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In this paper, an approximate solution using layer-wise theory for the vibration analysis of rotating laminated cylindrical shells with ring and stringer stiffeners under axial load and pressure is presented. The cylindrical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties and cylindrical shell reinforced by outer stiffeners while stiffeners are treated as discrete elements. The equations of motion are derived by the Hamilton’s principle. In deriving the governing equations three-dimensional elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial hoop tension. The layer-wise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. The edges of the shell are restrained by simply supported boundary conditions. The presented results are compared with those available in the literature and also with the FE results and excellent agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffened cylindrical shell and different geometry of stiffeners, stiffener type, rotating velocities, amplitude of pressure and amplitude of axial load.

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In this paper, simulation and analysis of thin steel cylindrical shells of various lengths and diameters and thickness with triangular cutouts have been studied. In this research buckling and post-buckling analyses were carried out using the finite element method by ABAQUS software. Moreover, the effect of cutout position and the length-to-diameter (L/D) and diameter-to-thickness (D/t) ratios on the buckling and post-buckling behavior of cylindrical shells have been investigated. In this work the cylindrical shells used for this study were made of mild steel and their mechanical properties were determined using servo hydraulic machine. Then buckling tests were performed using a servo hydraulic machine. In order to numerical analyze the buckling subject to axial load similar to what was done in the experiments; a displacement was applied to the center of the upper of the specimens. The results of experimental tests were compared to the results of the finite element method. A very good correlation was observed between numerical simulation and experimental result.

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In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the vibration of a Functionally Graded Material (FGM) cylindrical shell. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to different volume fraction functions. A FGM cylindrical shell made up of a mixture of ceramic and metal is considered herein. The set of governing equations of motion are numerically solved by the Meshless method in which a new variational trial-functional is constructed to derive the stiffness and mass matrices so the natural frequencies are obtained in various boundary conditions by using discretization procedure and solving the general eigenvalue problem. The influences of some commonly used boundary conditions, variations of volume fractions and effects of shell geometrical parameters are studied. The results show the convergence characteristics and accuracy of the mentioned method.

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In this paper, the free vibration of a two-dimensional functionally graded circular cylindrical shell is analyzed.To describe the material properties of the two-phased FGM material Mori–Tanaka micromechanical model is used. The spatial derivatives of the equations of motion and boundary conditions are discretized using the methods of generalized differential – Integral quadrature (GDIQ). To validate the results, comparisons are made with the solutions for FG cylindrical shells available in the literature. The results of this study show that the values of natural frequency of 2D FGMs are higher than those of 1D FGMs in parallel conditions. Furthermore, application of a confining elastic foundation increases the value of natural frequencies. The results of this study show that the values of natural frequency of 2D FGMs are higher than those of 1D FGMs in parallel conditions. Furthermore, application of a confining elastic foundation increases the value of natural frequencies. The results of this study show that the values of natural frequency of 2D FGMs are higher than those of 1D FGMs in parallel conditions. Furthermore, application of a confining elastic foundation increases the value of natural frequencies.

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In this paper, ratcheting behavior of stainless steel 304L cylindrical shells under cyclic combined and axial loadings are studied, experimentally. Tests were performed by a servo-hydraulic INSTRON 8802 machine and the shells were fixed normal and oblique under 20 degree and subjected to cyclic loads. In this paper, the effect of length of cylindrical shell and the effect of angle of cylindrical shell on ratcheting behavior were investigated. Based on the experimental results, it was found that bending moment plays a crucial role in waste of energy and increase in plastic deformations. Seen that due to the existence of bending moment in different cross section of oblique cylindrical shell, there are more plastic deformation and accumulation in comparison to normal cylindrical shell. Also, analyzing the loading history of cylindrical shell under combined loading, it has been seen that by keeping the mean force at constant value while increasing the force amplitude, the ratcheting displacement became higher and by the prior load with higher force amplitude retards the ratcheting behavior and plastic deformation with samller force amplitude.

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In order to analyze fatigue life of reinforced cylindrical shells, it is necessary to calculate stress and strain fields of the structure. The cost of three dimensional stress analysis of this structure is very high with respect to its geometric complexity. So the stress analysis of the problem is performed by shell-to-solid sub-modeling technique. For this purpose, the reinforced cylindrical shell is modeled using shell elements at first, which in this case all the bolts, rivets and spot welds are considered as bushing elements. Afterwards the candidate critical zones are modeled using 3D solid elements with the help of shell-to-solid sub-modeling technique and all the connections are also modeled using 3D elements. Then the fatigue life of the problem under multi-axial loading is estimated by Brown-Miller criterion. For this purpose a special script in ABAQUS software has been used.

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In this paper, buckling and energy absorption behavior of stainless steel semi-sphere, cylindrical and conical shells under axial loading are studied. Every shell with the same mass and different shapes with and without groove is designed. In this paper the effect of shape, thickness, height, groove of shells and distance between grooves, on buckling and energy absorption were investigated. In experimental test, Samples had same mass and thickness and also grooves had same depth and distance. Experimental tests were performed by a servo-hydraulic INSTRON 8802 machine. Numerical analysis is carried out by ABAQUS software and is validated with experimental results.

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The objective of this paper is representation an analytical solution to calculate sound transmission loss (TL) of infinite thick transverse-isotropic cylindrical shell immersed in a fluid medium with an uniform external airflow and contains internal fluids where external sidewall of the shell excited by an oblique plane wave. In order to derive the governing equations the third-order shear deformation theory (TSDT) is used. Also, equation of motion of shell is obtained using Hamilton's principle. With solving shell vibration equations and acoustic wave equations simultaneously, the exact solution for TL is obtained. Transmission loss resultant from this solution is compared with those of other authors. The results also indicate that TSDT is more powerful than FSDT and CST, especially in high frequency and less R/h.

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In this paper, the thermoelastic behavior of cylindrical sandwich shell with functionally graded (FGM) core under thermal shock is presented. Thermo mechanical properties of FGM layer are assumed to be independent of temperature and also, very continuously and smoothly functions in the radial direction as a nonlinear power function. The analytical solutions of governing partial differential equations for each layer of cylinder are solved by using Laplace transform and power series method. Mechanical boundary conditions and continuity equations for interfaces are used to obtain unknown parameters that get in recurrence equations for each layer of cylinder. The results in Laplace domain transferred to time domain by employing the fast inverse Laplace transform method (FLIT).The effects of FGM’s power on the dynamic characteristics of the FG thick sandwich cylindrical shell are studied in various points across the thickness of cylinder. The analytical presented method provides an appropriate field for analysis of transient radial and hoop stresses in a cylinder on various thermo mechanical load. Accuracy of gained equations is evaluated by similar articles. The results have a good agreement with published data in pervious researches.

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Bolt joints play an important role in the industries, so the estimation of fatigue life of bolts is an essential task. The aim of present study is estimation of fatigue life of connection bolts of two flanges in reinforced cylindrical shell with cutout. Two groups of data are needed for mentioned bolt: fatigue properties of bolt and value of stress of bolt due to applying load to structure. So, two paths have been gone. First, the fatigue properties of bolt have been measured in laboratory according to ISO 3800 standard. For this purpose a specific fixture was designed and manufactured which provided testing different bolts. By doing fatigue experiments, the fatigue properties of mentioned bolt such as fatigue limit and Basquin’s equation constants (fatigue strength coefficient and fatigue strength exponent) have been measured. Fracture mechanism and fracture surface have been investigated, too. Afterward, in the next step the value of stress in bolt that is subjected to mix loading has been calculated by using of FE modeling. Because of problem complexities, cost of three dimensional analysis of this problem increases, so analysis of the problem has been performed by shell-to-solid sub-modeling technique. At the end, by calculating the nominal stress of bolt from FE modeling and using fatigue properties witch obtained from experiments, life of the mentioned bolt has been estimated.

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In this research, a Mach reflection and its effect on explosive free forming of confined cylindrical shells are studied numerically. This shells were manufactured from extruded 6063-T5 Aluminum alloy. The diameter of shell was 1.5 times larger than its length. Its ends were sealed with rigid sheets. The simulation of formation of Mach reflection and plastic response of shell were done with Autodyn hydrocode and coupled Lagrangian - Eulrian spatial discretization. Formation of Mach reflection occurred on end plates. It is observed that the generated pressure in an area that is affected by Mach stem is higher than elsewhere. This phenomena causes rupture in boundaries area of shell to plate connections, before forming process. The maximum of transverse deformation that obtained from this study compared with experimental results which done in explosion mechanic laboratory in K. N. Toosi university of technology. The experimental and numerical results shows more than 93% agreement. Meanwhile, because of blast waves reflection and interaction of waves, coupled Lagrangian - Eulrian method is suitable method for investigation of internal explosion problems. In addition failure modes was simulated with finite element software Abaqus and good agreement was found between the results.

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In this article, an analytical procedure is presented for prediction of linear buckling load of a waffle cylinder stiffened by an array of equilateral triangles. The grid stiffened shell is subjected to axial loading condition. The shell has simply supported boundary conditions at its two edges. The equivalent stiffness of the stiffener and skin is computed by superimposing between the stiffness contributions of the stiffeners and skin with a new method. Total stiffness matrix of the shell is composed of stiffness matrix of skin and grids with special volume fractions. In this analysis, using energy method, equilibrium equations of the grid stiffened shell are extracted based on the thin shell theory of Flugge. The Navier solution is applied to solve the problem. A 3-D finite element model was also built in ANSYS software to show the accuracy and validity of the present solution. The results show that the present new approach has high accuracy and precision. The effect of various geometrical parameters on the critical buckling load is investigated. Due to the stability and accuracy, the present method can be used by many designers and engineers to improve their design quality.

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In this research, accumulation of plastic strain and softening behavior of stainless steel SS316L cylindrical shell under cyclic bending and combined loads (bending-torsion) are studied. Cyclic bending was under force-control and displacement-control but Combined loading was under displacement-control. Experimental tests were performed using an INSTRON 8802 servo-hydraulic machine. Under force-control loading with non-zero mean force, plastic strain was accumulated in continuous cycles that it was called ratcheting. Based on experimental results, linear relation was observed between plastic energy and rate of plastic deformation that shows the rigidity of fixtures using in experimental tests. Under displacement-control loading, softening behavior was observed due to growth of ovalization and the rate of softening became higher by using of the higher displacement amplitude. The crack growth up to failure is oblique in combined load due to torsion and bending loads whereas the crack growth is peripheral in bending load. The numerical analysis was carried out by ABAQUS software and nonlinear isotropic/kinematic hardening was compared with isotropic hardening and observed the nonlinear isotropic /kinematic hardening model simulates the softening behavior and accumulation of plastic strain of cylindrical shells under cyclic bending accurately.

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This study deals with thermo-elasto-plastic behaviour of functionally graded thick-walled cylinder that is exposed to internal pressure and temperature gradient. For this purpose, Von-Mises yield criterion and Prandtl-Reuss flow-rule under state of plane strain are utilized. The modulus of elasticity, the thermal conductivity and thermal expansion coefficients are assumed to obey the power function in the radial position according to Erdogan’s model. In this work, the presented approach leads to the definition of new formulation to determine the elastic limit pressure and predict the onset radius of yielding, spread and growth of plastic zone. The governing equilibrium equation of cylindrical shell in axi-symmetrical status is solved in order to determine the distribution of radial, circumferential stresses and radial displacement. Various examples are handled to investigate the effect of FG-power law parameters on the yield pattern and distribution of plastic zone. The distribution of radial displacement, radial and circumferential stresses are expressed as the functions of radial position. The numerical results show that by the appropriate choice of the FG parameters and the specified thermal gradient, the plastic zone can commence simultaneously from inside and outside or intermediate radius.

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In this paper, free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells surrounded by elastic foundation and subjected to uniform temperature rise loading is investigated. The material properties of FG-CNTRC are assumed to be graded through the thickness direction. Two kinds of carbon nanotube reinforced composites including uniformly distributed (UD) and functionally graded (FG) are considered. The elastic foundation is modeled by two-parameter Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effect of thermal loading is considered as a initial stress. Applying the Hamilton’s principle based on first-order shear deformation theory and considering Sanders and Donnell strain-displacement relation, the governing equations are obtained. Using the generalized differential quadrature method in axial direction and periodic differential matrix operators in circumferential direction, the equilibrium equations are discretized. The results are compared with those presented in literature. In addition, the effect of various parameters such as thermal loading, boundary conditions, elastic foundation and different geometrical conditions are studied. The results show that increase in the elastic foundation coefficients and initial thermal loading increase and decrease the non-dimensional fundamental frequency, respectively.

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The instability behavior of stiffened cylindrical shells and determination of the corresponding buckling loads under axial compression, according to the extended range of structural applications of them in various fields of engineering, has been paid a lot of attention from researchers and extensive amount of studies have been performed on it so far. Because of a lack of the general closed form responses due to complexity of the governing equations and analyses process, using the FE software codes as the main technique of the stiffened shell's buckling load determination is inevitable. Accordingly the present paper has been studied the reinforcement effects of ring and stringer and also compared the buckling loads which are evaluated by analysis of the FE numerical modeling in ABAQUS software with instability results that obtained from a general analytical equation derived by other references via applying the simplifying assumptions to the governing equations. Furthermore an attempt has been performed for extraction of the finite element instability load vs. structure reinforcement correspondence that enables the designers to accurately determine the instability load of structure for other values of structure's stiffening volume without performing additional FE analyses which are much more expensive in term of computer time.

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The objective of this paper is to analyze the nonlinear vibrations of simply supported pseudoelastic shape memory alloy (SMA) cylindrical shell under harmonic internal pressure based on Donnell-type classical deformation shell theory. The pressure is a function of time and space. The behavior of pseudoelastic SMA is simulated via the Boyd–Lagoudas constitutive model numerically implemented by the Convex Cutting Plane Mapping algorithm. The Hamilton’s principle is employed to obtain the equations of motion. Differential Quadrature Method (DQM) and Newmark time integration scheme are applied to get the time and frequency responses of the cylinder. Also, the natural frequencies of the shell are obtained for the case of pure austenitic phase to compare the frequency response of the present nonlinear system (phase transformation –induced material nonlinearity) with the linear one around them. Results indicate that the strength of the material will decrease during the phase transformation. This fact is proved by the softening behavior observed in the frequency response of the system due to the phase transformation. Further, the pure austenitic phase shell is simulated in ABAQUS to verify the results. A good agreement is found between two outcomes.

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In this paper, Taguchi statistical method is implemented in the design of energy-absorbing composite shell structures with cylindrical geometry. Six energy-absorbing structure design parameters considered in this study are: geometric parameters including internal diameter, length and thickness; the other parameters are the stacking sequence of layers, fiber reinforcement type and manufacturing process. The first three parameters and the remaining ones have four and two levels respectively. So the orthogonal array L16 (4 ** 3 2 ** 3) was used for analysis of Taguchi. The purpose of design of experiment in this study was to maximize the amount of specific energy absorbed in the structure. The result shows that the stacking sequence of layers and geometry parameter include internal diameter and thickness had an effect on the opposite side, the other parameters had Minimal effect on specific energy absorbing. The first three parameters had most important role in design of energy absorbing structures. Another important result of this analysis was to determine the optimal characteristics of composite energy absorbing shells with stacking sequence of layers (90/0), internal diameter 63 mm, thickness 2 mm, vacuum bag molding process (VB), the fiber reinforcement type carbon and the length 160 mm.

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Careful and numerical analysis eccentrically stiffened shells in the industry is a major step forward in the design of these shells. In this paper, a careful analysis of post-buckling behavior of eccentrically stiffened FGM thin circular cylindrical shells is surrounded by an elastic foundation and external pressure is presented. The two parameter elastic foundation based on Winkler and Pasternak elastic model is assumed. Stringer and ring stiffeners are internal. Shell properties and eccentrically stiffened are FGM. Fundamental relations and equilibrium equations are derived based on the smeared stiffeners technique and the classical theory of shells and according to von- Karman nonlinear equations. The three-term approximation for the deflection shape, including the pre-buckling, linear buckling shape and nonlinear buckling shape was chosen that using the Galerkin method, the critical load and post-buckling pressure-deflection curves is calculated. The effects of different dimensional parameters, buckling modes, volume fraction index and number of stiffeners are investigated. Numerical results show that stiffeners and elastic foundation enhance the stability of the shells. Increasing the shell thickness, reducing the volume fraction index, raising the number of Stringer and ring stiffeners and applying foundation elastic, causes the critical buckling load is increased, too.

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In this paper a method has been developed to obtain an optimum material distribution for a cylindrical shell with Functionally Graded (FG) material and additional piezoelectric outer layer. The objective of the optimization is to satisfy full stress loading criterion. For this purpose; firstly, a solution method has been outlined in which, the governing equations are developrd by combining First order Shear Deformation Theory (FSDT) and Maxwell equations, with the use of Hamilton principle. Dynamic analysis is a major concern in this solution method because of the significant dynamic displacements, strains and stresses due to the effect of moving load. Hence, the time dependent transient responses of the structure and stress distribution have been obtained. At the next stage, a methodology has been introduced to obtain the optimum material distribution. In this method, instead of using pre-assumed material distribution functions which impose limitations to the manufacturing of the shell and also to the optimization solution, control points with Hermite functions are used. The thickness of the shell and volume fraction of the FG material at these points have been regarded as optimization variables. The optimization method is based on the genetic algorithm and to reduce the solution time, calculations are carried out using parallel processing in four cores. The results show that the developed method is capable of analyzing the FG structures and provide optimum solution. The major advantage of this method is its flexibility in providing volume fraction distribution of the material.