Journal of Solid Mechanics
http://jsm.iau-arak.ac.ir/
Journal of Solid Mechanicsendaily1Wed, 01 Jun 2022 00:00:00 +0430Wed, 01 Jun 2022 00:00:00 +0430On Validity of Analytical Method in Cracked Column Post-Buckling Analysis Using Empirical and Numerical Investigations
http://jsm.iau-arak.ac.ir/article_685550.html
The three analytical, finite element and experimental methods are applied to study the nonlinear buckling of cracked columns.&nbsp; The original aim of this research is to investigate the validity of the common analytical method in an analogy with the experimental method and the finite element method of MATLAB programming-based. The literature review shows that papers applied this analytical method without considering its drawbacks to determine the post-buckling results. Results in the linear part of the analytical method are in close accordance with the two others, while a clear difference in the nonlinear part of the analytical method is observed with the actual results obtained from the experimental tests and numerical results of the finite element method. An in-depth discussion is represented to find out the main reasons of this difference.&nbsp; The conversion matrix technique in the finite element method and dividing the column into two segments in the analytical method are used to include the crack parameters in relations according to the continuity conditions in the crack tip. An investigation is performed to study the effect of the crack depth and position on the critical buckling load and the post-buckling path.&nbsp;Multi-Objective Optimization of Shot-Peening Parameters Using Modified Taguchi Technique
http://jsm.iau-arak.ac.ir/article_685547.html
Shot-peening is a surface treatments utilized extensively in the industry to enhance the performance of metal parts against fatigue. This paper aimed to find the optimal parameters of the shot-peening process based on the finite elements model and the Taguchi method. The effects of three peening parameters (shot diameter, shot velocity, coverage percentage) are investigated on residual stress and roughness using Taguchi method. A new Taguchi technique is proposed by combining it with desirability function to optimize the shot-peening parameters that simultaneously provide two or more responses in an optimal mode. The results show that the coverage percentage has the most influence on the surface stress and maximum compressive stress whereas the velocity and diameter of the shot are the most effective parameters on the depth of compression stress. The shot velocity is the main factor of the surface roughness due to the shot peening. Through the proposed structure, optimal conditions can be obtained for surface stress and roughness simultaneously with high-coverage and low-velocity. Eventually, results reveal the effectiveness of the proposed strategy in stand point of saving time and cost.Elasticity Exact Solution for an FGM Cylindrical Shaft with Piezoelectric Layers Under the Saint-Venant Torsion by Using Prandtl’s Formulation
http://jsm.iau-arak.ac.ir/article_686310.html
Functionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigators due to its prominent features, and have extensively used in almost every discipline of engineering which in turn significantly increases the number of research publication of FGM. In this paper the exact elasticity solution for an FGM circular shaft with piezo layers is analysed. piezoelectric layers are homogeneous and the modulus of elasticity for FGM varies continuously with the form of an exponential function. The shear modulus of the non-homogeneous FGM shaft is a given function of the Prandtl&rsquo;s stress function of considered circular shaft when its material is homogeneous. state equations are derived. The Prandtl&rsquo;s stress function and electric displacement potential function satisfy all conditions. The shearing&nbsp; stresses, torsional rigidity, torsional function for FGM layer and shearing&nbsp; stresses, electric displacements, torsional rigidity, electrical torsional rigidity ,torsional&nbsp; and electrical potential functions for piezoelectric layers are&nbsp; obtained. Exact analytical solution for hollow circular cross-section presented. At the end some graphs and conclusions are given.Fatigue Life Analysis of the Propeller Shafting System of a VLCC Ship Powertrain System Using Finite Element or Distributed-Lumped Methods
http://jsm.iau-arak.ac.ir/article_686212.html
In this study, the dynamic behavior of the propulsion system of a VLCC (Very Large Crude oil Carrier) ship is investigated using a multi-input multi-output model. In this system the engine ordered speed and the number of active cylinders are assumed as inputs and the dynamic parameters of the engine such as torque and speed are considered as outputs. In this research, the effects of sea wave and wind on the system dynamic behavior have been investigated. In addition, the ship powertrain system is investigated in which the intermediate shaft and propeller shaft are analyzed using lumped parameter method, finite element method, distributed-lumped method and the results of these modeling techniques are compared to the modeling results in which the connecting shafts were considered as rigid body. Comparison of the results shows that there are significant differences between the results of rigid body method and other three types of system modeling. On the other hand, the time required to run the distributed-lumped model is much shorter compared to other methods that are considered in the study for the dynamic behavior of the ship's powertrain systems. On the other hand, the fatigue analysis of the ship power transmission shafts shows that the fatigue life assessment of these shafts is of great importance and should be considered in the design phase.&nbsp;Analytical Solutions of Finite Wedges Coated by an Orthotropic Coating Containing Multiple Cracks and Cavities
http://jsm.iau-arak.ac.ir/article_682153.html
This paper presents a general formulation for an isotropic wedge reinforced by an orthotropic coating involving multiple arbitrarily oriented defects under out of plane deformation. The exact closed form solution of the problem weakened by a screw dislocation in the isotropic wedge is obtained by making use of finite Fourier cosine transform. Also, the closed-form solutions of the out of plane stress and displacement fields are obtained. After that, by making use of a distributed dislocation approach, a set of singular integral equations of the domain involving smooth cavities and cracks subjected to out of plane external loading are achieved. The cracks and cavities are considered to be only in the isotropic wedge. The presented integral equations have Cauchy singularity and must be evaluated numerically. Multiple numerical examples will be presented to show the applicability and efficiency of the presented solution. The geometric and point load singularities of the stress components are obtained and compared with the available data in the literature.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The Fracture Toughness of the Welding Zone in Gas Transfer Steel Pipes by Experimental and Numerical Methods
http://jsm.iau-arak.ac.ir/article_684701.html
Fracture toughness is a criterion to determine the resistance of materials against small longitudinal and peripheral cracks, which can be created in the effect of welding or peripheral effects. Therefore, it is extremely important to scrutiny the factors that impress crack treatment and the way that it grows. In this research, fracture toughness was investigated on the peripheral welding zone in gas and oil transfer pipelines made in steel API X65. The fracture toughness is derived by using two different methods. At first, the three-point bending test method was used on samples that made up of the peripheral welding zone. Then, with a numerical simulation it was calculated by ABAQUS software v6/10. The comparison of experimental results and computer simulation results shows good agreement from two methods. The fracture toughness of the welded zone, obtained in this study, was compared with that of the base metal. The results showed that fracture toughness on the welding zone in gas and oil transfer steel pipelines decreased 43% compared to the base metal. This issue shows that peripheral welding on gas and oil transfer pipelines has more talent for crack growth compared to the base metal.Analysis of Nonlinear Vibration of Piezoelectric Nanobeam Embedded in Multiple Layers Elastic Media in a Thermo-Magnetic Environment Using Iteration Perturbation Method
http://jsm.iau-arak.ac.ir/article_688232.html
In this work, analysis of nonlinear vibration of piezoelectric nanobeam in a thermo-magnetic environment embedded in Winkler, Pasternak, quadratic and cubic nonlinear elastic media for simply supported and clamped boundary conditions is presented. With the considerations of Von- Karman geometric nonlinearity effect and with the aids of nonlocal elasticity theory as well as Euler&ndash;Bernoulli beam model, the equation of motion for the nanobeam is derived using Hamilton&rsquo;s principle. The nonlinear dynamic model is solved using Galerkin-decomposition coupled with iteration perturbation method. From the parametric studies, it is shown that the frequency of the nanobeam increases at low temperatures but decreases at high temperatures. The nonlocal parameter decreases the frequencies of the piezoelectric nanobeam. An increase in the quadratic nonlinear elastic medium stiffness causes a decrease in the first mode of the nanobeam with clamped-clamped supports and an increase in all modes of the simply supported nanobeam at both low and high temperatures. When the magnetic force, cubic nonlinear elastic medium stiffness, and amplitude increase, there is an increase in all mode frequencies of the nanobeam. An increase in the temperature change at high temperature reduces the frequency ratio but at low or room temperature, an increase in temperature change, increases the frequency ratio of the structure nanotube. The significance of this study is evident in the design and applications of nanobeams in thermal and magnetic environments.New Two 20-Node High-Order Finite Elements Based on the SFR Concept for Analyzing 3D Elasticity Problems
http://jsm.iau-arak.ac.ir/article_688588.html
This paper proposes conforming and nonconforming 20-node hexahedral finite elements. The elements&rsquo; formulation stems from the so-called Space Fiber Rotation (SFR) concept, allowing a spatial rotation of three-dimensional virtual fiber within the elements. Adding rotational degrees of freedom results in six degrees of freedom per node (three rotations and three translations) which enhances the approximation of the classical displacement field. The incompatible modes approach has been adopted in the nonconforming element formulation in order to avoid numerical deficiencies associated with the Poisson&rsquo;s ratio locking phenomenon. The accuracy of the proposed elements is examined through a series of three-dimensions linear elastic benchmarks including beam, plates, and shell structures. The proposed elements were shown to give better results than the standard 20-node hexahedron especially when mesh distortion is applied.&nbsp; This confirms that the two proposed elements are less sensitive to mesh distortion. The elements also show good performance when compared with analytical and numerical solutions from the literature.Dynamic 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_686214.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.Analysis of a Functionally Graded Finite Wedge Under Antiplane Deformation
http://jsm.iau-arak.ac.ir/article_687867.html
The antiplane deformation of a wedge made of a functionally graded material (FGM) with finite radius has been investigated analytically in the present article. In relation to the boundary conditions imposed on the arc portion of the wedge, displacement or traction, two problems have been studied. In each of the problems three various kinds of boundary conditions (traction-displacement, displacement-displacement and traction-traction) have been applied to the radial edges of the wedge. The governing differential equations have been solved by employing finite Fourier transforms and Green&rsquo;s function method. The closed form solutions for stress and displacement distribution have been achieved for the whole domain. Explicit relations have been extracted for the order of stress singularity in all cases. These relations indicated the dependence of the order of stress singularity on the boundary conditions, material property and wedge angle. In fact, despite of an isotropic wedge, for which the order of stress singularity depends only the geometry of the wedge, in an FG wedge the order of stress singularity depends both the geometry as well as the material property.Analytical Study on the Effect of Stacking Sequence on the Maximum Allowable Heat Flux in Perforated Symmetric Composite Laminates Subjected to Uniform Heat Flux
http://jsm.iau-arak.ac.ir/article_687647.html
An analytical solution was used for obtaining the maximum allowable heat flux in symmetric composite laminates containing a quasi-square cutout with different stacking sequences subjected to uniform heat flux. The Tsai-Hill criterion was used to assess the maximum allowable heat flux of the laminate. The analytical solution was obtained based on the thermoelasticity theory and the Lekhnitskii&rsquo;s method. Furthermore, by employing a suitable mapping function, the solution of symmetric laminates with a circular cutout was extended to the quasi-square cutout. The quasi-square cutout was studied in a symmetric laminate made of Glass/epoxy with different stacking sequences of [0/90]S, [45/-45]S , [30/-30]S. The results showed that the maximum allowable heat flux experienced in perforated plates can be improved by considering the appropriate stacking sequence and the optimal values of the cutout parameters. According to the results, the best cutout geometry was not always a circle, as in some cases by choosing the appropriate values of bluntness parameter, cutout orientation, heat flux angle, cutout aspect ratio and laminate stacking sequence, a non-circular cutout provided higher maximum allowable heat flux value for a perforated plate than a circular cutout.Transient Dynamic Analysis of Grid-Stiffened Composite Conical Shells
http://jsm.iau-arak.ac.ir/article_683575.html
In this study, the transient dynamic analysis of grid-stiffened composite conical shells is discussed. The transient dynamic response of the composite conical shell with simply supported boundary conditions under the lateral impact load, which is applied extensively and uniformly on a certain surface, is obtained using the convolution integral and based on the method of addition of modes. The validation of the obtained results has been done with the help of references and ABAQUS finite element software. The effects of various parameters such as fiber angle, geometric ratios, type, etc. have been investigated in forced vibrations. Finally, the effect of reinforcing the conical shell with the help of grid-stiffened structures has been studied.A Novel Spring-Based Model for Damage Investigation of Functionally Graded Beams
http://jsm.iau-arak.ac.ir/article_686067.html
In this paper, free vibration analysis of damaged functionally graded beams based on the first-order shear deformation theory (FSDT) is carried out. In this regard, a new model of springs is introduced to model the damaged elements of the beam. The proposed model is achieved from stress resultants. The springs equations for homogeneous and functionally graded (FG) beams are presented; furthermore, equations for equivalent springs are also provided which can be used for both homogeneous and FG beams. The proposed method can be applied for the analysis of structures with fewer computation costs and high accuracy. To show the accuracy of the proposed model, the natural frequencies of the beams with real elements and the ones which are modeled by the proposed springs are compared considering various support conditions. Good agreement has been observed. Thereafter, the model is used to detect the damaged elements. The result shows that the model can properly detect the damage location.&nbsp;Investigating Stress Intensity Factor and Fatigue Life Using Extended Isogeometric Analysis Based on Bézier Extraction of NURBS
http://jsm.iau-arak.ac.ir/article_689234.html
In this paper, the extended isogeometric analysis based on B&eacute;zier extraction of NURBS is applied for Investigating stress intensity factor and fatigue life in the two-dimensional crack problems with thermal and mechanical cyclic loading. By transforming NURBS function to linear combination of Bernstein functions defined over C0-continuous B&eacute;zier elements, the extended isogeometric analysis can be implemented in the extended finite element method framework. Grid points around the crack line and crack tip are identified by the level set representation. Then, discontinuous enrichment functions are added to the isogeometric analysis approximation. Thus, this method does not require remeshing. The interaction integral method and Paris law has been used to extract stress intensity factor and evaluate fatigue life, respectively. Numerical examples are examined to validate the efficiency of the proposed method. The effect of adaptive refinement strategies on computational cost and convergence is studied. Numerical examples showed that the presented method produces highly accurate results, yet it is beneficial to implement. &nbsp;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.Static Analysis and Fatigue of DHS Implants to Treatment Femoral and Intertrochanteric Neck Fractures Using Ti6Al4V and SS316 Alloys, A finite Element Analysis
http://jsm.iau-arak.ac.ir/article_686096.html
The neck fractures and the femurs intertrochanteric are common complications that are recovered by a multicomponent implant called dynamic hip screw (DHS). In the present study, a standard four-hole DHS with Ti6Al4V (Ti6) and SS316l (SS) alloys for static mode (slow walking) and fatigue mode like normal walking (NW), descending stairs (DS), and falling (FA) by finite elements analysis (FEA) have been evaluated (ANSYS software). The results have been confirmed by similar studies in static mode and maximum Von Mises stress and strain are obtained for Ti6 about 145 MPa and 0.191%, and SS about 196MPa and 0.121%. Most critical stress points occur in cortical screws, plate holes, compression screws, and lag screws, respectively. DHS components with Ti6 alloy have infinite life in NW and DS, also in FA, they have a finite life (〖〖10〗^7-10〗^8 cycle) with alternating Von Mises stress (&sigma;_amax) ~ 425MPa, while for SS they have finite life in all activities, which NW~〖10〗^7 cycle,DS~〖10〗^6 cycle, and even in FA cortical screw life of failure reaches to 98 cycles and〖 &sigma;〗_amax=486Mpa. The critical regions are the same as the failure regions common in biomechanical and clinical studies. These regions are mainly concentration stress points that lead to DHS failure as the crack grows.The Modelling of the Mechanics of Deformation in Plane Strain Upsetting of Round Cross-Section Billets Between the Flat and V-Shaped Dies
http://jsm.iau-arak.ac.ir/article_686896.html
Plane strain upsetting of round cross-section billets between the flat and V-shaped dies has been studied in this paper. A deformation model has been proposed and the geometry of the deformed billet cross-section is determined for a given displacement of the top flat die. To analyze the process, the slab method of analysis has been applied and for a given process conditions, the required forming load has been estimated. The process under consideration has been performed also with the finite-element method to predict the forming load and the material flow. The calculated forming load and the deformed billet cross-section geometry compare well with the FE simulations data. The effects of friction factor and the angle of the V-shaped bottom die on the forming load have been investigated. The theoretical results have been indicated that as the bottom die angle decreases the forming load decreases and the forming load is not influenced by friction in case of small bottom die angles.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.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.Numerical and Experimental Analysis of Impact and Damage on Composite Sandwich Panels with Grid-Stiffened Core
http://jsm.iau-arak.ac.ir/article_688762.html
A composite grid sandwich panel consists of a core with a composite grid structure and two faces on both sides of the core. This study investigated low-velocity impact in grid sandwich panels with grid cores experimentally and numerically by constructing and performing experimental tests using Abaqus finite element software. In the experimental part, three sandwich panels with grid cores were made for the low- velocity impact test. In the numerical part, three-dimensional elements were used, and damage was solved via programming in the Fortran language in Abaqus software. The results showed that the use of foam in the core of these structures reduced deflection due to impact despite a slight increase in the final weight of the structures.A composite grid sandwich panel consists of a core with a composite grid structure and two faces on both sides of the core. This study investigated low-velocity impact in grid sandwich panels with grid cores experimentally and numerically by constructing and performing experimental tests using Abaqus finite element software. In the experimental part, three sandwich panels with grid cores were made for the low- velocity impact test. In the numerical part, three-dimensional elements were used, and damage was solved via programming in the Fortran language in Abaqus software. The results showed that the use of foam in the core of these structures reduced deflection due to impact despite a slight increase in the final weight of the structures.Fatigue Failure Analysis of Trailing Arm Using Numerical Methods
http://jsm.iau-arak.ac.ir/article_689361.html
The suspension system, one of the essential parts of any vehicle which has a significant role in vehicle steering, accelerating, and braking. One of the suspension system's main components is the trailing arm, which is exposed to frequent loadings and is made by welding method. Due to the use and nature of this piece, its fatigue analysis is crucial. Since this part is made by welding process, its fatigue analysis is much more complicated than other parts. In this paper, fatigue life of the trailing arm is investigated by using different numerical method. At first, safety factor of the component is calculated using dang van criteria. Dang van is one of the most famous and appropriated method for multi axial non proportional loads. However it is not a good criterion in order to calculate the damage of the weld line. So Volvo method that developed base on the weld process and properties is consider for fatigue analysis of the weld line. The obtained results improve the necessity of using this kind of method for welding process.&nbsp; Finally, it could be concluded that for fatigue analysis of a welded component such as trailing arm, using both method are necessary. Considering two different criteria for a component and comparing the obtained results of the trailing arm under non proportional applied load is one of the achievement of this paper. Of course by using this method, the calculated fatigue life of the trailing arm is accurate. At the end, it should be noted that the both applied methods, Dang Van and Volvo, are completely verified by the available experimental result in the reliable references.