Postbuckling Region Research Articles

Postbuckling of Laminated Composite Circular Conical Shells Under Combined Thermo-Mechanical Loads

In this paper, the postbuckling characteristics of cross- and angle-ply laminated composite conical shells subjected to combined thermo-mechanical loading are studied using shear deformable semi-analytical finite element. The nonlinear governing equations, considering geometric nonlinearity based on Sanders type of kinematic approximations, are solved using Newton-Raphson iteration procedure coupled with adaptive displacement control method to trace the postbuckling equilibrium path. It is brought out from the study that the inward displacement in the postbuckling region is significantly higher as compared to the outward one. The ratio of the lowest load in the postbuckling path and the bifurcation load increases with the increase in the pressure loading proportion and decreases with the increase in the axial loading proportions. The relative load carrying capacity of shells under different set of loading combinations changes with the increase in the maximum postbuckling displacement. It is also observed that the nonlinearity in the load interaction relation corresponding to lowest load in the postbuckling path is less compared to that for bifurcation load.

Optimization design and secondary buckling of bio-inspired helicoidal laminated plates under thermomechanical loads

Bio-inspired helicoidal carbon fiber reinforced polymer composite (CFRPC) laminates are one of the novel composite structures that have potential applications in many engineering fields. The optimization design of helicoidal layups with linear, nonlinear Recursive, Fibonacci, Exponential and their combination-form arrangements are carried out using ABAQUS and ASA algorithm on Isight platform. Two cases of the compressive postbuckling under uniaxial compression and the thermal postbuckling under uniform temperature rise of helicoidal CFRPC laminated plates stacked with optimal layups are performed and the secondary buckling and mode jumping in the postbuckling region are examined for the first time. Numerical investigations are carried out for 16-ply symmetrical helicoidal laminated plates with various width-to-thickness ratios under different boundary conditions and are compared with quasi-isotropic counterparts. The results show that the bio-inspired helicoidal CFRPC laminated plates can enhance the buckling load and the buckling temperature as well as the compressive and the thermal postbuckling strength. In some cases, the secondary buckling and mode jumping may occur for rectangular helicoidal laminated plate in the postbuckling region.

Numerical shape, thickness and stacking sequence optimisation and experimental study of hybrid composite plates under in-plane shear loading

Shape, thickness and stacking sequence optimisation of a damage tolerant hybrid (GFRP-CFRP) composite laminate is performed using the commercial Optistruct solver. The results of the optimisation study are compared to both a benchmark non-damage tolerant CFRP laminate (without protective surface GFRP plies known as type 1 laminate) and a damage tolerant traditionally optimised hybrid CFRP-GFRP laminate (having X shape CFRP plies known as type 2 laminate), designed and tested in a previous study. The optimised laminate is manufactured using three different manufacturing techniques. The experimental buckling and post-buckling performance of the manufactured laminates are investigated. The optimised hybrid laminate is approximately 8% heavier than the type 1 but 17% lighter than type 2, but with the benefit of protective surface GFRP plies in favour of a damage tolerant design as shown in a previous study. Both numerical and experimental buckling and post-buckling performance studies show that the optimised laminates demonstrate higher pre-buckling stiffness compared to the type 1 design. However, the experimental buckling and failure/collapse loads, unlike the numerically predicted loads, are 24.31% and 26.70% lower, respectively. This is due to the significant number of ply drop-offs in the hybrid laminate design, and hence geometric imperfections and stress concentration effects at these locations leading to early buckling and failure in the post-buckling region.

Experimental investigation of mechanical properties and energy absorption capabilities of hybrid lattice structures manufactured using fused filament fabrication

Hybrid lattice structures are composed of several dissimilar unit cells arranged in specific patterns. Unlike their one-phase counterparts, hybrid lattices remain relatively unexplored. In this work, novel hybrid lattice structures composed of Pillar Octahedral (PO) and Rhombic Dodecahedron (RD) lattices having variable strut diameters are arranged in different orders to form hybrid vertical piles (HVP), 2D and 3D chessboard order (HCh2D and HCh3D), are proposed, and their mechanical properties, energy absorption characteristics, and deformation modes are investigated under quasistatic compression. The empirical results indicated that the mechanical properties of hybrid lattice structures are the average of those of their parent lattices. HVP lattice structure has a high yield stress of 1.2, 2.22, and 3.54 MPa when strut diameter is 1.5, 1.75, and 2 mm respectively, and stable post-buckling region. It was also observed that hybrid lattice structures are more efficient in absorbing the energy of the deformation. When strut diameter is 1.5 mm, PO lattice structure has an efficiency of 50%, while HVP, HCh2D, and HCh3D lattices have an efficiency of about 70–80%. Finally, Gibson-Ashby models were proposed to predict the mechanical properties of lattice structures as the function of relative density.

Failure study of compressed thin-walled composite columns with top-hat cross-section

This paper presents considerations on the failure of axially compressed thin-walled composite structures with open sections (using an top-hat section structure). The analyzed columns were made of composite material — carbon fiber reinforced polymer (CFRP) using the autoclave technique. The study was conducted in a comprehensive approach using both experimental methods and advanced numerical simulations based on the finite element method (in ABAQUS® program). Investigations were performed up to the total failure of the structure, while considering the phenomena directly contributing to the failure (damage initiation, damage evolution, delamination). During the conducted experimental studies, both the postbuckling equilibrium paths obtained from the universal testing machine and the acoustic emission signals were registered. Regarding the simultaneously conducted numerical simulations, two independent advanced damage models (progressive failure analysis — PFA and cohesive zone model — CZM) were used, allowing for a thorough analysis of the complex mechanism of the composite material failure phenomenon. Both numerical and experimental results show high agreement. This paper provides a more comprehensive understanding how failure occurs such that the design of the analyzed composite sections. The most important aspect of this paper is the potential to enable to understand the failure of the top-hat stiffeners during post buckling such that made it possible to utilize the stable, undamaged region of the post-buckling region. In addition, the paper conducts an advanced study based on the simultaneous use of two independent damage models, allowing in particular for a thorough analysis of the damage with delamination phenomenon detection, on structures with a complex shape of the end cross-sections of the structure.

An asymptotic modeling and resolution framework for morphology evolutions of multiple-period post-buckling modes in bilayers

A stiff thin film bonded to a compliant substrate initially buckles into wrinkles, following with some intricate advanced instability modes when the compression exceeds higher thresholds. Here, we present an asymptotic modeling and resolution framework to quantitatively predict and continuously trace secondary bifurcation transitions in the non-linear post-buckling region. An advantage of this framework, besides its applicability to finite-strain deformations, is its asymptotic consistency with the three-dimensional (3D) field equations and interface continuity conditions in a pointwise manner. Based on our model, we reveal intricate post-buckling responses involving successive advanced mode transitions, i.e., period-doubling, period-tripling, period-quadrupling, ridge, and hierarchical wrinkles in film–substrate bilayers upon excess compression. Apart from modulus ratio, pre-stretch and pre-compression of the substrate can alter surface morphology of film–substrate bilayers. With substrate pre-compression, a bilayer may eventually involve into a period-tripling or period-quadrupling mode. We observe hierarchical wrinkles and ridges in films attached on pre-stretched substrates. With high substrate pre-tension and modulus ratio, a novel pattern, namely, periodic ridges, appears at the secondary bifurcation. Fundamental understanding and quantitative prediction of non-linear morphology evolutions of soft bilayers play important roles in rational designs of wrinkle-tunable functional surfaces.

Influence of couple stress size dependency in thermal instability of porous functionally graded composite microplates having different central cutouts

In the present study, the isogeometric numerical solving process incorporating non-uniform rational B-splines is put to use to analyze the size-dependent thermal postbuckling behavior of porous functionally graded (FG) microplates having a central cutout with different shapes. Accordingly, the modified couple stress continuum elasticity is employed within the framework of a hybrid-type quasi-3D higher-order plate theory to take the through-thickness deformations into consideration by only four variables. On the basis of a refined power-law function together with the Touloukian scheme, the porosity-dependent as well as temperature-dependent material properties are achieved. The couple stress-based thermal postbuckling equilibrium paths are acquired corresponding to various geometrical and material parameters and different boundary conditions. It is found that the gap between thermal postbuckling equilibrium paths relevant to various patterns of the porosity dispersion is a bit higher for the couple stress-based case than the classical one. Furthermore, it is indicated that a central cutout causes to change the trend of the load-deflection response that leads to decrease the initial thermal postbuckling strength, while it enhances the microplate strength in deep thermal postbuckling region.

Analytical study of thermal buckling and post-buckling behavior of composite beams reinforced with SMA by Reddy Bickford theory

Shape memory alloys are used in composite structures due to their shape memory effect and phase transformation. The recovery force of the shape memory alloy improves the post-buckling behavior of the structure. In this study, the thermal buckling and post-buckling of Shape Memory Alloy (SMA) hybrid composite laminated beam subjected to uniform temperature distribution is investigated. To this purpose, considering Von-Karman non-linear strain terms for large deformation, the non-linear equations of SMA reinforced beam based on Reddy Bickford theory have been derived. Besides, the recovery stress of the restrained SMA wires during martensitic transformation was calculated based on the one-dimensional constitutive law of the Brinson’s model. A numerical solution using Galerkin’s method has been presented for solving the nonlinear partial differential equations to obtain the critical buckling temperature and transverse deformation of the beam in the post-buckling region in both symmetric and anti-symmetric layups. The effect of SMA volume fraction, pre-strain, the boundary condition of the beam, stacking sequence, and its geometric properties have been studied. The results show that even by adding a small amount of SMA to the composite, the critical buckling temperature increases significantly, and the beam deflection decreases. Besides, using this theory has an evident effect on the anti-symmetric layup, especially for the thick beams.

In-plane stiffness of imperfect thin rectangular plates subjected to biaxial loads in elastic post-buckling region

The elastic post-buckling behavior of thin plates covers a relatively vast region in which geometry nonlinearity (large deflection) and material linearity (Hooke's low) are realized. In this region, a thin rectangular plate has constant stiffnesses in both orthogonal directions. Few simplified analysis guidelines have been analytically represented for in-plane stiffnesses of an elastic post-buckled thin plate subjected to biaxial loads. In this study, Marguerre's equations (the generalized form of von Karman equations), which describe the elastic post-buckling behavior of imperfect thin plates, are solved. Galerkin's method is used to solve these equations in a semi-analytical procedure. Simply supported imperfect thin rectangular plates are considered, and the stresses and displacements functions are obtained in two orthogonal directions to determine corresponding in-plane stiffnesses of the plate. Also, the maximum applicable load is obtained so that the material's linear behavior is maintained. The semi-analytical procedure has accuracy enough to predict the in-plane stiffness of post-buckled plates and can be easily used for practical purposes.

Thermal Nonlinear Buckling of Shear Deformable Functionally Graded Cylindrical Shells with Porosities

In this paper, for the first time, two-term deflection is suggested for nonlinear analysis of shear deformable cylindrical shells and, to the authors’ knowledge, a first investigation on thermal nonlinear buckling behavior of functionally graded material (FGM) cylindrical shells including porosities is presented. Material properties are assumed to be temperature dependent, volume fractions of constituents are graded in the thickness direction according to a power law, and effective properties of porous FGM are estimated according to a modified rule of mixture. Porosities are evenly or unevenly distributed within the shell. Mathematical formulations are based on a first-order shear deformation theory taking into account geometrical nonlinearity and elasticity of in-plane restraints of edges. Two-term deflection and a multiterm stress function are assumed to satisfy simply supported boundary conditions. The Galerkin method and an iteration procedure are employed to evaluate critical buckling temperatures and trace temperature-deflection paths in the postbuckling region. The two-term solution of deflection is a significant suggestion for nonlinear buckling analysis of shear deformable cylindrical shells in general and thermal postbuckling analysis of porous FGM cylindrical shells in particular. This two-term solution includes inherent uniform deflection at the prebuckling state and overcomes mathematically tremendous difficulty in using three-term deflection for shear deformable cylindrical shells. Besides this innovative approach, the obtained results are of great interest for many engineering applications. Unlike the case of mechanical loads, porosities have beneficial influences on the stability of thermally loaded FGM cylindrical shells.

Intricate evolutions of multiple-period post-buckling patterns in bilayers

Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling, shape-morphing for camouflaging skins, and micro/nano-scale surface patterning control. However, it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region. Here, we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems. Based on our models, we reveal an intricate post-buckling phenomenon involving successive flat-wrinkle-doubling-quadrupling-fold bifurcations. Pre-stretch and pre-compression of the substrate, as well as bilayer modulus ratio, can alter surface morphology of film/substrate bilayers. With high substrate pre-tension, hierarchical wrinkles emerge in the bilayer with a low modulus ratio, while a wrinkle-to-ridge transition occurs with a high modulus ratio. Besides, with moderate substrate pre-compression, the bilayer eventually evolves into a period-tripling mode. Phase diagrams based on neo-Hookean and Arruda-Boyce constitutions are drawn to characterize the influences of different factors and to provide an overall view of ultimate pattern formation. Fundamental understanding and quantitative prediction of the nonlinear morphological transitions of soft bilayer materials hold potential for multifunctional surface regulation.

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.

Investigations on the buckling and dynamics of diving-inspired systems when entering water

This work provides comparative modeling approaches to determine the velocities and natural frequencies of plunge-diving bird and bioinspired drone systems when entering water. These systems are chosen to further explain the survival of diving birds as they impact water and to provide insight into the design geometry and material choice of bioinspired diving drones. A nonlinear reduced-order model is developed and utilized to analyze the dive at impact considering both Timoshenko and Euler–Bernoulli beam theories. Using Hamilton’s principle, the equations of motion are first derived. Then, static and dynamic buckling analyses are conducted. For this study, a geometrically simplified cone-beam system is considered, where the cone represents the head and the beam represents both the neck and body of the plunge-diving systems. The first study is to analyze the effects different diving drone materials and cone dimensions play on the sensitivity of the system. The second study applies geometric parameters to the cone-beam system representative of a plunge-diving bird (Northern gannet) and a surface-diving bird (Double-crested cormorant). The results show that choosing a material with a higher Young’s modulus and a cone with a smaller half angle increase the velocity at which buckling occurs. The buckling velocities of the predicted Northern gannet model appear to be much greater than the average recorded diving speeds, suggesting that the bird is capable of plunge-diving at more extreme conditions. The natural frequencies are found for the aforementioned plunge-diving systems to predict failure if any external frequencies are known to act on the system while on a mission, such as conditions dependent on the climate or environment. It is shown in all buckling studies that the Euler-Bernoulli beam theory consistently overestimates the responses when compared with the Timoshenko beam theory. In the dynamic responses, Euler–Bernoulli beam theory overestimates for the pre-buckling region, then underestimates at the start of the post-buckling region until a point where the two theories cross paths. The amount of error with Euler–Bernoulli beam theory depends heavily on the slenderness ratio of the beam due to the theory being a simplification of the Timoshenko beam theory. It is noted that as the development of a more realistic bird model improves, the thickness will become significant and the use of Euler–Bernoulli beam theory at the point of impact will no longer be a valid assumption.

Bilinear Load–Displacement Curve of Semi-supported Steel Shear Walls

Elastic stiffness and ultimate shear capacity are two main parameters of a structural system to obtain its ideal bilinear load–displacement. In the previous studies, the ultimate shear capacity of semi-supported steel shear walls (SSSW) which are a new lateral resisting system, has been determined. In this system, wall plates do not have any direct connection to the main columns of structure and they are connected to secondary columns which do not carry the gravity loads. The used thin plate in the SSSW elastically buckles at low levels of lateral loads and the wall plate stays on a fairly vast region with elastic post-buckling behavior (elastic stiffness). In this study, the Von-Karman plate equations are solved by the Galerkin method to find displacement field of the wall plate in the elastic post-buckling region as well as the maximum shear load after which the plasticity expand in the wall plate. Thus, the elastic stiffness of system is calculated. As the analytical procedure is complicated, the method is applied on 144 examples with different material and geometrical properties. Using linear regression technique, a concise formula is proposed to predict the elastic stiffness of system. The dimensions of wall plate are only the effective parameters in the suggested formula and the elastic stiffness is independent of the overturning moment, section of secondary columns and yield stress of material. Using the ultimate shear capacity and elastic stiffness, an ideal bilinear curve is obtained for the lateral load versus the horizontal displacement. The shear capacity at the end of elastic post-buckling region and out of plane displacement are acceptably validated with those of FE analysis for some examples.

Modeling the behavior of inclusions in circular plates undergoing shape changes from two to three dimensions.

Growth of biological tissues and shape changes of thin synthetic sheets are commonly induced by stimulation of isolated regions (inclusions) in the system. These inclusions apply internal forces on their surroundings that, in turn, promote 2D layers to acquire complex 3D configurations. We focus on a fundamental building block of these systems, and consider a circular plate that contains an inclusion with dilative strains. Based on the Föppl-von Kármán (FvK) theory, we derive an analytical model that predicts the 2D-to-3D shape transitions in the system. Our findings are summarized in a phase diagram that reveals two distinct configurations in the post-buckling region. One is an extensive profile that holds close to the threshold of the instability, and the second is a localized profile, which preempts the extensive solution beyond the buckling threshold. While the former solution is derived as a perturbation around the flat configuration, assuming infinitesimal amplitudes, the latter solution is derived around a buckled state that is highly localized. We show that up to vanishingly small corrections that scale with the thickness, this localized configuration is equivalent to that expected for ultra-thin sheets, which completely relax compressive stresses. Our findings agree quantitatively with direct numerical minimization of the FvK energy. Furthermore, we extend the theory to describe shape transitions in polymeric gels, and compare the results with numerical simulations that account for the complete elastodynamic behavior of the gels. The agreement between the theory and these simulations indicates that our results are observable experimentally. Notably, our findings can provide guidelines to the analysis of more complicated systems that encompass interaction between several buckled inclusions.

A new stabilisation approach for level-set based topology optimisation of hyperelastic materials

This paper introduces a novel computational approach for level-set based topology optimisation of hyperelastic materials at large strains. This, to date, is considered an unresolved open problem in topology optimisation due to its extremely challenging nature. Two computational strategies have been proposed to address this problem. The first strategy resorts to an arc-length in the pre-buckling region of intermediate topology optimisation (TO) iterations where numerical difficulties arise (associated with nucleation, disconnected elements, etc.), and is then continued by a novel regularisation technique in the post-buckling region. In the second strategy, the regularisation technique is used for the entire loading process at each TO iteration. The success of both rests on the combination of three distinct key ingredients. First, the nonlinear equilibrium equations of motion are solved in a consistent incrementally linearised fashion by splitting the design load into a number of load increments. Second, the resulting linearised tangent elasticity tensor is stabilised (regularised) in order to prevent its loss of positive definiteness and, thus, avoid the loss of convexity of the discrete tangent operator. Third, and with the purpose of avoiding excessive numerical stabilisation, a scalar degradation function is applied on the regularised linearised elasticity tensor, based on a novel regularisation indicator field. The robustness and applicability of this new methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples, ranging from benchmark two-dimensional (plane stress) examples to larger scale three-dimensional applications. Crucially, the performance of all the designs has been tested at a post-processing stage without adding any source of artificial stiffness. Specifically, an arc-length Newton-Raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 10− 12.

Role and significance of thermal loading on the performance of carbon nanotube-based mass sensors

Insights on the sensitivity of carbon nanotube-based mass sensors subject to a uniform thermal environment are provided. The thermal loads are introduced as a means of buckling nonlocal carbon nanotube-based mass sensors in an effort to obtain high frequency shifts before and after the deposition of a nanoparticle on a carbon nanotube (CNT), leading to improved mass detection. In introducing thermal loads, the critical buckling temperature, pre-buckling, and post-buckling behaviors of CNTs with an arbitrary deposited mass are investigated. The CNT is modeled as an Euler-Bernoulli beam and the nonlinear governing equations of motion are derived by virtue of the Hamilton's principle. Eringen's nonlocal theory is employed to account for the interatomic long-range interactions, i.e., the size dependent phenomena occurring at the nano-scale. The proposed model allows for an arbitrarily positioned atomic-mass particle and accounts for the effects of the thermal field and the nonlocal parameter on the pre-buckling and post-buckling dynamics of clamped-clamped nanobeams. It is demonstrated that the temperature change has a remarkable influence on the frequency shift and hence on the sensitivity of the CNT-based mass sensor. The results show that augmenting the temperature in the pre-buckling regime leads to a decrease in the frequency shift, while the temperature rise in the post-buckling configuration has an increasing effect on the sensitivity of the CNT-based mass sensor. Also, it is found that when the temperature exceeds a certain point in the post-buckling region, higher frequency shifts can be obtained compared to the pre-buckling regime. In varying parameters, such as the length, diameter, number of walls (single-walled CNTs or multi-walled CNTs), location of the deposited mass, and nonlocal parameter, greater frequency shifts can be obtained in the post-buckling configurations of the CNT, leading to enhanced sensitivity in the system.

Skin–Stiffener Separation in T-Stiffened Composite Specimens in Postbuckling Condition

An experimental and numerical investigation was conducted to study the skin-stiffener separation of single T-shape stiffener specimens in postbuckling condition. Three specimens were manufactured with a centrally located Teflon insert, and were loaded in compression until collapse. Deformation patterns and separation evolution were monitored during the tests. To measure the full-field displacements and the strain distributions of the specimens, a digital image correlation (DIC) system was used. Skin-stiffener separation was observed and measured with an ultrasound system. Finite-element (FE) analyses were conducted to capture interlaminar damage mechanism based on the virtual crack closure technique. The numerical analysis accurately predicted the postbuckling deformation and the skin-stiffener separation behavior. The close correlation between the experimental and numerical results allows for further exploitation of the strength reserve in the postbuckling region and wider design options for the next generation of composite aircraft designs.

Influence of the 3D material tailoring on snap-through and snap-back post-buckling behaviors of steel-wire-reinforced hybrid 3D graded orthotropic shallow cylindrical panels

Simultaneous application of composite layers and steel bars/wires may considerably increase buckling strength of the civil structures. In the present paper, influence of the material heterogeneity on snap-through and snap-back post-buckling behaviors of the steel-wire-reinforced hybrid functionally graded orthotropic shallow cylindrical panels is investigated. In this regard, various arrangements are adopted for the steel-wires to constitute 3D (simultaneous radial, circumferential, and axial) gradations of the materials within some layers in addition to using some traditional composite layers in between. The non-linear governing equations of post-buckling are derived based on the principle of minimum potential energy. Sanders’ shell theory is utilized to ensure that the results are reliable in the deep post-buckling region. A nonlinear finite element scheme is employed to trace the post-buckling paths using the modified arc-length method. Finally, some parametric studies in terms of material arrangement, size of the embedded steel wires, the overall lamination scheme, and geometric parameters of the shell are performed. Results emphasize the significant effects of the steel wires on the post-buckling strength and indicate the advantage of using steel fibers with exponential or uniform longitudinal distributions and linear transverse distribution, for weight optimization.

Effect of asymmetric meshing on the buckling behavior of composite shells under axial compression

ABSTRACTAsymmetric meshing technique (AMT) is a perturbation method to introduce disturbances (i.e., imperfections) in a finite-element model without changing geometry, boundary conditions, or loading conditions. For cylindrical shells under axial compression, asymmetric meshing in the form of a square patch of three different surface areas and a band in axial and/or circumferential directions with different areas is discussed in the first half of the article. The element size in the patch or band is lowered to a varying degree as compared to the rest of the shell in order to produce the asymmetry. The reduction in the buckling load was observed from 15% to 20%, which depends mainly on the total area of asymmetric meshing, and less on the amplitude of asymmetry, i.e., reduction in element size. While loading the shell, an isolated dimple formed near the bifurcation point that increased in size to reach a stable state in the postbuckling region corresponding to the postbuckling plateau load. The load-displacement behavior using asymmetric meshing is similar to the experimental results and the numerical results obtained by introducing initial geometric imperfections. Asymmetric meshing in the form of varying element size in both axial direction and circumferential direction of the shell is discussed in the second half of the article. Asymmetric meshing showed reduction in the buckling load up to 7% with small amplitude of asymmetry that further increases with increase in amplitude of asymmetry in meshing. Asymmetric meshing has relatively less influence on predicted buckling load but significant effect on load displacement behavior in the postbuckling range; overall buckling behavior depends on the directionality of asymmetric meshing employed in the model.