• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.22 no.2
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• pp.411-427
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• 2016

In this study, by using finite element non-linear static analysis and comparing it with experimental models, the buckling and post-buckling behavior of bracing gusset plates has been investigated. The effects of such parameters as dimension and thickness of the gusset plate and the influence of position of the bracing member on the behavior of gusset plate have been examined. The results of the analyses clearly suggest that capacity, buckling and post-buckling behaviors of gusset plates depend on the position of the bracing splice plate with respect to the free bending line as well as on the size and thickness of the gusset plate. Also, with respect to numerical analysis results, some practical graphs for the calculation of buckling capacity of gusset plate connections are presented. For steel structures, the proposed method is apparently more accurate than available code procedures.

• Steel and Composite Structures
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• v.34 no.2
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• pp.289-297
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• 2020

In the present research post-buckling of a cut out plate reinforced through carbon nanotubes (CNTs) resting on an elastic foundation is studied. Material characteristics of CNTs are hypothesized to be altered within thickness orientation which are calculated according to Mori-Tanaka model. For modeling the system mathematically, first order shear deformation theory (FSDT) is applied and using energy procedure, the governing equations can be derived. With respect to Rayleigh-Ritz procedure as well as Newton-Raphson iterative scheme, the motion equations are solved and therefore, post-buckling behavior of structure will be tracked. Diverse parameters as well as their reactions on post-buckling paths focusing cut out measurement, CNT's volume fraction and agglomeration, dimension of plate and an elastic foundation are investigated. It is revealed that presence of a square cut out can affect negatively post-buckling behavior of structure. Moreover, adding nanocompsits in the matrix leads to enhancement of post-buckling response of system.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.709-725
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• 2006

In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

• Structural Engineering and Mechanics
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• v.9 no.3
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• pp.289-304
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• 2000

This study discusses on the experimental and analytical results of the global buckling tests, carried out on aluminum alloy double layer space grids composed of tubular members, ball joints and connecting bolts at the member ends, with the purpose of demonstrating the effectiveness of a simplified analysis method using an equivalent slenderness ratio for the members. Because very few experiments have been carried out on this type of aluminum space grids, the buckling behavior is investigated experimentally over the post buckling regions using several space grid specimen with various values for the member slenderness ratio. The observed behavior duping the experiments is compared with the analytically obtained results. The comparison is made based on two different schemes; one on the plastic hinge method considering a bending moment-axial force interaction for members and the other on a method using an equivalent slenderness ratio. It is confirmed that the equivalent slenderness method can be effectively applied, even in the post buckling regions, once the effects of the rotational rigidity at the ball joints are appropriately evaluated, because the rigidity controls the buckling behavior. The effectiveness of the equivalent slenderness method will be widely utilized for estimation of the ultimate strength, even in post buckling regions for large span aluminum space grids composed of an extreme large number of nodes and members.

• Steel and Composite Structures
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• v.31 no.3
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• pp.243-259
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• 2019

This study deals with the nonlinear static analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells subjected to axial load based on the classical shell theory. Detailed studies for both nonlinear buckling and post-buckling behavior of truncated conical shells. The truncated conical shells are reinforced by single-walled carbon nanotubes which alter according to linear functions of the shell thickness. The nonlinear equations are solved by both the Airy stress function and Galerkin method based on the classical shell theory. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behavior of FG-CNTRC truncated conical shells are presented. The proposed results are validated by comparing with other authors.

• Advances in nano research
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• v.12 no.4
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• pp.427-440
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• 2022

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

• Advances in nano research
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• v.7 no.6
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• pp.405-417
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• 2019

This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

• Structural Engineering and Mechanics
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• v.49 no.5
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• pp.569-595
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• 2014

In this paper, a novel semi-energy finite strip method (FSM) is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick functionally graded (FG) plates under uniform end-shortening. In order to study the effects of through-the-thickness shear stresses on the post-buckling behavior of FG plates, two previously developed finite strip methods, i.e., semi-energy FSM based on the concept of classical laminated plate theory (CLPT) and a CLPT full-energy FSM, are also implemented. Moreover, the effects of aspect ratio on initial post-buckling stiffness of FG rectangular plates are studied. It has been shown that the variation of the ratio of initial post-buckling stiffness to pre-buckling stiffness ($S^*/S$) with respect to aspects ratios is quite independent of volume fractions of constituents in thin FG plates. It has also been seen that the universal curve representing the variation of ($S^*/S$) with aspect ratio of a FG plate demonstrate a saw shape curve. Moreover, it is revealed that for the thin FG plates in contrast to relatively thick plates, the variations of non-dimensional load versus end-shortening is independent of ceramic-metal volume fraction index. This means that the post-buckling behavior of thin FG plates and the thin pure isotropic plates is similar. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results may have a great influence in design of FG plates encountering post-buckling behavior.

• Steel and Composite Structures
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• v.45 no.3
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• pp.349-367
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• 2022

In this research, an approach combining a semi-analytical method and an analytical method is presented to investigate the static and dynamic post-buckling behavior of the sandwich functionally graded (FG) porous cylindrical shells exposed to external pressure. The sandwich cylindrical shell considered is composed of a viscoelastic core and two FG porous (FGP) face layers. The viscoelastic core is made of Kelvin-Voigt-type material. The material properties of the FG porous face layer are considered continuous through each face thickness according to a porosity coefficient and a volume fraction index. Two types of sandwich FG porous viscoelastic cylindrical shells named Type A and Type B are considered in the research. Type A shell has the porosity evenly distributed across the thickness direction, and Type B has the porosity unevenly distributes across the thickness direction. The FG face layers are considered in two cases: outside metal surface, inside ceramic surface (OMS-ICS), and inside metal surface, outside ceramic surface (IMS-OCS). According to Donnell shell theory, von-Karman equation, and Galerkin's method, a discretized nonlinear governing equation is derived for analyzing the behavior of the shells. The explicit expressions for static and dynamic critical buckling loading are thus developed. To study the dynamic buckling of the shells, the governing equation is examined via a numerical approach implementing the fourth-order Runge-Kutta method. With a procedure presented by Budiansky-Roth, the critical load for dynamic post-buckling is obtained. The effects of various parameters, such as material and geometrical parameters, on the post-buckling behaviors are investigated.