Although many researchers investigated the effect of GEOMETRICAL IMPERFECTION on the buckling load of unstiffened shells, the stiffened shells have not been studied yet. In this paper, the effects of GEOMETRICAL IMPERFECTION the buckling load of unstiffened and stiffened composite shell with and without cutout are investigated. For this goal, several specimens are manufactured and tested. The mechanical properties of fibers and resin matrix and volume fraction of fibers in the shell and the stiffeners are determined based on the standard tests. Finally, the mechanical properties of each component are calculated by micromechanical relations. These properties are used for finite element modeling by ABAQUS package. Linear eigenvalue analysis and nonlinear RIKS method -which can consider the GEOMETRICAL IMPERFECTION- are used. FE results are validated in comparison with experimental tests. Using FE model, the effects of IMPERFECTION amplitude on the buckling behavior of unstiffened and stiffened shell with and without cutout are studied. The results show that GEOMETRICAL IMPERFECTIONs have more effect on the buckling load of unstiffened shells in comparison with stiffened ones. Nevertheless, ignoring these IMPERFECTIONs and using eigenvalue analysis overestimates the buckling load. This fact is further evidence for shells without an opening. In perforated shells, the cutout itself represents an IMPERFECTION that is much more significant than geometric IMPERFECTIONs.

When a cylindrical shell subject to a compressive load, because of various IMPERFECTIONs happened during processes as manufacturing, handling, assembling and machining, buckling occurs in loads lower than corresponding static failure load. Still many of cylindrical shell structures are designed against buckling based on experimental data introduced by NASA SP-8007 as conservative lower bound curves. In the manuscript, non-linear methods of Modified Linear Buckling Modeshaped IMPERFECTIONs (M-LBMI) and Single Perturbation Load IMPERFECTIONs (SPLI) for composite cylindrical shell with and without cutout are investigated. In order to evaluate the numerical results composite cylinder with stacking sequence of [90/+23/-23/90] are manufactured by using filament winding method and buckling tests are performed under axial loading. Non-linear numerical results in cylinder with and without cutout are close together and have good agreement with experimental data. It was concluded that buckling load predicted by SPLI and modified LBMI method on cylinder with cutout is close to result of case without apply geometric IMPERFECTIONs. In summary, it was concluded that cutout on the cylinder body act as an IMPERFECTION to trigger buckling of the structures so there is no need to apply GEOMETRICAL IMPERFECTIONs.

One of the common failure modes of thin cylindrical shell subjected external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the GEOMETRICAL IMPERFECTIONs present in the cylindrical shell which are very difficult to alleviate during manufacturing process. In this work, only three types of GEOMETRICAL IMPERFECTION patterns are considered namely (a) eigen affine mode IMPERFECTION pattern, (b) inward half lobe axisymmetric IMPERFECTION pattern extended throughout the height of the cylindrical shell and (c) local GEOMETRICAL IMPERFECTION patterns such as inward dimple with varying wave lengths located at the mid-height of the cylindrical shell. ANSYS FE non-linear buckling analysis including both material and GEOMETRICAL non-linearities is used to determine the critical buckling pressure. From the analysis it is found that when the maximum amplitude of IMPERFECTIONs is 1t, the eigen affine IMPERFECTION pattern gives out the lowest critical buckling pressure when compared to the other IMPERFECTION patterns considered When the amplitude of IMPERFECTIONs is above 1t, the inner half lobe axisymmetric IMPERFECTION pattern gives out the lowest critical buckling pressure when compared to the other IMPERFECTION patterns considered.

Thin wall shell structure has low weight and high resistance. The load capacity, buckling behavior and post buckling behavior of steel tanks thin wall, is very sensitive to geometric IMPERFECTIONs. Due to the small wall thickness of the shell structures enabling the creation of any deformation and there is a disturbance on the surface of the wall. Considering the types of errors occurred when build or assembled these structures, are not built these structure, ideally.This IMPERFECTIONs may be in the process of rolling, removable panels, installation or welding arise. Incomplete reports about the negative impact of the effect of welding on the axial bearing capacity.Comprehensive research on the effects of IMPERFECTION of initial GEOMETRICAL shape on the steel tank vibration modes, and its effect on the bearing capacity steel storage tanks that considerable research It's not done. In this research, the actual behavior of cylindrical shells with initial geometric IMPERFECTIONs on mode shapes steel tanks in the pre-buckling and post-buckling. And the effect of initial geometric IMPERFECTIONs on steel tanks slashing been paid. Using finite element software, ABAQUS, and verification of the results of the analysis and nonlinear analysis with experimental results. Been paid. Imperfect geometric shape has changed mods. The effect of these changes on slashing are very small.

Buckling analysis of rectangular functionally graded plates with GEOMETRICAL IMPERFECTIONs is studied in this paper the equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first order shear deformation theory. It is assumed that the non-homogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive load. Resulting equations are employed to obtain the closed-form solutions for the critical buckling load of an imperfect functionally graded plate. The influence of transverse shear on buckling behavior of the plate is discussed. The results are validated with the known data in the literature.

In this study, the effect of material IMPERFECTION on the free vibration response of perfect and imperfect FG plate is studied. A new hyperbolic shear deformation function is presented in this paper. The new hyperbolic function is chosen in such a way that the degree of the function is reduced as much as possible, despite the sufficient accuracy, so that the calculation speed is greatly reduced. The properties of the FG plate varied along the thickness according to power law. The material composition in production process cannot be completely in accordance with the expected pattern, which leads to the production of imperfect FG material. The governing differential equations are derived using the Hamilton’s principle. The obtained equations were solved using the Navier method with simple boundary conditions. The effects of important geometric and mechanical parameters of perfect model and two types of imperfect model, including length to thickness ratio, length to width ratio, wave number and power-law exponent on natural frequency response of imperfect FG plate are investigated. To verification, the analytical results obtained in this study are compared with the results presented in the literature, and in this comparison, a good agreement was obtained, which shows the correctness theory, deriving and solving equations.

This article presents the study of wave mechanics in a multiferroic structure having IMPERFECTION in the structure’s interface. This article reflects the study of shear horizontal (SH) wave propagation in a layered cylindrical structure consisting of thin layers of different materials (reinforced material and piezomagnetic material) with an imperfect interface. The interface considered between both materials is mechanically imperfect. Dispersion relations are achieved analytically. Distinct graphs are drawn (numerically) to exhibit the influence of parameters like rotation, initial stress, and mechanically imperfect parameters on phase velocity. Numerical results are drawn analytically and explained for each affecting distinct parameters for materials and interface. Parametric results on the phase velocities yield a significant conclusion of which some are: (a) Performance of Piezo with reinforcement material have an influential impact on wave velocity. (b) The mechanical IMPERFECTION affects the significantly on wave velocity (c) The Reinforcement/PM stiffening can monotonically up the velocity of phase velocity.

1. Introduction:Free forms are usually used to refer double curve surfaces which are independent from groups of GEOMETRICALly or mechanically constrained forms. GEOMETRICALly constrained forms are only conditioned by a GEOMETRICAL definition, like it could be done on basis of simple surfaces. When there is a close relationship between forms and forces, the forms are mechanically constrained [1]. In the present study, behavior of double domes free form single layer space structures as a group of free form structures are investigated. Gaussian curvature of double domes can be positive and negative, unlike regular domes. In single layer reticulated space structures, local instability with nodal snap-through phenomenon could result in propagation in whole structure [2], so stability behavior of double domes free form single layer space structures should be investigated. The parametric study is performed in order to evaluate the effects of different variables on the stability behavior of double domes free form space structures.

In this study, based on the third-order shear deformation theory the equations of motion are obtained to analyze the deformation of a long and slender composite beam. The beam has initial geometric IMPERFECTION and is subjected to impact load. The impact procedures are applied by rigid body with a specific speed, off-center and at a certain distance from the beam's surface. Hamilton’s principle and the von-Karman nonlinear strain-displacement relationship are used to obtain the equations of motion that are based on displacement and in a set of coupled nonlinear partial differential equations in dynamic mode. The generalized differential quadrature Method (GDQM) is used to discretize the obtained equations and convert them into a set of ordinary differential equations. Newton-Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Then, by solving the equations of the system, the effects of initial geometric IMPERFECTION on the beam’s deflection have been studied. Also, the effects of mass and the initial velocity of the impactor on the beam’s deformation are investigated. The results of this research show that an increase in the amount of the initial velocity and mass of the impactor entail an increase in the beam deformation.