Buckling Of Plates Research Articles

Quantifying the sensitivity of plate aspect ratio and edge boundary conditions on CFRP plate impact and post impact residual strength

Much literature exists on composite plate impact damage and residual strength post impact, but there is limited work which systematically examines how plate behaviour alters with plate aspect ratio and edge rotational restraint. Through simulation of composite stiffened plates under low velocity impact and Compression After Impact loading, the presented work demonstrates that laminate impact response and subsequent residual strength is highly sensitive to both plate aspect ratio and boundary conditions. Increasing edge restraint for low aspect ratio plates results in a moderate increase (up to 13.3%) in residual strength. Conversely, for higher aspect ratio plates (representative of aircraft stiffened panel components), the same change in edge restraint results in an equivalent decrease in residual strength (up to 13.0%). In particular, the interaction between impact induced damage and the onset of plate buckling observed in higher aspect ratio plates, and the subsequent effect on predicted residual strength, is not captured when examining low aspect ratio plates utilised in traditional material coupon testing practices.

Investigation on buckling and mode jumping of composite plates under thermomechanical loads

This paper presents an experimental and numerical study of composite plates, analyzing the interaction between mechanical and thermal loads related to buckling and the occurrence of mode jumping. A novel experimental setup for thermomechanical testing was developed. The setup is conceived around a frame with a low coefficient of thermal expansion, so that the plate can experience buckling and mode jumping when heated; and when compressed, interactions between the two loading states can be studied. Experimental results of plates loaded under diverse load cases are delivered in the form of load vs out-of-plane deflection graphs, deflection plots and buckling charts, where all buckling and mode jumping bifurcation points are registered. The influence of combined loading over mode jumping phenomena was successfully captured. Numerical predictions are able to estimate general tendencies in the occurrences of both buckling and mode jumping and in the mutual influence of thermal and mechanical loads.

Analysis of the impact of shear stress at the flange-web junction on the web behavior under concentrated and patch load

This article focuses on realistic predictions of the buckling of web plates under concentrated and patch load conceptually isolated from I-beams or box-beams. Under certain simplifications (which usually approximate practical conditions), girder web can be treated, for two limiting cases, as simply supported or simply supported and clamped rectangular plate under in-plane non-uniform loads. Any problem, including very demanding patch loading case, can then be tackled accurately using Ritz’s energy technique with double Fourier series for the deflection profile and exact stress distributions throughout the plate. The article firstly explains defined distribution of shear stresses on web-flange junction adopted, for the first time, in the analytical patch load model, and then proceeds to consider two different (but related) thematic problem types which concern various aspects of the introduction of such shear effect on stability problems of webs: firstly, how the shear stresses affect the buckling coefficients of plates and lead to an increase in load capacity due to more realistic web behavior and secondly, is there any influence of shear stresses on the existing values and shapes of interaction curves and surfaces. Analytical results in this article are compared with numerical finite element (FE) values.

Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates

In this article, the free vibration and buckling of multi-directional porous FGM sandwich plates are investigated. The material properties of FGM sandwich plates are assumed to be varying continuously in the longitudinal and transverse direction. The material properties are evaluated based on Voigt’s micro-mechanical model considering power law distribution method with arbitrary power index. Equilibrium equations for the vibration and buckling analysis of porous multi-directional FGM sandwich plate are obtained based on sinusoidal shear deformation theory. Analytical solution for simply supported multi-directional porous FGM sandwich plate is carried out using Navier’s solution technique. The FGM sandwich plate considered in this work has a homogeneous ceramic core and two functionally graded face sheets. To incorporate porosity in the FGM face sheet, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven porosity distribution models are considered and analyzed. Influence of volume fraction index in the longitudinal and transverse direction, layer thickness, porosity models, porosity coefficient, and geometrical parameter over natural frequency and critical buckling load of multi-directional FGM sandwich plate is investigated.

Static, buckling, and free-vibration analysis of plain-woven composite plate with finite thickness using VAM-based equivalent model

In this article, to remove the periodicity requirement in the thickness direction of plain-woven composite plates with finite thickness, a novel equivalent plate model (2D-EPM) based on the variational asymptotic method was established to study the static and dynamic behavior of plain-woven composite plates under different boundary and load conditions. The effective plate properties were obtained by the constitutive modeling of the unit cell, and inputted into the 2D-EPM to perform static and dynamic analysis. The accuracy and computational efficiency of the equivalent model were verified by comparing with the static and dynamic results of a three-dimensional finite element model (3D-FEM). The influence of the geometric parameters (yarn width, height, and spacing) and yarn laying angle on the equivalent stiffness and vibration characteristics of the plate were also examined. The results of the proposed model more closely with the experimental data than those of the 3D-FEM. This was possibly because the periodic boundary conditions in the thickness direction overestimated the stiffness of the plate. In addition, the local field distributions within the unit cell were well captured. The non-interlaced parts of the yarns were most likely to fail or become damaged. Overall, this research work has shown the ability of the 2D-EPM to predict the static displacement, global buckling and free vibration of plain-woven composite plates with finite thickness.

Postbuckling mechanics in slender steel plates under pure shear: A focus on boundary conditions and load path

Slender steel plates used in buildings, bridges, aircraft, and ships have postbuckling shear strength that is mobilized in design. Despite a century of research on this topic, the mechanics (load path and failure mechanisms) of the postbuckling behavior are still not fully understood. Proper boundary conditions are vital for studying the mechanics in finite element (FE) models, yet several different boundary conditions have been proposed by researchers. This paper uses FE models to examine various boundary conditions on a slender plate under pure shear loading. The models are benchmarked against 16 experimental tests, with a range of web depths (D), panel aspect ratios, and web slenderness ratios. The effects of boundary conditions on the normal stresses on the web plate edges and principal stresses in the web are examined for panel aspect ratios of 1, 2, and 3. The flanges, stiffeners, and “panel extensions” (which extend the web and flange a distance D/2 beyond the stiffener on either side of the panel) are used as boundary conditions (with axially free vertical edges at the ends of the panel). The analysis results show negligible participation from the stiffeners and flanges in the load path up to the ultimate postbuckling shear load, while compressive membrane stresses in the web are observed to redistribute and continue to increase after elastic buckling, in some regions at a greater rate than before buckling. This study advances the understanding of postbuckling shear load path that can be used in code development and performance enhancements for shear buckling in slender plates.

Shaking table test of a prefabricated steel frame structure with all-bolted connections

To study the seismic performance of an all bolt-connected prefabricated steel frame structure (ABPSFS), a shaking table test was conducted of a 1:4 scaled ABPSFS model in which high-strength bolts were used for column-to-column and beam-to-column connections. The dynamic properties, seismic responses, and failure mechanisms of the ABPSFS under different peak ground accelerations (PGAs) were analysed. This research also examined the dynamic failure mechanism of column-to-column bolted flange connections and proposed corresponding performance objectives in the seismic design of ABPSFS. The results indicated that the failure modes of ABPSFS were the warping of flange plates, the slipping of washers in bolted joints, and the cracking of concrete floors. With an increase in PGA, the fundamental frequency and stiffness of the structural model decreased while the damping ratio increased. The splicing layer became the weak layer of the entire structure and its acceleration amplification coefficient significantly increased in line with PGA. The dynamic failure mechanism of column-to-column bolted flange connection (CBFC) was buckling of the flange plate, opening of flange gap, and bolt fracture. For ABPSFS, 1/350 rad is recommended as the elastic storey drift angle and 1/70 rad as the elastic–plastic storey drift angle.

Equivalent Geometric Imperfections for Local Buckling of Slender Box-section Columns

Determining the plate or the local buckling resistance is highly important in designing steel buildings and bridges. The EN 1993-1-5Annex C provides a FEM-based design approach to calculate the buckling resistance based on numerical design calculations (geometrical and material nonlinear analysis - GMNIA). Within the GMNIA analysis-based stability design, the application of the imperfections has a special role. Thus, the applicability of the EN 1993-1-5 based buckling curve (Winter curve) has been questioned for pure compression, and previous investigations showed the buckling curve of EN 1993-1-5 Annex B is more appropriate for the design of slender box-section columns subjected to pure compression, the magnitude of the equivalent geometric imperfection to be applied in numerical models for local buckling is also questioned and investigated by the authors within the current paper. The aim of the current research program is to investigate the necessary equivalent geometric imperfections to be applied in FEM-based design calculations using GMNIA calculations. A numerical parametric study is executed to investigate the imperfection sensitivity of box-section columns having different local slenderness. The necessary imperfection magnitudes are determined to each analyzed geometry leading to the buckling resistance predicted by the standardized buckling curves. Based on the numerical parametric study, a proposal for the applicable equivalent geometric imperfection magnitude is developed, which conforms to the plate buckling curves of the EN 1993-1-5 and giving an improvement proposal to the local buckling imperfection magnitudes of the prEN 1993-1-14, which is currently under development.

Static, buckling and free vibration analyses of composite sandwich plate with bi-directional trapezoidal cores using VAM-based reduced plate model

The geometry of the composite sandwich plate with bi-directional trapezoidal cores (BTCs) is characterized by its novel cores with trapezoidal convex and concave corrugations in two in-plane directions. To solve the related difficulties in mechanical problems, a reduced plate model is established and written as a variational formulation based on the variational asymptotic method (VAM). That is, the original 3D plate problem was reduced to unit cell analysis (providing effective plate properties, such as the A, B, and D matrices) and two-dimensional (2D) reference plane analysis. To validate the accuracy and effectiveness of the reduced plate model, we analyze the static displacement, global buckling, and free vibrations of the composite sandwich plate with BTCs under different boundary and load conditions. Finally, we investigate the influence of the layup configurations of the face sheet and geometric parameters of the BTCs on the effective plate properties, buckling loads, and natural frequencies of the plate, which can provide useful reference for the structure optimization of composite sandwich plate with BTCs.

Thermal buckling analysis of cross-ply plates based on new displacement field

A higher-order displacement field is used for the analysis of the thermal buckling of composite plates subjected to thermal load; it is based on a constant ‘‘m’’, which is optimized to get results relatively close to those given by 3D elasticity theory. Adequate transverse shear strains distribution through the thickness and free stress surfaces of the plate is satisfied using this theory. Hamilton’s principle is used to derive equations of motion, which are solved using Navier-type series for simply supported plates. Thermal buckling of cross-ply laminates with various (α2 / α1) ratios, number of layers, aspect ratios, E1/E2 ratios, and stacking sequence for thick and thin plates is studied in detail. It is concluded that the obtained results using this displacement field are close to those calculated by 3D elasticity theory and other shear deformation plate theories when m=0.05.

Buckling problems of patch loaded plates with and without stiffeners – analytical approach

AbstractGeneralized analytical approach, with exact stress solutions, to buckling problems of in‐plane loaded plate with and without stiffeners has been presented through the case of locally distributed direct stresses. Several mathematical models have been chosen to represent high webs of steel girders under the patch load. Initially, the basic model has been built to simulate a girder used in the experimental research where the external load is equilibrated by support reactions. The second, more complex model included shear stresses along vertical stiffeners with a task to equilibrate the external loads, simulating a single web segment between the stiffeners of a long girder. The upgrade of the second model by adding a longitudinal stiffener resulted in the third model. Considering the complexity of stress distributions within the plate under such a demanding load, an analytical model for these problems has not been presented earlier. For the first time the influence of flexural stiffeners' rigidity on the plate buckling has been analysed with the exact solutions for in‐plane stress distributions, for simply supported plate. Results confirm the high quality of the analytical solution for the first and the second model and speak in favour of this approach and its potential for further upgrading in the case of the third model.

Assessment of the Imperfections for Plate Buckling of Unstiffened Plates

AbstractIn this study different approaches and combinations of imperfections using GMNIA of unstiffened plates are examined. The imperfections have a crucial influence for the determination of the load bearing capacity of thin plates. According to EN 1993‐1‐5 Annex C, when using GMNIA, the user can choose between equivalent geometric imperfections and a combination of the geometrical and the structural imperfections. The exact influence of the individual imperfections and their combination on the load bearing behavior has not been conclusive clarified. Furthermore, EN 1993‐1‐5 Annex C does not recommend a suitable residual stress model. This study aims to compare the ultimate loads due to compression loading using different imperfection approaches. Ten different combinations are investigated by using GMNIA. The results show that for larger plate slenderness, many of the ultimate loads are above the Winter‐Curve. The influence of the structural imperfections on the ultimate load is higher than the influence of the geometrical imperfections. An appropriate residual stress model is recommended. The geometrical imperfections should be given as a function of the plate slenderness.

Bending and Buckling of Circular Sandwich Plates with a Hardened Core.

Hard-core sandwich plates are widely used in the field of aviation, aerospace, transportation, and construction thanks to their superior mechanical properties such as sound absorption, heat insulation, shock absorption, and so on. As an important form, the circular sandwich is very common in the field of engineering. Thus, theoretical analysis and numerical simulation of bending and buckling for isotropic circular sandwich plates with a hard core (SP-HC) are conducted in this study. Firstly, the revised Reissner’s theory was used to derive the bending equations of isotropic circular SP-HC for the first time. Then, the analytic solutions to bending deformation for circular and annular sandwich SP-HCs under some loads and boundary conditions were obtained through the decoupled simplification. Secondly, an analytic solution to bending deformation for a simply supported annular SP-HC under uniformly distributed bending moment and shear force along the inner edge was given. Finally, the differential equations of buckling for circular SP-HCs in polar coordinates were derived to obtain the critical loads of overall instability of SP-HC under simply supported and fixed-end supported boundary conditions. Meanwhile, the numerical simulations using Nastran software were conducted to compare with the theoretical analyses using Reissner’s theory and the derived models in this study. The theoretical and numerical results showed that the present formula proposed in this study can be suitable to both SP-HC and SP-SC. The efforts can provide valuable information for safe and stable application of multi-functional composite material of SP-HC.

A discrete differential geometry-based approach to buckling and vibration analyses of inhomogeneous Reddy plates

In this paper, a novel discrete differential geometry-based numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. In the proposed approach a plate is discretized using a finite number of rigid bars, lumped masses, and elastic rotational springs to simulate both bending and shear deformation responses, allowing the analysis of thick plates through the adoption of the Reddy’s third-order shear deformable plate theory. An interesting analogy between the proposed model and the central finite difference method for solving a set of partial differential equations is also highlighted, showing how the former can be seen as the physical model behind the mathematical representation of the latter. The numerical results presented show both the versatility and the accuracy of the proposed approach.

Buckling optimization of composite rectangular plates by sequential permutation search with bending-twisting correction

Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency.

Local buckling of FRP thin-walled plates, shells and hollow sections with curved edges and arbitrary lamination

Extensive studies have been undertaken on the local buckling of FRP members. However, the scope of the existing research largely remains limited to those with rectangular faces. As the geometry of the member faces can affect the local buckling capacity, thin-walled members can possess higher buckling loads for a given volume of material when properly shaped. As such, consideration of non-rectangular faces is necessary, not only to cater for applications where non-rectangular profiles are commonly used, but also to exploit the potential for optimization of buckling capacity capable by using nonstandard cross-sections. In addition, the fibre layup of the lamella, and therefore the resulting mechanical properties of the face laminates, also influences the buckling capacity of the structural member. Hence, the optimal section geometry should also consider the fibre layups of the laminate. This paper presents a semi-analytical solution for the local buckling capacity of thin-walled members with faces of arbitrary geometry and material stacking sequence. The methodology adopts a Rayleigh–Ritz energy approach in combination with a Discrete Plate Analysis. Verifications have shown that the solution is capable to predict the local buckling capacity of the sections with acceptable levels of accuracy.

Analysis of thermal effect on buckling of imperfect FG composite plates by adaptive XIGA

This paper presents an effective computational framework based on adaptive extended isogeometric analysis (XIGA) for analyzing thermal buckling stability behavior of functional graded plates (FGPs) with flaws (e.g., holes, cracks). In this model, the locally refined non-uniform rational B-splines (LR NURBS), which can exactly represent the structure geometry and carry out the local refinement of the mesh, are used as the basis functions; and the first-order shear deformation theory is adopted to describe the kinematics of plates. According to the enhanced stresses on the mid-plane under the first critical buckling mode, a posteriori error estimator is evaluated. In addition, based on the posteriori error estimator, the meshes are automatically locally refined through refining the basis functions with large error. The obtained results illustrate the accuracy and reliability of the developed method, and show that the adaptive local refinement has better convergence ratio and higher computational efficiency than those of the uniform global refinement. Addressing the influence of some numerical aspects such as gradient index, direction and location of crack, and hole size on the critical thermal buckling temperature is also given.

A meshfree method with gradient smoothing for free vibration and buckling analysis of a strain gradient thin plate

In this paper, a meshfree Galerkin approach is presented for analysis of free vibration and buckling of a strain gradient thin plate. A cubic moving least square or reproducing kernel approximation with C2 continuity is used to ensure convergence. Due to smoothness of the meshfree approximation, the only variable is the deflection of a thin plate. To improve the computational accuracy, a consistent integration scheme with gradient smoothing is introduced to construct stiffness and geometrical stiffness matrices. The effectiveness of such an approach is confirmed by numerical results, and it is superior to a standard Gauss integration based meshfree Galerkin method. Further, the influence of classical and high order boundary conditions is investigated on the natural frequencies and critical buckling loads of strain gradient thin plates.

Buckling and post-buckling of an elastica under a lateral restraining force

Buckling of structures under lateral load restraint has been found to differ from the conventional bifurcation problems and cannot be handled with conventional analysis. Towards a better understanding of this type of unconventional buckling problems, this work investigates the upheaval buckling of an elastica resting on a smooth surface and restrained by a lateral constant force. Analytical solutions for the Mode-1 and Mode-2 post-buckling responses and configurations of the elastica are established. Stability of the post-buckling configurations under force-control are investigated via the energy method. An energy barrier is found to exist and the buckling load depends on the restraining force and perturbation energy. The imperfection sensitivity of the system is different from the conventional buckling ones, and a characteristic imperfection is found to exist that can transform a snap-through instability into a bifurcation buckling. As a first attempt to address the problem of flange wrinkling under a constant blank-holding force during the cup-drawing process, the fundamental solutions are extended to study the wrinkling of a shrinking elastic annulus under a constant lateral restraining force. The post-wrinkling responses are established and an energy barrier is found to exist for each wrinkling mode. A characteristic imperfection is also found to exist for each mode, which eliminates the energy barrier and enables bifurcation wrinkling. The linear relationship between the critical restraining force that prevents the wrinkling of the elastic annulus and the imperfection amplitude is established, which is also verified by numerical simulations. This study contributes to a better understanding of load-restrained buckling problems and is expected to shed light on the elastoplastic buckling of plates and shells under lateral load restraints in general, and on the wrinkling of a thin sheet during cup-drawing in particular.

Ground Motion Intensity Measures for Seismic Vulnerability Assessment of Steel Storage Tanks With Unanchored Support Conditions

Abstract This paper aims to comprehensively evaluate the performance of a series of ground motion intensity measures (IMs) used in the seismic vulnerability assessment of steel storage tanks with unanchored support conditions. Sixteen well-known IMs are thus selected, which are classified into amplitude-, frequency-, and time-based categories. A comparative study is then performed on four different unanchored steel storage tanks subjected to a suite of 140 ground motion records that is comprised of seven different bins of records with different hazard levels. In this regard, the tanks are appropriately modeled based on a simplified approach, whose uplift and sliding nonlinear behaviors are properly implemented based on a three-dimensional nonlinear pushover analysis of the tanks. Four characteristics of the examined IMs including efficiency, practicality, proficiency, and sufficiency are evaluated based on a probabilistic seismic demand model of two critical failure modes of the tanks, i.e., plastic rotation of the shell-to-bottom connection and elephant's foot buckling of the shell plate. According to the comparative study, frequency-based IMs demonstrate their superior performance for all criteria compared with other groups; in particular, the average spectral acceleration gains the highest ranking. Finally, an appropriate range of the upper period considered in the average spectral acceleration IM is then proposed to optimize the efficiency of this IM for the examined tanks.