Postbuckling Behavior Of Plates Research Articles

Investigation of the incremental and deformation theories of plasticity on the elastoplastic postbuckling of plates

This article investigates the elastoplastic response of buckling and postbuckling behavior of plates under uniaxial and biaxial end-shortening considering incremental theory and deformation theory of plasticity. According to elastoplastic buckling and postbuckling behavior of plates, the finite element code considering geometrically and material nonlinearities is developed based on incremental theory and deformation theory of plasticity. The results show that boundary conditions, loading ratios, and aspect ratios of a plate have a significant effect on the discrepancy between incremental theory and deformation theory. Moreover, differences in estimating the buckling point using incremental theory and deformation theory are less than 10%, while in a number of plates at the last loading steps, postbuckling paths determined by incremental theory and deformation theory are diverted from each other. Also the difference between these two theories in the postbuckling region is more noticeable by increasing the thickness of plates.

Description of delaminations in composite multilayered structures – comparison of numerical and experimental results for compressed plates

The buckling loads and the post-buckling behavior of the perfect and imperfect delaminated plate are investigated in the paper. For this purpose the concise formulations enabling to derive pre- and post-buckling behaviour of plates with embedded delaminations is presented. The computations are made using FE package NISA II and Mathematica package. Obtained results for buckling loads and the post-buckling behaviour are compared with the experimental results. The Digital Image Correlation (DIC) technique is employed to verify the uniformity and homogeneity of deformations.

Shell instability analysis by using mixed interpolation

In this paper, buckling and post-buckling behavior of plates and shells are investigated. An efficient triangular shell element having six nodes is employed in this study. To consider large deflection and rotation, total Lagrangian formulation is utilized. The authors employ mixed interpolation for strain fields to deviate shear and membrane locking phenomena. The effects of different types of boundary conditions and geometry properties of plates and shells are studied. An almost complete literature review is also provided to show the progress of researches about the current topics. Various states of buckling including bifurcation and snap-through are assessed in different problems. In this study, the popular benchmarks of shell structures are analyzed to show the accuracy and capability of element. In addition, some new benchmarks which can be used by other researchers are also introduced and solved. Further, a comparison study between the proposed element and NLDKGQ element in OpenSees software is implemented for some complex curved shell structures.

A comparative study on the postbuckling behaviour of circular plates

Materials/metals, polymers, reinforced plastics, composites, functionally graded materials, ceramics and nano materials find significant place in many engineering and scientific applications. The material structural members such as plates and beams are subjected to structural deformation owing to several external and internal factors such as temperature, hysteresis and so on. Therefore, to analyze the structural deformation of these material structures, its nonlinear behavior modeling is relevant. The rapid progress in high speed computing devices resolve research problems involving material non-linearity behavior such as post-buckling behavior in varied structures. The post-buckling behavior of commonly used structural elements especially plates under thermal and mechanical loads are of great practically important research topic. Therefore, a comparative study on the thermal post buckling behavior of plates by various numerical methods such as finite element formulation, shear deformation theory, Rayleigh – Ritz method, iteration methods and so on will be helpful to obtain a cutting edge on numerical solutions and their applications in varied engineering applications. This paper reports a novel mathematical formulation involving substitution method to evaluate and compare the thermal post buckling load carrying capacity of circular plates with minimal errors.

Axisymmetric post-buckling behavior of saturated porous circular plates

This study aimed to investigate axisymmetric post-buckling behavior of a circular plate made of porous material under uniformly distributed radial compression with simply supported and clamped boundary conditions. Pores are saturated with fluid and plate properties vary continuously in the thickness direction. Governing equations are obtained based on classical plate theory and applying Sanders nonlinear strain-displacement relation. Shooting numerical method is used to solve the governing equations of problem. Effects of porosity coefficient, pore distribution, pore fluid compressibility, thickness change and boundary conditions on the post-buckling behavior of the plate are investigated. The results obtained for post-bucking of homogeneous/isotropic plates and critical buckling load of porous plates are compared with the results of other researchers.

Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 2: Numerical results and discussions

Based on the first-order shear deformation plate theory (FSDT), the smeared stiffeners technique and Galerkin method, the analytical expressions to determine the static critical buckling load and analyze the post-buckling load-deflection curves of FGM plates reinforced by FGM stiffeners resting on elastic foundations and subjected to in-plane compressive loads or thermal loads are established in part 1. In this part, we will use them to study the effects of temperature, stiffener, volume fraction index, geometrical parameters, elastic foundations on the buckling and post-buckling behavior of plates. In addition, the results in comparisons between the classical plate theory (CPT) and the first order shear deformation theory (FSDT) also are carried out and shown that the buckling and post-buckling behavior of more thick plate should be studied by FSDT.

On the applicability of simple shapes of delaminations in buckling analyses

The possibility to accurately analyse the buckling and postbuckling behaviour of plates with delaminations of irregular shapes by utilisation of circular or elliptic delaminations was studied. The behaviour of compressed plates with delaminations of irregular and corresponding smallest enclosing circular and elliptic shapes was predicted by computational analyses and compared in terms of buckling loads and maximum values of the energy release rates found along the delamination boundaries. The study indicates that utilisation of circular delaminations could provide highly inaccurate results. Moreover, for truly accurate analyses of the buckling and postbuckling behaviour of delaminated structures it seems to be inevitable to use as precise representation of the shape of delaminations as possible.

Improved Secant Matrices for the Postbuckling Analysis of Thin Composite Plates

To study the postbuckling behavior of imperfect laminated composite plates, improved incremental or secant matrices are presented in this paper using what is called additional displacement formulation (ADF). These secant matrices are derived using the Marguerre's shell theory and they can be used in combination with any thin plate finite element. The advantage of the present formulation is that it involves no numerical approximation in forming the initial imperfection matrices as opposed to earlier secant matrices published in the literature using total displacement formulation. With the addition of shear stiffness matrix and little modification, the present incremental matrices could be extended to model postbuckling behavior of plates using the first-order shear deformation theory. The secant matrices presented in this study are shown to be very accurate in tracing the postbuckling behavior of thin isotropic and laminated composite plates with general initial imperfections.

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.

On the post-buckling behaviour of plates under stress gradient

In this paper the elastic post-buckling behaviour of plates under non-uniform compressive edge stress is investigated. The compatibility differential equations is first solved analytically and then an approximate solution of the equilibrium equation is obtained using the Galerkin method. Explicit expressions are derived for the load-deflection, ultimate strength and membrane stress distributions. Analytical effective width formulations, based on the characteristics of the stress field of the buckled plate, are proposed for this general loading condition. The predicted load-deflection expression is compared with independent test results. Results are also presented detailing the load-deflection behaviour and stress distribution for various aspect ratios.

Postbuckling of Orthotropic Plates on Two-Parameter Elastic Foundation

A postbuckling analysis of an uniformly in-plane loaded, simply supported, orthotropic rectangular plate resting on a two-parameter (Pasternak-type) elastic foundation is presented in this paper. The formulations are based on the large-deflection theory, and the nonlinear, generalized Karman-type equations of orthotropic plates are solved. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. The initial geometrical imperfection of the plate is taken into account. Numerical examples relating to the performances of isotropic and orthotropic, perfect and imperfect rectangular plates resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a special case, are presented. An elastic foundation's effect on the postbuckling behavior of plates is also evalutated for various values of foundation stiffness parameter. Typical results are presented in nondimensional graphical form. To the best o...

Postbuckling analysis and imperfection sensitivity of viscoplastic plates and cylindrical panels

The postbuckling behaviour of elastic-viscoplastic rectangular plates and cylindrical panels is analysed. The rate-dependent inelastic material behaviour is modelled by a unified theory of viscoplasticity. Initial geometrical imperfections of the inelastic structure are included and their effect on the postbuckling behaviour is investigated. The analysis relies on an incremental approach in which at each loading increment the Galerkin method is employed. Results are presented for a plate made of an elastic-viscoplastic material and subjected to a uniaxial compression, applied at a constant strain rate on both edges. The results display the applied loading against the out-of-plane displacement, and the effects of loading rate and imperfection sensitivity. It turns out that there is a significant difference between the postbuckling behaviour of a plate in the two cases: (1) when the bifurcation buckling of a geometrically perfect plate occurs in the elastic region, and (2) when it occurs after a plastic flow takes place.

Collapase analysis of ship hulls

This paper presents an efficient finite element procedure for the collapse analysis of ship hulls under complicated loads. A set of finite elements, such as beam-column elements, stiffened plate elements, and shear panel elements are developed, directly accounting for the geometrical and material non-linearities and initial imperfections. Elastic-plastic stiffness matrices for elements have been derived by combining elastic large displacement analysis theories with a plastic hinge model. The buckling and post-buckling behaviour of plates is included using an effective width concept. The procedure is effective, since few mode-points are necessary and numerical integration for evaluating stiffness matrices is avoided. Fracture mechanics criteria are introduced in order to account for tension tearing rupture and brittle failure of the material. Practical applications to ultimate longitudinal strength analysis of ship hulls and tanker collision analysis are presented. The procedure can also be used for collapse analysis of offshore and onshore structures.

Postbuckling analysis of plates on an elastic foundation by the boundary element method

The postbuckling behavior of plates on an elastic foundation is studied by using the boundary element method (BEM). A new fundamental solution of lateral deflection is derived through the resolution theory of a differential operator, and a set of boundary element formulae in incremental form is presented. By using these formulae, the BEM solution procedure becomes relatively simple. The results of a number of numerical examples are compared with existing solutions and good agreement is observed. It shows that the proposed method is effective for solving the postbuckling problems of plates with arbitrary shape and various boundary conditions.

Postbuckling behavior of anisotropic laminated plates under pure shear and shear combined with compressive loading

In the current work a postbuckling analysis for anisotropic plates under combined compressive and shear loading is presented. A pair of governing equations in the von Karman sense are solved in conjunction with simply supported boundaries. A series of computations is carried out for plates having different lay-ups, dif- ferent materials, and different aspect ratios. The emphasis of these investigations is put on the effect of shear direction on the postbuckling behavior of the plates. The results of the computations reveal that the post- buckling behavior of anisotropic plates is completely different when the applied shear directions are alternated for the plate under either shear loading or combined loading. HE postbucking behavior of composite plates under shear loading has been studied experimentally by a few investigators.13 It was reported that the ultimate loads of plates made of boron/epoxy, carbon/epoxy, or graphite /epoxy could be considerably higher than the initial buckling loads. However, so far, few postbuckling analyses are available for anisotropic plates under shear or combined loading. In previous work46 it was pointed out that the shear direction has a significant influence on the initial buckling behavior of anisotropic plates under pure shear or under the combination of compressive and shear loading. Thus it is natural to raise the question: How does the shear direction affect the postbuckling behavior of the anisotropic plates? The present work answers the question. In the current work a postbuckling analysis for plates of composite material with midplane symmetric lay-up is presented. A pair of governing equations in the von Karman sense, in which the effects of boundary moments are included, are solved in conjunction with simply-supported boundaries. As examples, a series of computations are carried out for plates having different fiber directions, different stacking sequences of layers, different materials, and different aspect ratios. The results reveal that the direction of applied shear with respect to the fibers of the layers is very important for postbuckling behavior of anisotropic plates under shear loading or the combination of compression and shear. This means that the postbuckling behavior of anisotropic plates will depend greatly upon the directions of the shear acting on the plates.

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigen mode of the panel. In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths. The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.

Post-buckling behaviour of plates with discontinuous change of thickness

A theoretical study of the compressional behaviour of plates with discontinuous change of thickness across the width is presented. The analysis considers each portion with a different thickness as an individual plate. The deflections of the plate in the loaded direction are assumed to be sinusoidal, and polynomial functions are used to describe the deflected shape across the plate. By matching the boundary conditions of each portion, the basic equations are solved together using the semi-energy approach. The effect of initial imperfections are also examined. Typical results from an experimental investigation are presented to verify the validity of the analysis.

Buckling and Post-buckling Behaviour of Plates with Holes

SummaryThis paper gives details of theoretical and experimental investigations into the behaviour of simply-supported uniformly compressed square and rectangular plates with central circular holes. The theoretical analysis employs an approximate approach using a combination of Rayleigh-Ritz and finite-element methods. The experimental investigation consisted of a number of experiments on plates with hole diameters from one- to seven-tenths of the plate width. Agreement between experiment and theory is shown to be good at buckling. In the post-buckling range it is found that the theoretical analysis is reasonably accurate for small holes, but loses accuracy when dealing with large holes.

Postbuckling Behavior of Flat Plates

Results obtained by various investigators of postbuckling behavior are summarized; effect of postbuckling behavior of plates on overall buckling strength of columns and beams; concept of effective width and crippling strength are illustrated by results of test of thin-walled compression member; methods of treating postbuckling strength of flat plates in specifications for structures. (32 refs.)