Post 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.

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.

The objective of this article is to analytically investigate the free vibration of shape memory alloy hybrid composite (SMAHC) beams in thermally pre/post-buckled domains. Non-linear equations of motion of SMAHC beams are derived based on the first-order shear deformation theory and von Karman geometrical non-linearity via the extended Hamilton principle. The recovery stress generated by temperature-induced martensitic phase transformation of the pre-strained SMA fibers is computed by means of the Brinson model. Exact closed-form solutions are presented for the buckling temperature, post-buckling deformation and temperature-deformation equilibrium path of symmetric and asymmetric simply supported SMAHC beams under uniform temperature rise. The vibration of the symmetric SMAHC beam around the first buckled configuration is also investigated and an analytical solution for the fundamental frequency and its associated mode shape is obtained. Based on the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of SMA fibers volume fraction, pre-strain in the SMA fibers, location of SMA fibers, temperature rise and geometrical parameters on the static and dynamic responses of the SMAHC beams in the thermally pre/post-buckling regimes. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem.

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.

In this paper, a detailed analysis is conducted to study the influence of the geometric parameters, boundary conditions as well as initial imperfections on the nonlinear response and imperfection sensitivity of L-frames. An efficient nonlinear finite element formulation for the analysis of planar elastic frames is used together with incrementaliterative strategies. This enables one to obtain the highly nonlinear equilibrium paths exhibited by L-frames under certain loading conditions and identify the bifurcation and limit points along these equilibrium paths. These results provide some insight as to the source and mechanism of asymmetric bifurcation and imperfection sensitivity in frames thus helping engineers to evaluate the importance of geometric nonlinearities in the analysis and design of slender elastic frames.

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.

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.