Journal of Solid Mechanics
Volume:13 Issue: 1, Winter 2021

These pressure vessels are made by different type of heads. One of them is hemi-spherical head. The area of geometrical discontinuity, like the connection of the cylinder to its hemi-spherical head, are the most susceptible areas for crack initiation along their welds. So it is worthwhile to consider cracks located at this connection. The purpose of this article is to investigate the effect of variation of stress field and geometry of problem on distribution of Stress Intensity Factor (SIF) for a semi-elliptical surface crack which is located at the connection of cylinder to its hemispherical head. The three dimensional finite element analysis is performed by employing singular elements along the crack front. The ratio of crack depth to crack length (a/c) ranged from 0.3 to 1.2; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the cylinder geometry parameter of vessel  ranged from 1.2 to 2. For better comparison the results are normalized and reported in non-dimensional formats. The results show that the crack configuration, vessel thickness and radius have significant influence on the stress intensity factor distribution along the crack front. Also For a fixed    and    the maximum value of SIF occur in the cylindrical part and approximately near the deepest point of crack; not on the deepest point of crack depth and this may be due to changing stress field in this connection. The stress intensity factors are presented in suitable curves for various geometrical configurations providing useful tool for the fracture mechanics design of cracked pressure vessels.

This paper represented a numerical technique for discovering the vibrational behavior of a two-directional FGM (2-FGM) nanobeam exposed to thermal load for the first time. Mechanical attributes of two-directional FGM (2-FGM) nanobeam are changed along the thickness and length directions of nanobeam. The nonlocal Eringen parameter is taken into the nonlocal elasticity theory (NET). Uniform temperature rise (UTR), linear temperature rise (LTR), non-linear temperature rise (NLTR) and sinusoidal temperature rise (STR) during the thickness and length directions of nanobeam is analyzed. Third-order shear deformation theory (TSDT) is used to derive the governing equations of motion and associated boundary conditions of the two-directional FGM (2-FGM) nanobeam via Hamilton’s principle. The differential quadrature method (DQM) is employed to achieve the natural frequency of two-directional FGM (2-FGM) nanobeam. A parametric study is led to assess the efficacy of coefficients of two-directional FGM (2-FGM), Nonlocal parameter, FG power index, temperature changes, thermal rises loading and temperature rises on the non-dimensional natural frequencies of two-directional FGM (2-FGM) nanobeam.

Friction stir welding (FSW) is a solid state bonding process in which the parts are joined together at the temperature below the melting point. In present study, a modified model was developed based on the partial sticking/sliding assumption in the tool-workpiece interface and the dependence of the thermal energy equations on the temperature-dependent yield stress to determine heat generation in FSW process that is independent from coefficient of friction. So to eliminate the dependence of the final equations on the coefficient of friction, an equation was used which the coefficient of friction was expressed as a function of workpiece yield stress. To validate the model, the FSW process was simulated by the finite element package ABAQUS and two subroutines of DFLUX and USDFLD and then the simulation results were compared with the experimental ones. The results showed that the modified model is appropriately capable of predicting the temperature and the residual stresses in the different zones of welded section.

In this research, the thermal buckling analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained  by using the Euler`s and the Trefftz equations .Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear strain-displacement relations are obtained according to the von Kármán assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling.

Repairing cracked aerial structures using patches is a common way to restore mechanical properties, strength and extend fatigue life. The performance of such patches can be obtained by comparing the maximum amount of force tolerated by the repaired piece with the unrepaired piece. The shape and dimensions of the patch used to repair the crack and the way the patch is bonded affect the repair quality which are of great importance. Therefore, in this paper, we investigate the factors affecting the diffusion bonding between the patch and the piece. The impact of the shape of the aluminum patch attached on a 10 mm central crack piece and perpendicular to the loading direction (mode I) is studied experimentally and numerically. The optimum conditions for the diffusion connection including the pressure, time and temperature of the connection were obtained experimentally using a composite rotatable centered design and in the connection made under these conditions, the patch shape and aspect ratio was considered as variables of design, and the results were obtained for square, rectangular, circular and elliptical patches. At the end, it was found that the best connection under the pressure conditions of 570 °C, 70 bar and 100 min was formed and the rectangular patch efficiency was greater whereas its extent is more in line with crack than the other modes. At a fixed area, the different patch geometries investigated in this study were able to influence up to 80% of the maximum force tolerated by the repaired parts. Also, there is an acceptable convergence between experimental and numerical results.

Structural and crack parameters in a continuous mass model are identified using Observer Kalman filter Identification (OKID) and Eigen Realization Algorithm (ERA). Markov parameters are extracted from the input and out responses from which the state space model of the structural system is determined using Hankel matrix and singular value decomposition by Eigen Realization algorithm. The structural parameters are identified from the state space model. This method is applied to a lumped mass system and a cantilever which are excited with a harmonic excitation at its free end and the acceleration responses at all nodes are measured. The stiffness and damping parameters are identified from the extracted matrices using Newton-Raphson method on the structure. Later, cracks are introduced in the cantilever and all structural parameters are assumed as known priori, the unknown crack parameters such as normalized crack depth and its location are identified using OKID/ERA. The parameters extracted by using this algorithm are compared with other structural identification methods available in the literature. The main advantage of this algorithm is good accuracy of identified structural parameters.

The present article express the magneto thermo electric deformation of composite nano fiber reinforced by graphene oxide powder (GOP). To reach the governing equation of the problem a higher-order trigonometric refined beam model is utilized according to Hamilton’s principle. The effect of a nonuniform magnetic and  thermo piezo electric field is applied to the governing equations by combining the field relations with the displacement field equations. Then, obtained equations are solved by using Galerkin’s method to consider the influence of different boundary conditions on the vibrational responses of the fiber. The accuracy and efficiency of the presented model is verified by comparing the results with that of published researches. Further, the effects of different variant on the dimensionless frequency of GOP reinforced magneto piezo thermo elastic composite fibers are highlighted through tables and dispersion curves. The weight fraction of GOP and the magneto thermo electro effects have significant influence in the stiffness of the nano composites.

Herein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag  model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-dimensional quantities. The simple power law has been presumed to take the material in radial direction. The series solution has been established to derive the solution analytically. The relations of frequency equations for the continuation of viable modes are developed in dense form. The analytical results have been authenticated by the reduction of nonlocal and three–phase–lag parameters. To investigate the quality of vibrations, frequency equations are determined by applying the numerical iteration method. MATLAB software tools have been used for numerical computations and simulations to present the results graphically subject to natural frequencies, frequency shift, and thermoelastic damping. The numerical results clearly show that the variation of vibrations is slightly larger in case of nonlocal elastic sphere in contrast to elastic sphere.