In this work, the nonlinear BUCKLING and POST-BUCKLING behavior of shallow arches made of Shape Memory Alloy (SMA) is investigated. Arches are susceptible to large deflections, due to their slenderness, especially when the external load exceeds the serviceability limit point. Beyond this, loss of stability may occur, the famous snap-through BUCKLING. For this reason, curved beams can be used in passive vibration control devices for seismic response mitigation, and the geometrically nonlinear analysis is needed for the accurate prediction of their response. Thus, in this research effort, the assumptions of the Euler-Bernoulli beam theory are considered, and the Von Karman strain field is employed to account for large deflections. The formulation of the problem is displacement-based regarding the axial (tangential) and transverse (normal) displacements, while the two governing equations are coupled and nonlinear. In order to introduce the SMA constitutive law, the stress-strain experimental curves described in the literature are employed together with a fiber approach at specific control cross-sections along the beam. The numerical solution of the longitudinal problem is achieved using the Analog Equation Method (AEM), a Boundary Element Method (BEM) based technique, and the iterative procedure is based on a Newton-Raphson scheme by using a displacement control algorithm to trace the fully nonlinear equilibrium path and overcome the limit points. Several representative examples are studied, not only to validate the proposed model but also to investigate the nonlinear BUCKLING and POST-BUCKLING of SMA shallow arches.

BUCKLING and POST BUCKLING of cylindrical shells under hydrostatic pressure is regarded as important issue in structure of submarines. These cylindrical shells have variable thickness due to construction process which effected by pressure of BUCKLING and its destruction. In this paper, effects of changing thickness on BUCKLING and destruction pressure under external hydrostatic pressure of a shell are studied. Results of BUCKLING pressure of cylindrical shell have been obtained with theoretical relations and finite element method. Then, using machining process a sample of cylindrical shell with variable thickness has been produced. BUCKLING pressure and POST BUCKLING of the constructed sample have been obtained with the reservoir under closed-ended hydrostatic pressure. Changes of the test sample size have been considered with closed-ended testing apparatuses which are used for new evaluation of BUCKLING. In this research, results of the pressure have been obtained in terms of the volume change. At the end, results of the finite element method have been compared with results of the analytical solutions and experimental data. Results show that the shell with variable thickness has BUCKLING pressure close to shell bucking pressure with mean thickness.

In this paper the behaviour of steel frames is investigated under an applicable range of initial rotational geometric imperfection in joints, which are mostly created during the manufacturing process. A nonlinear analysis is applied in both geometry and material behaviour of steel frames. The results show considerable reduction in BUCKLING and ultimate load carrying capacity of portal frames, when they are affected by a rotational imperfection.

The POST-BUCKLING behavior of rectangular frames in elastic domain is studied in depth. In analysis, unsymmetrical geometry, sway possibility and support conditions are considered in order to find their influences on load- deflection path and non-linear deformations. The static perturbation technique is used for analysis and discussion. The first, second and third order perturbation problem, as an accuracy measurement, for the frame are solved and the solutions are compared with previously published papers. The results reveal that the symmetric frame with sway movement, due to non-axial force in beam, has symmetric bifurcation point in the first order perturbation analysis. However, the POST-BUCKLING behavior of un-symmetric frames with or without sway is bifurcated in an asymmetric manner.        

This paper presents the theoretical developments of two finite strip methods, i.e. semi-analytical and full-analytical for the POST-BUCKLING analysis of isotropic plates In the semi-analytical finite strip approach all the displacements are POSTulated by the appropriate shape functions while in the development process of the full-analytical approach the Von-Karman's equilibrium equation is solved exactly to obtain the BUCKLING loads and the out-of-plane BUCKLING deflection modes The investigation of the plates-BUCKLING behaviour is then extended to the POST-BUCKLING study with the assumption that the deflected form after the BUCKLING is a combination of the first second and higher (if required) modes of BUCKLING Thus the full-analytical POST-BUCKLING study is an effective multi term analysis In this method the Von-Karman's compatibility equation is used together with a consideration of the total strain energy of the strut Through the solution of the compatibility equation, the in-plane displacement functions, which are themselves related to the Airy stress function, are developed in terms of the unknown coefficients in the assumed out-of-plane deflection function The in-plane and out-of-plane deflection functions are substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficients.

The effect of central opening on the BUCKLING and nonlinear POST-BUCKLING response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on BUCKLING and POST-BUCKLING behavior are analyzed. In order to derive the basic formulations of plate the Mindlin plate theory is applied. Furthermore, nonlocal elasticity theory is applied to consider the size-dependent effect. Analytical approach and Newton-Raphson iterative technique are utilized to calculate the impact of cut out on the BUCKLING and nonlinear POST-BUCKLING response of micro composite plate. The variation of BUCKLING and POST-BUCKLING of micro composite cut out plate based on some significant parameters such as volume fraction of CNTs, small scale parameter, aspect ratio, square cut out and elastic medium were discussed in details. According to the results, it is concluded that the aspect ratio and length of square cut out have negative effect on BUCKLING and POST-BUCKLING response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the BUCKLING and POST-BUCKLING behavior of plate. Meanwhile, considering elastic medium increases the BUCKLING and POST-BUCKLING load of system.

This paper presents a novel scheme for large deformation analysis of space truss structures, including both geometric and material nonlinearities, using a predictor-corrector procedure, titled as fixed incremental displacement (FID) method. The nonlinear equilibrium equations are solved using an incremental-iterative method based on the displacement control scheme, as, by employing a specified displacement, the corresponding load will be obtained. In the present method, the ratio of the size of increment displacement vector to that of total displacement is assumed to be constant at the beginning of each increment. The geometric nonlinearity is considered based on an updated Lagrangian formulation, while the material nonlinearity is accounted for by tracing a complete stress-strain relationship. A computer program based on the algorithm is developed for analysis of space structures with complex behaviors, including snap-through BUCKLING, snap-back, unloading and inelastic POSTBUCKLING analysis. This algorithm can accurately trace the equilibrium path of nonlinear problems. To demonstrate the efficiency and accuracy of the method developed here, some well-known trusses are investigated and analyzed using the aforementioned algorithm and the results are compared with those of cylindrical arc-length method.