A New Plate Buckling Design Formula (3rd Report) (original) (raw)
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Determination of the Buckling Loads of Irregularly Shaped Plates Using a New Design Approach
2019
Elastic buckling is one of a number of modes of failure that needs to be considered during the design of structures. Although elastic buckling has been researched for decades there is still a need to develop fast and comprehensive procedures that will reduce product design time especially during the pre-sizing stage. This paper presents a novel equation and parameters for the buckling analysis of plates that accounts for the interaction of geometry parameters, boundary conditions and different load distributions. The method covers geometrical plate shapes such as triangular, evolutive, and slightly curved plates. In the place of classical methods the new procedure called the Parametric Buckling Analysis (PBA) combines a number of concepts in a novel heuristic manner to achieve a comprehensive solution. Among the concepts is an extension of the Euler column buckling boundary condition coefficients to various possible plate edge boundary condition combinations. Geometry parameters reflect the combined effect of plate aspect ratio and the number of buckle waves. A load parameter introduces a regularising factor that allows the effect of different load distributions to be included in the equation. The method is tested for flat plates of different rectangular, triangular, trapezoidal shapes and for slightly curved plates with cylindrical geometries. Eighteen different combinations of free, simple support and clamped edge boundary conditions are considered. Uniform and linearly varying edge stress loading conditions are also considered. The results obtained are compared with those obtained using analytical and finite element analysis. .
An applicable formula for elastic buckling of rectangular plates under biaxial and shear loads
Aerospace Science and Technology, 2016
As thin plates have relatively big thickness ratios, their elastic buckling usually occurs before the yielding. From beginning of the previous century, many researchers have considered various in-plane loading states on thin plates and have strived to find simple equations to predict the buckling load. However, there are few valid equations with negligible errors for a thin plate, when it is under all of in-plane loads. In this paper, using energy method, an applicable formula is suggested for a simply supported rectangular plate, which is under biaxial and shear loads. The biaxial loads can be applied in the compressive/compressive, compressive/tensile, and tensile/tensile states on the plate. Generally, 15 129 examples are considered for this problem. The aspect ratio of plates varies from 1 to 5 and for each case and with the known load ratios, the plate buckling coefficient is calculated. Then, by using the regression techniques and interpolation, it is tried to estimate a simple equation with minimum error to predict the buckling load. The confirmed results show that for the biaxial compression and shear state, the maximum error is 8% and for the compression-tension-shear and biaxial tension and shear states, it increases until 20%.
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.
In this study, exact trigonometric displacement function was used to solve the buckling problem of a three-dimensional (3-D) rectangular plate that is clamped at the first-three edges and the other remaining edge simply supported (CCCS) under uniaxial compressive load. Employing 3-D constitutive relations which consist of entire components, the functional for total potential energy was obtained. After that, the rotation and deflection at x-axis and y-axis were formulated from the established compatibility equations to get an exact trigonometric deflection function. The characteristics equation was obtained by differentiating energy equation with respect to deflect to obtain the relations between deflection and rotation. The equation of the total potential energy is minimized with respect to the deflection coefficient after incorporating the deflection and rotation function, the critical buckling load formula was established. The solution for the buckling problem gotten shown that the structure of the plate is safe when the plate thickness is increased as the outcome of the study showed that the critical buckling load increased as the span-thickness ratio increased. The overall difference in form of percent between the present work and previous studies recorded is 5.4%. This shows that at about 95% certainty, the present work is perfect. The comparison of this study with the results of previous similar studies revealed the uniformity 3-D plate theory and the variations of CPT and RPT theories in the exact buckling analysis of a rectangular plate. However, this approach which includes all the six stress elements of the plate material in the analysis produced an exact deflection function unlike the previous studies which used assumed functions. Furthermore, the theoretical analysis of this study demonstrates a novel approach to solve the buckling problem rectangular plate which is capable of analyzing rectangular plates of any thickness configuration.
Matlab Based Buckling Analysis of Thin Rectangular Flat Plates
American Journal of Engineering Research, 2019
One of the major problems of rectangular platebuckling under in-plane load is the rigorous approach use in its analysis. In this study, the problem of buckling was addressed by developing a Matlab based computer program for ease of analysis of rectangular plates for critical buckling load, which is needed for safe design.The plates were assumed to be loaded axially along the x-axis, and polynomial shape functions used in Ritz energy equation to formulate a general solutionwhich is computer user-friendly. The critical buckling load coefficients’ 'n' values obtained from this program were compared with thoseavailablein scholarly literaturesso as to demonstrate theirvalidity. These values were found to be very close to existing values in literature. It therefore implies that, this general computer program for buckling analysis of rectangular plates is a better and quicker means of obtaining the critical buckling load of rectangular thin isotropic plates.
Closed form buckling analysis of thin rectangular plates
IOSR Journals, 2019
This paper presents closed form buckling analysis of rectangular thin plates. It minimizes the total potential energy functional with respect to deflection function and obtained the Euler-Bernoulli equation of equilibrium of forces for the plate. Using split-deflection method, the equilibrium equation was uncoupled into two separate equations. The function satisfying each of the two equations was determined. Exact solution of Euler-Bernoulli governing equation for the plate was obtained as a product of the functions. Nine distinct deflection functions for plates were obtained after satisfying nine different boundary conditions. The paper went further to obtain the formula for calculating the critical buckling load of the plate by minimizing the total potential energy functional with respect coefficient of deflection. Numerical examples were carried out using two plates. One of the plates has two adjacent edges clamped and the other edges simply support (ccss). The other plate has one edge clamped and the other three edges simply supported (csss). The critical buckling loads obtained for the two plates were compared with the ones from an earlier study, which used polynomial deflection equation. For square ccss the values of the non dimensional critical buckling loads are 61.706 and 64.73 for the present and past studies respectively. For csss plate the values are 56.429 and 56.807 respectively for the present and past studies. The percentage difference between the values from the present and past studies are 4.67% for ccss and 0.67% for csss. It could be seen that the differences are not too significant.
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
A Parametric Study on the Buckling Behavior of Square Steel Plates under Uniaxial Compression
Civil Engineering and Architecture, 2021
Steel plates are common in thin walled structures. They are used in various forms and geometries such as intact (not perforated) plates, stiffened plates, perforated, or perforated stiffened plates. This study employs nonlinear pushover finite element analysis to determine the critical buckling strength as well as the plate maximum strength for uniaxially square plates in the form of intact, stiffened, perforated, as well as perforated stiffened plates under uniaxial uniform compression. Curves representing the load axial displacement relationship as well as load buckling relationship were plotted. Tables summarizing the plate critical buckling strength and the plate maximum strength for each of the four plate forms were presented in order to specify the controlling failure for each form, which is considered as a vital factor for the design process. The study indicates that the critical buckling stress for stiffened plates always increases as the number of stiffeners increases. Nonetheless the critical buckling stress decreases as the number of perforations increases. Thus, a stiffened perforated plate would be a proper solution if perforations are unavoidable. The study concluded that in both stiffened square plates and in stiffened perorated plates, the ratio of the plate area to the sum of stiffeners areas tentatively indicate the possible occurrence of stiffener tripping. Ansys software was utilized to perform the analysis that was validated in calculating the critical buckling strength as well as maximum plate strength of intact plate subjected to axial compression.
Use of Buckling Coefficient in Predicting Buckling Load of Plates with and without Holes
Buckling, a form of failure happened to plated structures, is investigated in this study. The main focus is to investigate the effects of thickness of the plates having through-thickness holes on buckling when the plate is subjected to in-plane compression. Plates having length of 200mm and width of 100mm are chosen to have thickness in range from 0.50mm to 10mm. Two holes of diameters of 20mm are implemented in plates. The finite element procedure using ABAQUS is applied for analyses. Then using the Gerard and Becker equation compressive buckling coefficients, Kc, are calculated and presented to enable engineers to calculate buckling load for the desired plate with holes in specific dimension. In order to generalize the obtained results, verification analysis has been performed by taking plates having different dimensions from the original ones used in this study. The verification showed the capability of buckling coefficients to predict buckling stresses of plates in various dimensions.
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