculations and postbuckling analysis. [ABSTRACT FROM AUTHOR]

Highlights: [•] Critical review of design methods for slender RC panels under eccentric axial load. [•] Experimental campaign on cracked and uncracked centrally reinforced panels. [•] Improved capacity prediction using a computational model with lumped plasticity. [•] Testing and calculations combined with a Design Assisted by Testing (DAT) approach. [•] Novel and more efficient design capacity curve derived using the DAT procedure. [Copyright &y& Elsevier]

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: Modern aircraft wings are thin-walled structures composed of ribs, spars and stiffened panels, where the top skin is subject to compressive forces in flight that can cause buckling instability. If these panels are machined from a single billet of metal then the initial buckling performance can be significantly improved by increasing the fillet radius along the line junction between the stiffener webs and skin. Typically thin-walled structures are usually modelled with two dimensional elements. To model the stiffened panel with fillets three dimensional elements are required. For the stiffened panel selected for the analysis the paper shows that the three dimensional model shows a substantial increase in skin initiated buckling if the fillet is taken account of. A 5mm radius leads to an increase of 34% increase in local buckling load performance for a skin portion of breath to thickness ratio of 100. The associated overall buckling load increases by 1.8%. The mass penalty for a 5mm radius is 5.1%. To avoid local and overall buckling interaction an accurate measure of both buckling loads is very important and may have impact for designers. The three dimensional models with no fillets show very good agreement with the two dimensional models. [Copyright &y& Elsevier]

Abstract: Inelastic buckling and postbuckling behavior of stocky plates under combined shear and in-plane bending stresses are investigated and compared to slender plates. Aluminum and steel plates having various slenderness ratios are modeled and analyzed by means of (i) numerical nonlinear finite element method and (ii) theoretical p-Ritz energy method; and both results are compared to the classic interaction equation. It is observed that whereas in slender plates, elastic buckling occurs prior to the material''s proportional limit load, stocky plates buckle in an inelastic way within the post-yield stage. In contrast to slender plates with considerable postbuckling reserves, the buckling of stocky plates is immediately followed by softening. In addition, it is shown that the classic interaction equation overestimates buckling loads; and therefore, a modified equation that can safely be applied to both stocky and slender plates is proposed. [Copyright &y& Elsevier]

Abstract: A new model based on the high order sandwich panel theory is proposed to study the effect of external loads on the free vibration of circular cylindrical composite sandwich shells with transversely compliant core, including also the calculation of the buckling loads. In the present model, in contrast to most of the available sandwich plate and shell theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core material are determined through a 3D elasticity solution. The performance of the present theory is compared with that of other sandwich theories by the presentation of comparative results obtained for several examples encompassing different material properties and geometric parameters. It is shown that the present model produce results of very high accuracy, and it is suggested that the present model, which is based on a 3D elasticity solution for the core material, can be used as a benchmark in future studies of the free vibration and buckling of circular cylindrical composite sandwich shells with a transversely compliant core. [Copyright &y& Elsevier]

Abstract: An analytical investigation of the buckling/wrinkling behavior of GFRP webs in cell-core sandwiches subjected to combined in-plane shear and bending stresses is conducted. Web–core panels are modeled as long orthotropic plates stabilized by a relatively thick layer of elastic foam. The boundary condition of the plate is defined according to the interaction between the webs and face sheets in the presence of the core material by applying a series of numerical analyses using the three-dimensional finite element modeling. Two approaches are adopted to predict the wrinkling behavior. The first is to predict the buckling/wrinkling of webs subjected to combined shear and bending loads using a mixed-mode interaction formula. In the second approach, the wrinkling behavior of web–core panels is treated as a biaxial compression–tension local buckling problem. The developed approaches are applied to predict the wrinkling loads of thin-walled webs in GFRP cell-core sandwich beams designed for the GFRP cell-core sandwich roof of the Novartis Campus Main Gate Building constructed in Switzerland. [Copyright &y& Elsevier]

Abstract: Buckling response of orthotropic single layered graphene sheet (SLGS) is investigated using the nonlocal elasticity theory. Two opposite edges of the plate are subjected to linearly varying normal stresses. Small scale effects are taken into consideration. The nonlocal theory of Eringen and the equilibrium equations of a rectangular plate are employed to derive the governing equations. Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a power series (PS) solution is also developed. DQM results are successfully verified with those of the PS method. It is shown that the nonlocal effects play a prominent role in the stability behavior of orthotropic nanoplates. Furthermore, for the case of pure in-plane bending, the nonlocal effects are relatively more than other cases (other load factors) and the difference in the effect of small scale between this case and other cases is significant even for larger lengths. [Copyright &y& Elsevier]

Abstract: Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods. [Copyright &y& Elsevier]

Abstract: Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin''s plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties. [Copyright &y& Elsevier]

Abstract: A functional gradient for the buckling load (P) with respect to the structural shape function (S) is introduced for shape optimization. The gradient (P ,S) is derived analytically by functional differentiation of the governing equation with respect to S, where both P and the deflection (W) are considered as functionals of S. It is found that P , S is a functional of W and is not dependent explicitly on S. The P , S is combined with a simple gradient projection optimization method and a finite element program. The analytical gradient expression is independent of the FE model but requires its input. At each optimization step the buckling problem is solved numerically and the gradient is calculated. Then, a new improved design is computed. In the first part of the study 1D beam problems are solved. Results are compared with exact solutions and found to be more accurate than common numerical optimizations. An example of a clamped beam with two simple supports is studied. The optimal area distribution of a general unimodal 1D beam is found to be composed of sections with the same shape as for the basic simply supported case. The proposed method is generalized to 2D plates. The optimization is combined with a commercial FE package. For the case of simple square plates the optimization produces smooth thickness distribution showing higher buckling load improvement than common numerical optimization. The method was then applied to square plates with a central circular hole, where non-uniform FE meshes were used. The optimal shapes exhibited singularities resembling commonly used stiffeners. [Copyright &y& Elsevier]

Abstract: The present study analyses an aircraft composite fuselage structure manufactured by the Liquid Resin Infusion (LRI) process and subjected to a compressive load. LRI is based on the moulding of high performance composite parts by infusing liquid resin on dry fibres instead of prepreg fabrics or Resin Transfer Moulding (RTM). Actual industrial projects face composite integrated structure issues as a number of structures (stiffeners, …) are more and more integrated onto the skins of aircraft fuselage. A representative panel of a composite fuselage to be tested in buckling is studied numerically. This paper studies which of the real behaviours of the integrated structures are to be observed during this test. Numerical models are studied at a global scale of the composite stiffened panel. Linear and non linear analyses are conducted. The Tsai–Wu criterion with a progressive failure analysis is implemented, to describe the global behaviour of the panel up to collapse. Also, three stiffener connection methods are compared at the intersection between two types of integrated structures. Load shortening curves permit to estimate the expected load and displacements. [Copyright &y& Elsevier]

Abstract: The paper presents the solution of the buckling problem for an orthotropic rectangular plate having two parallel edges simply supported, one edge clamped and the remaining edge free (the SSCF plate). The plate considered is subjected to a linearly varying in-plane load that can take the form of uniform compression, combination of in-plane bending and uniform compression, or pure in-plane bending. The solution technique involves reduction of the relevant variational buckling equation to a one-dimensional form using the Kantorovich procedure and subsequent application of the generalised Galerkin method. The buckling problems are solved for isotropic and orthotropic plates with various aspect ratios. The analytical solution is verified using the finite-element analysis. The comparisons of computational results demonstrate the appropriateness and efficiency of the approach developed in this work for the calculation of critical loads of composite SSCF plates with various dimensional and stiffness parameters. [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: The onset of buckling in square laminated multi-layered composite plates, subject to unidirectional in-plane loads, is investigated within the framework of a generalized higher-order shear deformation theory suitable to capture significant transverse shear and thickness-wise deformation effects. The displacement field is expanded in a Taylor series of the thickness coordinate with arbitrary polynomial degree; in turn, the series coefficients, expressed as a superposition of admissible functions, are determined according to the Rayleigh–Ritz method. Truly higher-order polynomial terms, along with a sufficient number of in-plane admissible functions, are shown to be necessary for convergence towards the fundamental buckling load multiplier. As a by-product, reduced-order models are identified for various plate geometries and lamination schemes. The sensitivity of the lowest buckling load with respect to the nondimensional parameters (the thickness ratio, the ratio between the elastic moduli, the ply angle) is investigated. In particular, the attention is focused on the cross-over phenomenon between the lowest two buckling eigenvalues in multi-layered composite square plates with different lamination schemes. The presented results shed light onto the buckling behavior of thick shear-deformable multi-layered plates. [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: Solution of the buckling problem for the CCFF orthotropic plate subjected to in-plane pure bending is presented. The two parallel clamped edges of the plate are loaded by linearly distributed in-plane loads statically equivalent to the in-plane bending moments. The problem is solved using method of lines for partial differential equations and Galerkin’s method. The buckling problems are solved for isotropic, orthotropic and multilayered CFRP composite plates with various aspect ratios. Results of calculations of critical loads are compared with those based on finite-element modelling and analyses. The comparisons demonstrate efficiency of the proposed approach to the buckling analysis of composite CCFF plates with various dimensional and stiffness parameters. [Copyright &y& Elsevier]

Abstract: Buckling analysis of rectangular plates subjected to various in-plane compressive loads using Kirchhoff plate theory is presented. The method of discrete singular convolution has adopted. Linearly varying, uniform and non-uniform distributed load conditions are considered on two-opposite edges for buckling. The results are obtained for different types of boundary conditions and aspect ratios. Comparisons are made with existing numerical and analytical solutions in the literature. The proposed method is suitable for the problem considered due to its simplicity, and potential for further development. [Copyright &y& Elsevier]

Abstract: This paper deals with multiobjective optimization of symmetrically angle-ply square laminated plates subjected to biaxial compressive and uniform thermal loads. The design objective is the maximization of the buckling load for weighted sum of the biaxial compressive and thermal loads. The design variable is the fiber orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of buckling analysis of laminated plates. The modified feasible direction (MFD) method is used for optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the effect of different weighting factors, number of layers, aspect ratios, load ratios and boundary conditions on the optimal design is investigated. [Copyright &y& Elsevier]

Abstract: The available plate theories have been generally calibrated using linear strain–displacement expressions. Furthermore, many of them do not consider the transverse normal stress continuity and the transverse flexibility of the sandwich plates. Majority of the investigations performed so far in the buckling analysis of the sandwich plates, have been restricted to linear buckling analysis of the perfect sandwich plates based on theories that either violate the continuity condition of the transverse stresses at the layer interfaces or do not satisfy the mentioned condition when nonlinear strain–displacement expressions are used. Therefore, their results may be unreliable for nonlinear stress and buckling (especially in the postbuckling region) analyses. In the present paper, nonlinear strain–displacement expressions are employed for imperfect sandwich plates subjected to thermo-mechanical loads to propose an accurate global–local theory that satisfies the continuity of all of the transverse stress components. The theory is presented in a compact matrix form. Compatible Hermitian elements with C1 continuity are employed to enhance the results. Buckling and wrinkling loads are detected employing a criterion previously published by the author. Comparisons made in the paper with results reported by well-known references, confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm. [Copyright &y& Elsevier]

Abstract: The paper deals with the solution of the buckling problem for a rectangular orthotropic plate with two parallel free edges. The other two parallel simply supported opposite edges of the plate are loaded by a linearly distributed in-plane load which is equivalent to the pure in-plane bending. Buckling analysis is performed using the Levy-type solution and subsequent finite-difference approximation of the boundary-value problem. Solution of the corresponding eigenvalue problem yields the critical buckling coefficient and critical load. The problem is solved for isotropic and orthotropic composite plates. The design chart has been obtained for the isotropic plates with various aspect ratios from which the corresponding critical loads can be found. Critical buckling coefficients are determined for composite plates with various aspect ratios and angles of the reinforcement orientation. The optimum material reinforcement structure providing the maximum value of critical load is determined. [Copyright &y& Elsevier]

Abstract: In this paper, the effects of the delaminations size on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large delaminations are studied. A numerical and experimental study is carried out to determine the buckling load of rectangular composite plates. For the experiments (0°/90°/0°/90°)s oriented cross-ply laminated plates with multiple large delaminations and without delamination are produced by using hand lay-up technique. The experimental buckling loads of plates are found by clamping from the two edges and then these results are compared with the results obtained by ANSYS11.0 package. In addition, the compressive failure loads of composite laminates containing multiple large delaminations are found by compression test fixture. It is found that the longest and near-surface delamination size influences the buckling load and compressive failure load of composite laminates. However, the size of beneath delaminations has no significant effect on the buckling load and compressive failure load of composite laminates. [Copyright &y& Elsevier]