In the present research, an internal semi-elliptical surface crack in a FGM thick-walled Cylindrical vessel under internal pressure is assumed. The Poisson ratio is constant throughout the vessel and the material is considered to be isotropic with exponentially varying elastic modulus. The KI is calculated using the BEM and FEM for different values of the relative depths of crack and material gradients. The research results show that increasing the E2 /E 1, decreases SIF and when E 2 /E 1=10, the SIF of the FGM vessel is often lower than the corresponding homogeneous vessel. It can be observed that the relation between KI and internal pressure in FGM is linear as for homogeneous materials, so that increasing internal pressure KI increase as the same. The obtained results of BEM and FEM methods show that good agreement between the results can be seen.

In this paper, transient heat transfer analysis in composite metal Cylindrical vessel will be investigated using the layerwise theory and differential quadrature method. For this purpose, five samples from the metallic Cylindrical vessel and composite metal Cylindrical vessel has been under transient heat transfer analysis. Thermal conditions of governing the issue has been extracted from a practical and experimental conditions. The aim of this research is study and investigate the behavior of heat transfer in the vessels mentioned. Therefore, the governing equations of heat transfer is achieved in a multilayered Cylindrical vessel. Due to the different behavior of multilayer Cylindrical in heat transfer, the analysis is to be done using the layerwise theory in order to obtain more accuracy. Then, the governing equations of heat transfer are derived for this vessel and are solved by differential quadrature method. In differential quadrature method, to solve the governing relations, these equations must be in the form of the matrix equations. The MATLAB programming code to be used to solve this matrix equations. After extracting result, temperature changes and heat transfer behavior in multilayer Cylindrical vessel versus time have been discussed. To validate the resulting solution of the layerwise theory and differential quadrature method, modeling and numerical analysis of heat transfer in Abaqus finite element software done and the results of this software were compared with the solution of differential quadrature. Finally, the results of this study have been compared with exact solution of heat transfer equations in the several reference.

In this paper, numerical and analytical solutions of composite metal Cylindrical vessel are investigated under dynamic load using first-order shear deformation theory and differential quadrature method. For this purpose, the shell equilibrium equations are derived based on the first order shear deformation theory. The load applied to the shell is achieved from the experimental test of a double-base propellant, and then is applied to the model in numerical and theoretical analysis. The aim of this paper is to study and investigate the behavior of the composite metal Cylindrical vessel under dynamic load with first order shear deformation theory and compare its results with the numerical solution. Therefore, after extracting the shell equilibrium equations are used from differential quadrature method to solve the equations. Then, the governing equations are extracted in a composite metal Cylindrical vessel to form the matrix equations to solve with differential quadrature method. To apply boundary conditions from simply supported and clamped are considered and the results of these two modes are compared together.The MATLAB programming code is used to solve differential quadrature equations. To validate theoretical results, modeling and numerical analysis are done by Abaqus finite element software and the results are compared with the analytical solution using the differential quadrature method.

In this paper, a numerical analysis of stresses and displacements in FGM thick-walled Cylindrical pressure vessel under internal pressure has been presented. The elastic modulus is assumed to be varying along the longitude of the pressure vessel with an exponential function continuously. The Poisson’s ratio is assumed to be constant. Whereas most of the previous studies about FGM thick-walled pressure vessels are on the basis of changing material properties along the radial direction, in this research, elastic analysis of Cylindrical pressure vessel with exponential variations of elastic modulus along the longitudinal direction, under internal pressure, have been investigated. For the analysis of the vessel, the stiffness matrix of the Cylindrical pressure vessel has been extracted by the usage of Galerkin Method and the numerical solution for axisymmetric Cylindrical pressure vessel under internal pressure have been presented. Following that, displacements and stress distributions depending on inhomogeneity constant of FGM vessel along the longitudinal direction of elastic modulus, are illustrated and compared with those of the homogeneous case. The values which have been used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements and stress distributions. Finally, the results are compared with the findings of finite element method (FEM).

In this investigation, a suitable algorithm for the detection of cracks in the pressure vessels is presented. The equations of motion for the vessel are obtained and transferred into the wavelet space in a simplified form resulted from time and position approximations. The locations of cracks are randomly distributed in different regions of the structure to cover the whole geometry of the pressure vessel. Furthermore, the pressure vessel is installed vertically with a fixed end at the bottom of each of its four leg supports. Then, the results are transferred to the wavelet space using Daubechies wavelet families. From the comparison of the displacement results associated with the intact and damaged vessels, it can be clearly seen that the crack location can be accurately detected noting the alteration in the wavelet output diagrams. The results of the crack detection show that with the proper selection of the wavelet type, the wavelet based finite element method is a suitable and nondestructive method as well as a powerful numerical tool for the detection of cracks and other discontinuities in the pressure vessels. The results of this investigation can be used in the marine and aerospace industries as well as power stations.

This paper implements the J-integral method to numerically analyze a crotch corner crack in the shell-nozzle junction of an internally pressurized Cylindrical pressure vessel, which is used in oil and gas industry. Firstly, by using the three-dimensional domain integral method and for linear elasticity, the equations to calculate the J-integral have been derived. The distinct advantage of using this integral in fracture mechanics is its ability to accurately estimate the stress intensity factor of the crack at points far from its tip, where the stress and strain gradients are high. Secondly, the implementation of the methodology in Abaqus software is described in detail. The methodology can be extended to other locations of vessels and various types of cracks. In order to verify the model, numerical results have been compared with the analytical ones, and a good conformity between them was observed. In fact, the largest difference of 30% is due to correction and safety factors which are considered in WRCB-175. The path independence of the J-integral was also observed for all contours with the error less than 0.15%. In general, the outputs of this research will help inspectors and safety engineers involved in the oil, gas and petrochemical industry to make a more accurate assessment of the safety and health status of equipment.

The present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick Cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the existence of shear stress in the thick Cylindrical shell due to material and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT).These equations are in the form of a set of general differential equations with variable coefficients. Given that the FG cylinder is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses.The problem was also solved, using the finite element method (FEM), the results of which were compared with those of the multilayered method (MLM). Finally, some numerical results are presented to study the effects of applied pressure, non-homogeneity index, and power law index of FGM on the mechanical behavior of the Cylindrical shell.