POST BUCKLING ANALYSIS OF CENTRELINE STIFFENED FLAT RECTANGULAR PLATES (original) (raw)
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Buckling and Postbuckling Loads Characteristics of All Edges Clamped Thin Rectangular Plate
Previous studies on the buckling and postbuckling loads characteristics of thin rectangular plates that are subjected to uniaxial uniformly distributed in-plane loads were limited to all edges simply supported (SSSS) plate. Those studies were carried out using assumed displacement and stress profiles in the form of double trigonometric functions, never minding their inadequacies. Hence, major associated parameters: displacement parameter, Wuv, stress coefficient, Wuv2 and load factor, Kcx for such plate could not be determined. No study has considered the buckling and postbuckling loads characteristics of thin rectangular plate having all the four edges clamped (CCCC). This paper obtained the exact displacement and stress profiles of the buckling and postbuckling characteristics of thin rectangular CCCC plates by applying the direct integration theory to the Kirchhoff’s linear governing differential equation and von Karman’s non–linear governing differential compatibility equation respectively. With these exact profiles, the buckling and postbuckling load expression of the CCCC plate was obtained by applying work principle to the Von Karman’s non–linear governing differential equilibrium equation. Yield/maximum stress of the plate and those major related parameters were determined. Results of this present study show that for a CCCC plate material having yield stress of 250MPa, failure would occur at 0.0478h postbuckling out of plane deflection, contrary to the presumed critical buckling load. Hence, CCCC accommodates additional load beyond critical buckling load.
This paper presents an analytical modeling technique for non-linear buckling behavior of axially compressed rectangular thick plate under uniformly distributed load. The aim of this study is to formulate the equation for calculation of the critical buckling load of a thick rectangular plate under uniaxial compression. Total potential energy equation of a thick plate was formulated from the three-dimensional (3-D) static elastic theory of the plate, from there on; an equation of compatibility was derived by transforming the energy equation to compatibility equation to get the relations between the rotations and deflection. The solution of compatibility equations yields the exact deflection function which was derived in terms of polynomial. The formulated potential energy was in the same way used by the method of general variation to obtain the governing differential equation whose solution gives the deflection coefficient of the plate. By minimizing the energy equation with respect to deflection coefficient after the obtained deflection and rotations equation were substituted into it, a more realistic formula for calculation of the critical buckling load was established. This expression was applied to solve the buckling problem of a thick rectangular plate that was simply supported at the first and fourth edges, clamped and freely supported in the second and third edge respectively (SCFS). Furthermore, effects of aspect ratio of the critical buckling load of a 3-D isotropic plate were investigated and discussed. The numerical analysis obtained showed that, as the aspect ratio of the plate increases, the value of critical buckling load decreases while as critical buckling load increases as the length to breadth ratio increases. This implies that an increase in plate width increases the chance of failure in a plate structure. It is concluded that as the in-plane load which will cause the plate to fail by compression increases from zero to critical buckling load, the buckling of the plate exceeds specified elastic limit thereby causing failure in the plate structure.
Simple and Exact Approach to Post Buckling Analysis of Rectangular Plate
SSRG International Journal of Civil Engineering, 2020
This paper presents a new, simple and exact approach to post-buckling analysis of thin rectangular plates. In the study, the Airy's stress functions are not incorporated as the middle surface axial displacement equations are determined as direct functions of middle surface deflection. With this the bending and membrane stresses and strains, which are direct functions of middle surface deflection are obtained. These stresses and strains are used to obtain the total potential energy functional. The minimization of the total potential energy gives the governing equation and compatibility equation for rectangular thin plates buckling with large deflection. The compatibility equations and the governing equation are solved to obtain the deflection function for the problem. Direct variation is applied on the total potential energy function to get the formula to calculate the buckling loads. A numeric analysis is performed for a plate with all the four edges simply supported (SSS plate). It is observed that when deflection to thickness ratio (w/t) is zero the buckling load obtained coincides with the critical buckling from small deflection (linear) analysis. Another observation is that the values of buckling load for given values of w/t obtained in the present study do not vary significant with those obtained by Samuel Levy. The recorded average percentage difference is 12.65%. It is also observed that the maximum w/t to be considered when small deflection analysis is to be used is 0.225. When w/t is more than 0.225, using small deflection analysis will give erroneous results. Thus, large deflection analysis is recommended when w/t is above 0.25. We conclude and recommend that this new equation for analysis of thin plates is a better alternative to the popular von Karman equation. Key words: Post-buckling buckling load, membrane strains, total potential energy, minimization, direct variation
A REVIEW AND BUCKLING ANALYSIS OF STIFFENED PLATE
It happens many times that the structure is safe in normal stress and deflection but fails in buckling. Buckling analysis is one of the method to go for such type of analysis.It predicts various modes of buckling. Plates are used in many applications such as structures, aerospace, automobile etc. Such structures are subjected to heavy uniformly distributed load and concentrated load many times over it's life span. Strength of these structures are increased by adding stiffeners to its plate. This paper deals with the analysis of rectangular stiffened plates which forms the basis of structures. A comparison of stiffened plate and unstiffened plate is done for the same dimensions. In order to continue this analysis various research papers were studied to understand the previous tasks done for stiffened plate. Hyper mesh and Nastran is used in this research work.Buckling analysis is performed for the component with aspect ratio of 2.Rectangular flat bar is used as stiffener
Applied Mathematics and Mechanics, 1990
Full-range analysis for the buckling and postbuckhng of rectangular plates under inplane compresswn has been made by perturbation techmque which takes deflection as [td perturbatton parameter. In ttus paper the effects of inttial geometric imperfectton on the postbuckling behavior of plates have been dtscussed. It is seen that the effect of intttal imperfectton on the melastw postbuckhng of plates is sensittve. By comparison, tt is found that the theoretical results of thts paper are in good agreement wtth expertments.
A CONTRIBUTION TO THE BUCKLING ANALYSIS OF STIFFENED RECTANGULAR ISOTROPIC PLATES
1st International Civil Engineering Conference (ICEC 2018) Department of Civil Engineering Federal University of Technology, Minna, Nigeria, 2018
In this research paper, buckling analysis of stiffened rectangular isotropic plates elastically restrained along all the edges (CCCC), using work principle approach that is based on polynomial function were carried out. The stiffeners are assumed to be rigidly connected to the plate, such plates are widely used in civil engineering, marine, and aeronautic structures. Analysis for critical buckling of stiffened plates possessing different aspect ratios, varying stiffness properties and varying number of stiffeners were carried out. The governing differential equation for the stiffened plate system was obtained by super position principle. Polynomial functions were used in this study and the present analysis was carried out only for uniaxially stiffened plate, where longitudinal stiffeners are presented parallel to inplane load of the plate. Effects of the number of stiffeners, aspect ratios, boundary conditions, stiffener parameters upon the buckling coefficients, K of the stiffened plates were investigated. The results were obtained considering the bending displacements of the plate and the stiffener for all edge clamped conditions presented. Maximum percentage increase in buckling coefficients of stiffened plates for the case of one and two stiffeners is 20.586%. For the case of one and three stiffeners, the maximum percentage increase in buckling coefficients recorded is 48.2257%. Several numerical examples were presented to demonstrate the accuracy and convergence of the current solutions.
The present study investigates the problem of post buckling of thin steel plates subjected to in-plane patch compression loading. Finite difference method was used to treat the stability problems. The geometrically nonlinearity was considered. The present procedure is general and applicable to the buckling, post buckling and free vibration of thin rectangular plates. The influences of initial imperfection, thickness variation, plate aspect ratios, boundary conditions, and length of patch loading on the post buckling behavior are shown graphically. The plate was analyzed with different tapering ratios (t a /t o ) (1.0, 1.25, 1.5, 1.75 and 2.0) so different patch length ratio (S) (0.0-0.3) were taken. A comparison with previous works is made. Finally, it is shown that the post buckling behavior very sensitive for some effects such as initial imperfection, tapering ratio, and patch length ratio.
Mechanics and Mechanical Engineering, 2013
The paper presents results of comparative experimental examinations and numerical analyses of rectangular plates subjected to shear treated as a skin of half–monocoque aircraft structure. There were considered: the plate without stiffeners 2 mm thick and structure with 1 mm thickness, stiffened by 15 integral ribs. Results of nonlinear numerical FEM analyses and experimental investigations with use of 3D DIC method were compared to ones conducted for smooth plate with equivalent mass. It was documented that introduction of sub–stiffening significant influence on both the form of deformation and distribution of stress in the structure. For smooth plate low cycle fatigue test was conducted.
THE BUCKLING ANALYSIS OF A RECTANGULAR PLATE ELASTICALLY CLAMPED ALONG THE LONGITUDINAL EDGES
Applied Engineering Letters, 2016
The paper analyses the stability of a rectangular plate which is elastically buckled along longitudinal edges and pressed by equally distributed forces. A general case is analyzed – different stiffness elastic clamping and then special simpler cases are considered. Energy method is used in order to determine critical stress. Deflection function is introduced in a convenient way so that it reflects the actual state of the plate deformation in the best manner. In this way, critical stress is determined in analytic form suitable for analysis. With help of the equation it is easy to conclude how certain parameters influence the value of critical stress. The paper indicates how the obtained solution could be utilized for determining local buckling critical stress in considerably more complex systems – pressed thin‐walled beams of an arbitrary length.
The Buckling Analysis of a Elastically Clamped Rectangular Plate
Mobility and vehicles mechanics, 2022
The paper analyses the stability of a rectangular plate which is elastically buckled along longitudinal edges and pressed by equally distributed forces. A general case is analyseddifferent stiffness elastic clamping and then special simpler cases are considered. Energy method is used in order to determine critical stress. Deflection function is introduced in a convenient way so that it reflects the actual state of the plate deformation in the best manner. In this way, critical stress is determined in analytic form suitable for analysis. With help of the equation it is easy to conclude how certain parameters influence the value of critical stress. The paper indicates how the obtained solution could be utilized for determining local buckling critical stress in considerably more complex systemspressed thin-walled beams of an arbitrary length.