Elasto-plastic analysis for the buckling and postbuckling of rectangular plates under uniaxial compression

Full-range analysis for the buckling and postbuckling of rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as itsperturbation parameter.In this paper the effects of initial geometric imperfection on the postbuckling behaviorof plates have been discussed.It is seen that the effect of initial imperfection on the inelasticpostbuckling of plates is sensitive.By comparison,it is found that the theoretical results ofthis paper are in good agreement with experiments.     

Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression

In this paper, applving perturbation method to von Kármán nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments. The method suggested in this paper which has not been found in previous papers is rather simple and easy for the postbuckling analysis of rectangular plates.     

Postbuckling of long unsymmetrically laminated composite plates under axial compression

An approximate solution is given for the postbuckling of infinitely long and unsymmetrically laminated composite plates. This solution is obtained by superposing a polynomial transverse displacement given by bending due to unsymmetric laminate configurations and a simple functional representation for the buckling mode in conjunction with the Galerkin method. Nondimensional parameters are used to express the approximate solution in a very simple and clear formulation. The results given by this solution for axial compression in the longitudinal direction are compared with the results given by the nonlinear finite element method (FEM) for finite length rectangular long plates. The influence of the boundary conditions on postbuckling response is also studied. For the FEM analysis, two different simply supported boundary conditions on the long edges of the plate are considered. It is found that these two sets of boundary conditions give different results for the buckling and postbuckling finite element analysis. In most cases the FEM analysis overestimate and, respectively, underestimate the approximate closed form solution, depending on the type of simply supported boundary condition considered. Thus, the approximate solution appears useful for design purposes as an averaged quantity between the two FEM analyses. Also, it is found that the reduced bending stiffness method can be successfully used for determining the approximate solution.     

Postbuckling of bilaterally constrained rectangular thin plates

The post-buckling response of bilaterally constrained thin plates submitted to a height reduction is investigated by a joint experimental-theoretical-numerical study. A detailed determination of the shape of plates is compared to predictions based on modelling the plate as an Elastica and a phase portrait of the system is worked out. An integral relationship for unloaded plates is derived and checked experimentally. The variation of the length of flat contacts with compression is first identified from measurements and then introduced in a virtual work analysis so as to determine the plate reaction. The existence of asymmetric solutions is clarified and the robustness of the Elastica to friction is demonstrated. These results improve the predictions of the Euler model in the fully non-linear regime and validate its relevance beyond the ideal limits of frictionless rod or of frictionless infinite plate on which it is established. They should therefore be useful for addressing buckling in different, albeit close, configurations.     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

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Postbuckling of imperfect rectangular composite plates under inplane shear closed-form approximate solutions

In this paper, the postbuckling behavior of rectangular orthotropic laminated composite plates with initial imperfections under inplane shear load is investigated in a closed-form analytical manner. The plates under consideration are assumed to be infinitely long in the longitudinal direction. At the longitudinal edges, two different sets of boundary conditions are considered, specifically 1) simply supported edges and 2) fully clamped edges. Using Timoshenko-type shape functions for both the initial bifurcational buckling analysis and the subsequent Marguerre-type postbuckling studies, closed-form analytical solutions for the buckling loads and for the postbuckling state variables are derived. A comparison with geometrically non-linear finite element computations shows that the derived analysis approaches are suitable for postbuckling studies in load ranges not too far beyond bifurcational buckling as they are currently relevant for e.g., composite airframe structural analysis and design. Due to their strictly closed-form analytical nature, the presented analysis methods can be used conveniently in engineering practice for all application purposes where computational time is a crucial factor, especially for preliminary analysis and design or optimization procedures.     

Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings

A postbuckling analysis is presented for a simply supported, shear deformable functionally graded plate with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads. The temperature field considered is assumed to be of uniform distribution over the plate surface and through the plate thickness and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A two step perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FGM plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, volume fraction distribution, applied voltage, the character of in-plane boundary conditions, as well as initial geometric imperfections are studied.     

Postbuckling analysis of laminated composite plates subjected to the combination of in-plane shear,compression and lateral loading

This study deals with postbuckling behavior of laminated composite plates under the combination of in-plane shear, compression and lateral loading using an Element-based Lagrangian formulation. Natural co-ordinate-based strains, stresses and constitutive equations are used in the present shell element. The Element-based Lagrangian formulation described in this paper, in comparison with the traditional approaches, is more attractive not only because it uses only single mapping but also it converges faster. In addition, the finite element (FE) formulation based on the assumed natural strain method for composite structures shows excellence from the standpoints of computational efficiency as well as its ability to avoid both membrane and shear locking behavior. The numerical results obtained are in good agreement with those reported by other investigators. In particular, new results reported in this paper show the influence of various types of loading, materials and number of layers on postbuckling behavior.     

Postbuckling of imperfect stiffened cylindrical shells under combined external pressure and heating

1.IntroductionStiffenedcylindricalshellsarewidelyusedinmanytypesofstructures.Inpracticetheyoftensubjecttovarioustypesofcombinedthermalandmechanicalloadingandmayhavesignificantandunavoidableinitialgeometricalimperfections.Therefore,thepostbucklingbehaviorofimperfectstiITenedcylindricalshellsundercombinedexternalpress.ureandthermalloadingmustbewellunderstood.Manypostbucklingstudieshavebeenmadetbrstiffenedcylindricalshellsunderpureaxialcompression,uniformexternalpressureortheircombinations,where…     

Large deflections of prestressed simply supported rectangular plates under uniform pressure

The von Kármán large deflection equations for laterally loaded rectangular plates are extended to include uniform prestresses parallel to the edges and are solved for uniform load and for edges which are simply supported against movement normal to the plane of the plate and which are either held or free to move as a rigid body in the plane of the plate. Calculated values of center deflection and maximum stress parameters are given as functions of the load parameter for plates of various aspect ratios.     

Postbuckling behavior of circular cylindrical shells under compression

Applying the Galerkin procedure to the Donnell basic equations, reasonably accurate solutions are obtained for the postbuckling behavior of clamped circular cylindrical shells under axial compression. To make a distinct comparison with the previous experimental results, calculations are carried out for shells with the same elastic and geometric parameters and the relations between the waveform, axial shortening and maximum deflections with applied loads are clarified. The results here obtained are found to be in reasonable agreement with experimental ones throughout the regions with fairly large deformations.     

Ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression

1.IntroductionAsiswellthnown,thepostbucklingmetalplatescanbesuccessivelysubjectedtotheload.Forsomemetalplates,theultimatestrengthcanreachthirtytimesofthebucklingstressll].Inordertostudythebearingcapacityofthecompositeplatesthroughtestsandtheoreticalanalysis,f'ttiluretestsofthe283specimensofGFRPthinrectangularplatesundercompres.sionarecarriedout.ItisprovedthattheGFRPplatesinpostbucklingstillhavehigherbearingcapacity,forthetestedspecimensshowedultimatestrengthwhichisfourtotwenty-livetiniesth…     

Postbuckling prediction of double-walled carbon nanotubes under axial compression

An elastic double-shell model is presented for the buckling and postbuckling of a double-walled carbon nanotube subjected to axial compression. The analysis is based on a continuum mechanics model in which each tube of a double-walled carbon nanotube is described as an individual elastic shell and the interlayer friction is negligible between the inner and outer tubes. The governing equations are based on the Karman–Donnell-type nonlinear differential equations. The van der Waals interaction between the inner and outer nanotubes and the nonlinear prebuckling deformations of the shell are both taken into account. A boundary layer theory of shell buckling is extended to the case of double-walled carbon nanotubes under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the single-walled carbon nanotube and the double-walled carbon nanotube both have an unstable postbuckling behavior.     

An iteration algorithm for solving postbuckling equilibrium path of simply-supported rectangular plates under biaxial compression

In this paper,on the basis of von Kárman large deflection equations and itsdouble trigonometric series solution,we present a simple,fast and effective iterationalgorithm for solving simply-supported rectangular plate subjected to biaxial compression.     

On some problems for unsymmetrical lateral buckling of rectangular plates

The present paper investigates several problems for unsymmetrically lateral instability of rectangular plates by the energy method. In the text we discuss the minimum critical load of rectangular plates which possess the unsymmetrical supporters and to which the lateral buckling occurs unsymmetrically under a concentrated force, uniformly distributed load and the concentrated couples respectively.     

Combined longitudinal with lateral bending of rectangular plates supported at points of corners

This paper discusses the problems of combined longitudinal with lateral bending of rectangular plates which are supported at four points of corners by means of the variational calculus. In the text the lateral bending and the stability of thin plates are also treated respectively.     

Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear

One of the many uses of honeycomb is as core in sandwich plates, producing very high stiffness-to-weight ratio structures. The macroscopically observed crushing mechanism of these structures has its origin in instabilities at the local scale. Of particular interest here are the critical (i.e., onset of a buckling-type instability) loads and corresponding eigenmodes of honeycomb under general 3D loading involving simultaneous axial compression and transverse shear.