Post buckling Research Papers - Academia.edu (original) (raw)

This paper investigates the buckling and postbuckling of simply supported,
nanocomposite plates with functionally graded nanotube reinforcements
subjected to uniaxial compression in thermal environments. The nanocomposite
plates are assumed to be functionally graded in the thickness direction using singlewalled
carbon nanotubes (SWCNTs) serving as reinforcements and the plates’ effective
material properties are estimated through a micromechanical model. The
higher order shear deformation plate theory with a von Kármán-type of kinematic
nonlinearity is used to model the composite plates and a two-step perturbation technique
is performed to determine the buckling loads and postbuckling equilibrium
paths. Numerical results for perfect and imperfect, geometrically mid-plane symmetric
functionally graded carbon nanotube reinforced composite (FG-CNTRC)
plates are obtained under different sets of thermal environmental conditions. The
results for uniformly distributed CNTRC plate, which is a special case in the present
study, are compared with those of the FG-CNTRC plate. The results show that the
buckling loads as well as postbuckling strength of the plate can be significantly
increased as a result of a functionally graded nanotube reinforcement. The results
reveal that the carbon nanotube volume fraction has a significant effect on the buckling
load and postbuckling behavior of CNTRC plates.

- by and +1
- •
- Mechanics of fiber-reinforced polymer composites for construction, Post buckling, Functionally graded materials, Buckling

The present paper deals with the nonlinear thermal instability of geometrically imperfect sandwich cylindrical shells under uniform heating. The sandwich shells are made of a shape memory alloy (SMA)-fiber-reinforced composite and functionally graded (FG) face sheets (FG/ SMA/FG). The Brinson phenomenological model is used to express the constitutive characteristics of SMA fibers. The governing equations are established within the framework of the third-order shear deformation shell theory by taking into account the von Karman geometrical nonlinearity and initial imperfection. The material properties of constituents are assumed to be temperature dependent. The Galerkin technique is utilized to derive expressions of the bifurcation points and bifurcation paths of the sandwich cylindrical shells. Using the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of the SMA fiber volume fraction, SMA pre-strain, core thickness, non-homogeneity index, geometrical imperfection, geometry parameters of sandwich shells and temperature dependency of materials on the stability of shells. The results reveal that proper application of SMA fibers postpones the thermal bifurcation point and dramatically decreases thermal post-buckling deflection. Moreover, the induced tensile recovery stress of SMA fibers could also stabilize the geometrically imperfect shells during the inverse martensite phase transformation.

- by DR Aghdam and +1
- •
- Shape Memory Alloys, Post buckling, Smart Materials and Structures, Thermal Stability

This work presents an analytical approach to investigate buckling and post-buckling behavior of FGM plate with porosities resting on elastic foundations and subjected to mechanical, thermal and thermomechanical loads. The formulations are based on Reddy's higher-order shear deformation plate theory taking into consideration Von Karman nonlinearity, initial geometrical imperfections, and Pasternak type of elastic foundations. By applying Galerkin method, closed-form relations of buckling loads and post-buckling equilibrium paths for simply supported plates are determined. Numerical results are carried out to show the effects of porosity distribution characteristics (Porosity-I and Porosity-II), geometrical parameters, material properties and elastic foundations on the mechanical, thermal and thermomechanical buckling loads and post-buckling resistance capacity of the porous FGM plates.

- by Minh-Chien Trinh
- •
- Porous Materials, Porosity, Nonlinear Analysis, Post buckling

The paper presents an analytical formulation for the post-buckling analysis of composite aeronautical panels with omega stiffeners loaded in compression and shear. The formulation relies on an energy principle and the method of Ritz. In the first step, the panel is an assembly of plate elements, and the buckling analysis is performed. In the second step, the panel is an elastically restrained skin, and the post-buckling behaviour is studied. The comparisons with finite element analyses and experimental results from the literature reveal the ability of the formulation to assess the post-buckling response.

- by Riccardo Vescovini
- •
- Composite Materials and Structures, Post buckling

Laminated structures find many applications in various engineering fields namely aerospace, bio-medical, civil, marine and mechanical engineering due to easy handling, good mechanical properties and low fabrication cost. Laminated plates with round holes and other openings are extensively used as structural members in aircraft design. These holes are act sometimes as access holes, holes for hardware to pass through, or in the case of fuselage, windows and doors or simply used to reduce the weight of the structure. These laminated structures are often subjected to load in one or more direction in cycles or as intermittent load. Thus there is need to study the failure of these components under bi-axial loading with the view to optimize the shape and lay of the components so as they give maximum service and more life. In this paper bi-axial testing machine is developed to determine bucking load of different materials. Experiments are carried out on cross ply composite under various buckling loads on the bi-axial testing machine. The theoretical results, analytical and experimental results are compared with each other. It is observed that the strength of Bakelite composite plates is higher than glass epoxy laminated composite plate. So Bakelite is more suitable than glass epoxy.

This paper investigates the post-buckling behavior of a slender axially inextensible elastic rod with pinned-fixed end. The set of five first order nonlinear ordinary differential equations with boundary conditions specified at both ends constitutes a complex two point boundary value problem. By using multisegment integration technique, the highly nonlinear boundary value problems are numerically solved. Results are presented in non-dimensional graphs for a range of prescribed loading condition. The secondary equilibrium paths and the post-buckling configurations of the rod are presented.

The paper presents a procedure for the analysis of stability and initial post-buckling behaviour of spliced columns in sway and non-sway steel frames. The main assumptions are linear elasticity and geometrically perfect columns that are loaded by a compressive force which retains its direction as the column deflects. An energy-based formulation that includes a polynomial Rayleigh–Ritz approximation into the potential energy function, in combination with the Lagrange’s method of undetermined multipliers, has been found very convenient for this type of problem. The system is thus described by a set of kinematically admissible generalized coordinates and a single loading parameter. First, the critical state is characterized by means of linear eigenvalue analysis. A parametric study is implemented to assess the critical load. The numerical results are used to develop a relatively simple yet reasonably accurate engineering method for predicting the critical behaviour of spliced columns in sway and non-sway steel frames. The energy formulation is then applied to the search of post-buckling branches of bifurcation points. The approach embraces path-following methods based on perturbation schemes built on a Newton type iterative procedure. This is illustrated in the application to post-bifurcation in columns with different splice mechanical characteristics. The findings suggest that the splice tangent stiffness has a major influence on the overall column behaviour.

- by Pedro D Simão
- •
- Civil Engineering, Steel Structure, Structural Stability, Steel Structures
- by DR Aghdam and +1
- •
- Shape Memory Alloys, Post buckling, Buckling, Smart Materials and Structures

Sandwich panels with uni-directional stiffeners in the core are lightweight structures. When the voids between the stiffeners are empty, the global bending of the panel is accompanied by the secondary bending of the faces between the stiffeners. This study investigates the effect of the secondary bending on local buckling of the sandwich panel. Web-core steel sandwich panel is analyzed with finite element method using shell elements. The panel is studied under uni-axial loading in the direction of the stiffeners. The results show that the local buckling strength is higher at the unloaded edges where the secondary bending deformation is larger. This has a positive effect on the strength of the panel since it postpones the reduction of the load-carrying capacity. Local buckling occurs first in the center of the panel. The buckles have atypical shape with the wave-length significantly smaller than the width of the face plate between the stiffeners.

- by Jasmin Jelovica
- •
- Steel Structure, Compressive Strength, Post buckling, Buckling

A computational analysis for geometrically nonlinear responses of the pinned-pinned and fixed-fixed slender beams under transversely non-uniform temperature rise has been presented in this paper. The change of the elastic properties with temperature is accounted by using experimental data through nonlinear strain-temperature relation. The multisegment integration method has been employed in a two-point boundary value problem governed by a set of seven first-order nonlinear ordinary differential equations. Characteristics curves representing the secondary equilibrium paths of the thermal postbuckled beams are plotted. The postbuckling analysis of slender elastic beams subjected to both uniform and non-uniform temperature variation in the transverse direction is highly dependent on the prescribed end conditions. Due to the non-uniform heating and the induced thermal bending moment, the structure behaves like an initially deformed beam.

This paper investigates theoretically the compressive load-carrying behaviour of geometrically imperfect web-core sandwich plates. Slender plates, which first buckle globally, are considered. The study is carried out using two approaches, both solved with the finite element method. The first is the equivalent single-layer theory approach. First-order shear deformation theory is used. The second approach is a three-dimensional shell model of a sandwich plate. Plates are loaded in the web plate direction. Simply supported and clamped boundary conditions are considered with a different level of in-plane restraint on the unloaded edge. The results show that the behaviour of the sandwich plate is qualitatively equal to the isotropic plate of the same bending stiffness for deflections lower than the plate thickness. As the deflections increase, the lower in-plane stiffness of the sandwich plate results in lower post-buckling strength. Local buckling of face plates in the post-buckling range of the sandwich plate further reduces the structural stiffness.

The goal of the present research is the distortional-global (D-G) buckling interaction of cold-formed steel (CFS) lipped channel (LC) columns, in its buckling, structural behavior and strength nature. Some studies on this topic have been conducted in the literature, however, the D-G interaction is not well known and needs more attention.
For an elastic buckling analysis, a software entitled FStr Computer Application Program is developed. The application is based on the Finite Strip Method, mainly focused in a simple and accessible interface. The FStr program generates the modal shapes and insert as initial geometric imperfections in the finite element software ANSYS, in order to perform a geometric and material nonlinear analysis. Both, the FStr program and the finite element model are validated with available numerical examples and laboratory tests from the literature. Moreover, for the structural behavior and column strength, it is carried out stability paths from previous nonlinear analysis, for different combination of initial geometric imperfection of global and distortional modes. The buckling mode combination as initial geometric imperfection helps to understand the D-G buckling interaction, which is difficult to predict with a simple elastic buckling analysis. The results of the initial imperfection combination have shown that, for high yielding steel, the global initial geometric imperfection provides the most detrimental ultimate load. Additionally, a parametric study varying the column’s length have shown that the nominal axial strength for global buckling equation, already in the standards, is enough to cover the DG coupled phenomenon.

- by João Alfredo De Lazzari
- •
- Nonlinear Analysis, Compressive Strength, Post buckling, Buckling

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights a b s t r a c t In this article, large amplitude vibration and thermal post-buckling of shape memory alloy (SMA) fiber reinforced hybrid composite beams with symmetric and asymmetric lay-up are analytically investigated. To predict the behavior of the smart laminated beam, the EulereBernoulli beam theory and the nonlinear von-Karman strain field are employed. Also, one-dimensional Brinson SMA model is utilized to calculate the recovery stress of SMA fibers in the case of restrained strain. Nonlinear governing equations of motion are derived via the Hamilton principle. Using an analytical approach based on the Galerkin procedure together with the simple harmonic motion assumption, a closed-form solution is obtained for the thermal post-buckling and nonlinear free vibration analysis of SMA fiber reinforced hybrid composite beams. Due to lack of any results on the free vibration and thermal stability of SMA fiber reinforced composite beams, the results obtained from the present solution for laminated composite beams without SMA fiber are compared with counterpart data in the open literature, which validate the present solution. Then, a set of parametric study is carried out to show the influence of SMA volume fraction, amount of prestrain in the SMA fiber, orientation of composite fiber, SMA-reinforced layer thickness to total thickness ratio, location of SMA layer, vibration amplitude, boundary conditions and temperature on the vibration characteristic of the laminated beam reinforced with SMA in the pre-and post-buckled domains.

- by DR Aghdam and +2
- •
- Nonlinear vibrations, Post buckling, Buckling, Smart Materials and Structures
- by Tarek A. Elgohary
- •
- Computational Mechanics, Finite Element Methods, Post buckling
- by Anis Shatnawi
- •
- Post buckling, Elliptic Integrals

The present study is concerned with the thermal postbuckling analysis of slender elastic rods subjected to different sets of boundary conditions. The governing equations are obtained by means of accurate geometrically nonlinear theory for axially extensible Euler-Bernoulli beams. The thermal strain-temperature relationship is considered nonlinear and the material is assumed to be linearly elastic, homogeneous, and isotropic. Three different combinations of clamped and hinged edge boundary conditions are considered. The boundary value problem for the nonlinear ordinary differential equations is solved effectively using the multisegment integration method. Characteristics curves showing the
relationships between the rod deformation and temperature rise are presented. The thermal postbuckled configuration and the equilibrium paths of the rod are also presented and compared for different end conditions.

This paper presents an exact mathematical model for the postbuckling of a uniformly heated slender rod with axially immovable simply supported ends on the basis of geometrically nonlinear theory of extensible rods. The material is assumed linear elastic and its thermal strain-temperature relationship is considered nonlinear. Two approaches have been used in this study. The first approach is based on the extensible elastica theory. The governing equations are derived and solved analytically for the exact closed form solutions that include the equilibrium configurations of the rod, equilibrium paths, and temperature gradients. The exact solutions take the form of elliptic integrals of the first and second kinds. In the second approach, the multisegment integration technique is employed to solve a set of nonlinear differential equations with the associated boundary conditions. The equations are integrated by using the Runge-Kutta algorithm. A comparison study between the analytical elliptic integral solutions and the numerical multisegment integration technique solutions show excellent agreement of results. Special features of the solutions in the form of determination of buckling temperature, effects of slenderness ratio and nonlinear strain-temperature coefficients on the buckling and postbuckling behavior as a function of temperature are also discussed extensively.

This paper work aims to present analytical and numerical analysis, linear and nonlinear buckling and post buckling behaviour of piles fully embedded in ground. In the first step, we have used the Galerkin's Method for linear buckling and nonlinear post buckling analysis of piles with linear-elastic material behaviour. Then is continued with numerical buckling and post buckling analysis of the piles with nonlinear elasto-plastic material behaviour. For this, the Riks Method is used. Numerical analysis was performed in software Abaqus 6.13. This paper finally shows that the post buckling behaviour of the pile with ideal load stiffness increase after bifurcation point.

- by IAEME Publication
- •
- Nonlinear Analysis, Piles, Post buckling, Buckling

En este trabajo se estudian estructuras de arcos, realizando
un análisis no lineal para determinar la carga crítica
de pandeo y el comportamiento carga-desplazamiento
post-pandeo de la estructura, realizando un LBA (Linear
Buckling Analysis) y un NLBA (Non Linear Buckling
Analysis). Además se estudia la sensibilidad a imperfecciones
geométricas de la estructura. Éste análisis se realiza
con la implementación de elementos finitos corotacionales
como extensión del programa ArchFEM, validando
la herramienta desarrollada con ejemplos simples. Se analizan
arcos de curvatura constante y los resultados obtenidos
son comparados con varios autores.

- by Mihdí Caballero
- •
- Structural Engineering, Nonlinear Analysis, Post buckling, Buckling Analysis

Fiber Reinforced Polymer (FRP) strengthening of structures has been gaining increasing interest, traditionally in application with concrete structures, and more recently in application with
steel structures. Because of their unique blend of properties, composites reinforced with high performance fibers find use in many structural applications. This paper defines the effect of FRP layers on behaviour of steel plate. In this regard, some models are selected and tested by rigid frame
and actuator. The experimental model is connected to a rigid frame.
The FRP layer acts similar to a lateral support for the steel plate, and possesses the intelligent behavior (specified control for establishing of flexural line and further leaning towards post buckling condition), meaning that the FRP layer can lead the local flexural deflection towards the total flexure
of the steel plate and effectively contributes more in resisting the shear stresses and extension of post flexure lines in steel plate and formation of composite plate. This is due to involvement of more area of steel plate to resisting of the imposed stresses. Result shows, the FRP layers would increase the stiffness, energy absorption, shear capacity and will be decreasing the ductility of steel plate as compared with composited steel plate with other materials as reinforcement concrete.

- by Alireza Rahai and +1
- •
- Post buckling, Steel Plate Shear Wall, Composite Plates, FRP layer

The strength of a web-core steel sandwich plate is potentially reduced in a corrosive environment. This study is dedicated to the influence of a reduction in the thickness of the plates as a result of general corrosion on sandwich plate buckling strength and first-fibre failure. Two scenarios are investigated in which corrosion reduces the thickness of (a) the outer sides of the face plates and (b) all surfaces, including the core. The laser weld between the face sheets and the core is assumed to be intact. The assumptions are made on the basis of earlier experimental findings. Critical buckling and geometric non-linear analysis are carried out with the finite element method, with the kinematics being represented using two approaches: (1) equivalent single-layer with first-order shear deformation theory, and (2) a three-dimensional model of the actual geometry of the structure, modelled using shell and connector elements. The former is used to identify the effect of corrosion on the stiffness coefficients and, consequently, the buckling strength. The latter is used for verification and for stress prediction during post-buckling. A rapid decrease in the buckling strength was found for corrosion affecting the outer sides of the sandwich plate. The decrease in the buckling strength doubled in the case of the diffusion of moisture (water) into the core. The shear-induced secondary bending of the faces was found to affect the first-fibre yield.

In this article, both thermal buckling and postbuckling of pinned-fixed bar subjected to transverse non-uniform temperature rise have been investigated. Based on the accurate geometrically nonlinear theory for Euler-Bernoulli beams, considering both linear and nonlinear strain-temperature relationships, governing equations for large deformations of the bar are derived. The two point boundary value problem for the nonlinear ordinary differential equations is solved effectively using the multisegment integration method. The numerical results show that both the critical buckling temperature and the postbuckled temperature of the bar are sensitively influenced by the slenderness ratio and nonlinear strain-temperature coefficient. It is also found that for uniform heating, the magnitude of the axially constrained force reaches a maximum value at the onset of the buckling state and then decreases as the temperature increases in the postbuckling regime. In addition, effects of non-uniform heating on the postbuckling behaviors are critically analyzed for the non-symmetric end condition.

- by Anis Shatnawi
- •
- Post buckling, Elliptic Integrals
- by Anis Shatnawi
- •
- Post buckling, Elliptic Integrals

Elastic post-buckling analysis of imperfect rectangular plates subjected to a uniform compression stress along one direction is presented. The semi-analytical finite strip method is improved by generalization of its nonlinear formulation through inclusion of various types of strips and boundary conditions. The equations of balance are derived via incremental formulation of virtual work, while the Newton-Raphson and arc-length methods are implemented into a solver. Geometric initial imperfections are modeled as a scaled buckling mode of a structure. The presented theory is verified via comparison of results with the ones from literature and Abaqus. The semi-analytical finite strip method is ideally suited for this type of analysis due to good convergence properties.

- by Sasa Kovacevic and +1
- •
- Post buckling, Finite Strip Method
- by Alexandre Galvao
- •
- Mechanical Engineering, Civil Engineering, Stability, Structural Stability
- by Ali Ghamari
- •
- Civil Engineering, Post buckling, Cyclic Loading, Composite Shear walls