Journal of Solid Mechanics
http://jsm.iau-arak.ac.ir/
Journal of Solid Mechanicsendaily1Tue, 30 Mar 2021 00:00:00 +0430Tue, 30 Mar 2021 00:00:00 +0430Three-Dimensional Stress Analysis for Semi-Elliptical Cracks in the Connection of Cylinder-Hemispherical Head for Thick-Walled Cylindrical Pressure Vessels
http://jsm.iau-arak.ac.ir/article_680917.html
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)&nbsp;ranged from 0.2 to 0.8; and the cylinder geometry parameter of vessel&nbsp;&nbsp;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&nbsp; &nbsp;&nbsp;and&nbsp; &nbsp;&nbsp;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.&nbsp;&nbsp;Size-Dependent Higher Order Thermo-Mechanical Vibration Analysis of Two Directional Functionally Graded Material Nanobeam
http://jsm.iau-arak.ac.ir/article_680610.html
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&rsquo;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.A Modified Model to Determine Heat Generation in the Friction Stir Welding Process
http://jsm.iau-arak.ac.ir/article_680524.html
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.Thermal Buckling Analysis of Porous Conical Shell on Elastic Foundation
http://jsm.iau-arak.ac.ir/article_681301.html
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&nbsp; 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 K&aacute;rm&aacute;n 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.Experimental and Numerical Investigation on Geometric Parameters of Aluminum Patches for Repairing Cracked Parts by Diffusion Method
http://jsm.iau-arak.ac.ir/article_680848.html
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 &deg;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 Parameter Identification on Structures Using Observer Kalman Filter Identification/Eigen System Realization Algorithm
http://jsm.iau-arak.ac.ir/article_680769.html
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.Vibration Analysis of a Magneto Thermo Electrical Nano Fiber Reinforced with Graphene Oxide Powder Under Refined Beam Model
http://jsm.iau-arak.ac.ir/article_680847.html
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&rsquo;s principle. The effect of a nonuniform magnetic and&nbsp; 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&rsquo;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.Vibrations of Inhomogeneous Viscothermoelastic Nonlocal Hollow Sphere under the effect of Three-Phase-Lag Model
http://jsm.iau-arak.ac.ir/article_681012.html
Herein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag &nbsp;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&ndash;phase&ndash;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.The Frequency Response of Intelligent Composite Sandwich Plate under Biaxial In-Plane Forces
http://jsm.iau-arak.ac.ir/article_673985.html
This paper investigates the frequency response of a smart sandwich plate made of magnetic face sheets and reinforced core with nano-fibers. The effective elastic properties of composite core reinforced with carbon nanotube are estimated by the extended rule of Mixture. The orthotropic visco-Pasternak foundation is examined to study orthotropic angle, damping coefficient, normal, and shear modulus. The top and bottom face sheets of the sandwich are magnetic and their vibrations are controlled by a feedback control system and magneto-mechanical couplings. Also, the sandwich plate is subjected to the compression and extension in-plane forces in both x and y directions. Five coupled equations of motion are derived using Hamilton&rsquo;s principle. These equations are solved by the differential quadrature method. The analysis performed by the third-order shear deformation theory (Reddy&rsquo;s theory) shows useful details of the effective parameters such in-plane forces, modulus of elastic foundation, core-to-face sheet thickness ratio and controller effect of velocity feedback gain on the dimensionless frequency of the sandwich plate. The analysis of such structures can be discussed in the military, aerospace and civil industries.Magneto-Rheological Response in Vibration of Intelligent Sandwich Plate with Velocity Feedback Control
http://jsm.iau-arak.ac.ir/article_674337.html
This study deals with the free vibration of the sandwich plate made of two smart magnetostrictive face sheets and an electro-rheological fluid core. Electro-rheological fluids are polymer-based material that changes its viscosity under the applied electric field. A feedback control system follows the magnetization effect on the vibration characteristics of the sandwich plate when subjected to the magnetic field. It is assumed that there is no slip between layers, so the stress-strain relations of each layer are separately considered. Energy method is utilized in order to derive the five coupled equations of motion. These equations are solved by differential quadrature method (DQM). Results of this study show the rheology response of fluid in presence of electric field where the core gets hard and the dimensionless frequency increases. Also, the significant effect of thickness and aspect ratios and velocity feedback gain are discussed in detail. Such intelligent structures can replace in many of the systems used in automotive, aerospace and building industries as the detector, warning, and vibration absorber etc.Thermodynamic Stability of Sandwich Micro-Beam with Honeycomb Core and Piezoelectric / Porous Viscoelastic Graphene Facesheets
http://jsm.iau-arak.ac.ir/article_677554.html
Thermodynamic stability of sandwich micro beam with honeycomb core and piezoelectric / porous visco graphene sheets resting on visco Pasternak. In order to consider size effect, strain gradient theory is utilized. Using energy method and zigzag theory, final motion equations of sandwich micro beam are derived and solved by Galerkin method. The effects of parameters such as small scale, temperature changes, core to face sheets ratio, intensity of electric fields and elastic medium on the thermal dynamic stability of sandwich micro beam are investigated. Results indicated that by increasing temperature changes, the origins of the instability regions moves to lower excitation frequencies and decreases the width of the instability region of sandwich micro beam at a certain dynamic load factor. In addition, increasing porosity indexes leads to increase excitation frequencies and consequently cause to more stable system . The results of present work can be used to optimum design and control of micro-thermal/electro-mechanical devices.Study on Vibration Band Gap Characteristics of a Branched Shape Periodic Structure Using the GDQR
http://jsm.iau-arak.ac.ir/article_678297.html
In this study, a new periodic structure with special vibration band gap properties is introduced. This structure consists of a main beam and several cantilever beam elements connected to this main beam in the branched shape. Two models with different number of beam elements and geometrical parameters are considered for this periodic structure. The transverse vibrations of beams are solved using the generalized differential quadrature rule (GDQR) method to calculate the first four band gaps of each model. Investigating the influences of geometrical parameters on the band gaps shows that some bands are close to each other for specific ranges of geometrical parameters values. Furthermore, as the number of beam elements increases, the number of close band gaps increases. Having more than two close band gaps means that this periodic structure has a relatively wide band gap in total. Furthermore, this wide band can move to low frequency ranges by changing the geometrical parameters. Absorbing vibrations over a wide band gap at low frequency ranges makes this periodic structure a good vibration absorber. Verification of the analytical method using ANSYS software shows that the GDQR method can be used for vibration analysis of beam-like structures with high accuracyDynamic Stability Analysis of Bi-Directional Functionally Graded Beam with Various Shear Deformation Theories under Harmonic Excitation and Thermal Environment.
http://jsm.iau-arak.ac.ir/article_678358.html
In this article, dynamic stability analysis of bi-directional functionally graded materials (BDFGMs) beam rested on visco-Pasternak foundation under harmonic excitation is studied. Also, BDFGMs beam is subjected to a transversely uniformly distributed temperature rising and it is assumed that the material properties to be temperature-dependent. According to the exponential and power law distributions, thermo-mechanical properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions. Based on various shear deformation theories (e.g. Euler-Bernoulli, Timoshenko, third order shear deformation and sinusoidal shear deformation theories), the stability equations of BDFGMs beam is derived by applying the Hamilton's principle. The generalized differential quadrature method (GDQM) in conjunction with the Bolotin method is utilized to solve the differential stability equations under SS, SC and CC boundary conditions. To validate the present analysis, a comparison study is carried out with the results found in the literature and a good agreement is observed compared to the reported results. Finally, numerical results are presented to study the influences of the gradient index, length-to-thickness ratio, temperature rise and foundation parameters on the dynamic stability region of BDFGMs beam. The results of presented paper can be used to the optimal design and assessment of the structural failure.Free Vibration Analysis of Composite Grid Stiffened Cylindrical Shells Using A Generalized Higher Order Theory
http://jsm.iau-arak.ac.ir/article_681359.html
The present study analyzes the free vibration of multi-layered composite cylindrical shells and perforated composite cylindrical shells via a modified version of Reddy&rsquo;s third-order shear deformation theory (TSDT) under simple support conditions. An advantage of the proposed theory over other high-order theories is the inclusion of the shell section trapezoidal form coefficient term in the displacement field and strain equations to improve the accuracy of results. The non-uniform stiffness and mass distributions across reinforcement ribs and the empty or filled bays between the ribs in perforated shells were addressed via a proper distribution function. For integrated perforated cylindrical shells, the results were validated by comparison to other studies and the numerical results obtained via ABAQUS. The proposed theory was in good consistency with numerical results and the results of previous studies. It should be noted that the proposed theory was more accurate than TSDT. It should be noted that the proposed theory was more accurate than TSDT.