An Analytical 3-D Modeling Technique of Non-Linear Buckling Behavior of an Axially Compressed Rectangular Plate (original) (raw)
Related papers
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.
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.
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.
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.
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
Application of a New Trigonometric Theory in the Buckling Analysis of Three-Dimensional Thick Plate
In this paper, a new trigonometric shear deformation plate theory is developed for the buckling analysis of a three dimensional thick rectangular isotropic plate, elastically restrained along one edge and other three edges simply supported (CSSS) under uniaxial compressive load, using the variational Energy approach. Total potential energy equation of a thick plate was formulated from the three-dimensional constitutive relations, thereafter the compatibility equations was established to obtain the relations between the out of plane displacement and shear deformation slope along the direction of x and y coordinates. This total potential energy functional was differentiated with respect to deflection to obtain the governing equation. The functions for these slopes were obtained from out of plane function using the solution of compatibility equations while the solution of the governing equation is the function for the out of plane displacement. Finally, the total potential energy is minimized with respect to displacement coefficients, thereafter, the deflection and rotations were substituted back into the buckling equation derived to obtain the formulas for calculating the critical buckling load and other the mentioned functions. The three dimensional analysis for critical buckling of thick plates were carried out by varying parameters stiffness properties and aspect ratios. The proposed method obviates the need of shear correction factors which is associated with first order shear deformation theory for the energy equation formulation. The present theory unlike refined plate theories, considered all the stress elements of the plate in the analysis. From the numerical analysis obtained, it is found that the value of the critical buckling load increase as the span-thickness ratio increases. This suggests that as the thickness increases, the safety of the plate structure is improved.