Journal of Solid Mechanics
Volume:12 Issue: 4, Autumn 2020

This investigation deals with the vibration analysis of the sandwich beam with electro-rheological (ER) core embedded within two functionally graded (FG) carbon nanotubes (CNTs) reinforced composite (FG-CNTRC) layers. In this regard, the governing equations are extracted by the Hamilton principle and the rule of mixture is employed to calculate the effective mechanical and physical properties of the CNTRCs face-sheets. Don and Yalcintas shear modulus models are applied to simulate shear modules of the ER core of the beam. The elastic medium is simulated by Winkler-Pasternak model and then, the governing equations are analytically solved. Finally, a parametric study is carried out in details and the effects of some main designing parameters such as applied voltage, Winkler coefficient, Pasternak coefficient, core to face-sheets thickness ratios and the different pattern of the CNTs along the face-sheets and loss factors are examined on the natural frequency. Based on the obtained results, volume fraction of CNTs in face-sheets have significant influence on the natural frequency in which by increasing the volume fractions the flexural rigidity of the sandwich beam increases as well as natural frequency.

ABSTRACT The purpose of this paper is to investigate friction forces in the design of a single-core flexible cable in the deformation zone and the practical applicability of the results obtained for these purposes. The power interaction of the design of a single-core flexible cable during its deformation is considered. For the first time, formulas were obtained for determining the interaction forces between the constituent parts of a single-core cable as a composite multilayer beam. A calculation technique has been developed and shear force values have been determined for some types of single-core flexible cables. The nature of the change in these forces along the length of the cable is investigated. At the beginning of the cable deformation zone, the force value can fluctuate within its constant value. In the remaining part, the shear forces along the section are constant and only at the end of the deformation zone is zero. Practically, the formulas work for the tasks. The resulting expressions for shearing forces allow one to evaluate the tribological interaction of the constituent parts of each cable element and take into account their influence when creating multicore cables. The results of the research can be used to improve the reliability of the design of flexible cables at the design stage.

This paper develops the Refined Zigzag Theory (RZT) for nonlinear dynamic response of an axially moving functionally graded (FG) Nano beam integrated with two magnetostrictive face layers based on the modified couple stress theory (MCST). The Sandwich Nano beam (SNB) subjected to a temperature difference and both axial and transverse mechanical loads. The material properties of FG core layer depend on the environment temperature and are assumed to vary in thickness direction. The SNB is surrounded by elastic medium, which is simulated by viscoPasternak model. The von-Karman nonlinear strain-displacement relationships are employed to consider the effect of geometric nonlinearities. In order to obtain governing motion equations and boundary conditions the energy method as well as Hamilton’s principle is applied. The differential quadrature method (DQM) is used for space domain and the Newmark-β method is taken into account for time domain response of the axially moving SNB. The detailed parametric study is conducted to investigate the effects of surrounding elastic medium, material length scale parameter, magnetostrictive layers, temperature difference, environment temperature, velocity of the SNB, axial and transverse mechanical loads and volume fraction exponent on the dynamic response of the SNB. Results indicate that the maximum deflection of the system can be controlled by employing negative values of velocity feedback gain values. In addition, the system loses its stability when the velocity of SNB is increased.

In the present work, an attempt has been made to study and improve the physical and biomechanical properties of adding Titanium dioxide (TiO2 ) and yttria stabilized zirconia (Y-PSZ) Nano fillers ceramic particles for reinforced the high density polyethylene (HDPE) matrix Nanocomposites for fabricated six bio nanocomposites hybrid by using hot pressing technique at different compounding temperature of (180,190, and 200 °C) and compression pressures of (30, 60, and 90 MPa). The fabricated Nano systems were designed, produced and investigated for use in repairs and grafting of the human bones, which are exposed to accidents or lifethreatening diseases. The main current research results show that with the increase of the TiO2 filler contain from 0 to 10 %, the value bulk densities increase by 30.24 % and when adding 2% partial stabilized zirconia (YPSZ), this value was further increased by 13.91%. For the same conditions the value percentages true porosity decrease by 48.68 % and further by 84.85 %, respectively. For the same previous parametric values, it has also been accessed that the maximum compression strength for this study was increased by 33.34 % and then further by 22 %, where these values higher by 90.11% than the previous mentioned studies. The micro-Vickers Hardness increased by 30.11 % for the second manufacturing system comparing with the first one, while the maximum equivalent von–Misses Stresses obtained from the current work withstand higher stresses than the natural bone by 52.65 higher than the previous studies. The stress safety factors increase by 58.38 % and by 21.42 % for the first and second systems, respectively. The achieved results values for the modeled femur bone is equivalent to actual service of the activity during normal movement of the patient. These results give great the designers choices to use successful bio composites for in vivo tests according to the clinical situation, age and the static and dynamic loads when designing a material to repair the fractured bones due to different types of accidents

In this paper, the stability of a conical shell panel in elastic-plastic domain is considered. The shell is made of an isotropic material (316L steel) with linear work hardening behavior. The shell is placed on simply supported end constraints and the acting loads are in the form of longitudinal compressive force and lateral pressure. The incremental Prandtl-Reuss plastic flow theory and von Mises yield criterion are used in the analysis. The problem is formulated based on classical shell theory and nonlinear geometrical straindisplacement relations are assumed. The stability equations are derived using the principle of the stationary potential energy. Using Ritz method the equations are solved and the numerical results obtained for different values of semi vertex and subtended angles. The obtained results show that there is a distinct semi vertex angle in which the shell has the best stability conditions. Also, there will be a limiting condition for the semi vertex angels beyond which the instability will not occur.

During the pressure vessels' operating life, several flaws are likely to grow in long-term operations under cyclic loading. It is therefore essential to take practical and predictive measures to prevent catastrophic events to take place. Fitness for service (FFS) is one safety procedure that is used to deal with maintenance of components in the petroleum industry. In this method, proposed in Codes of practices such as API 579 and BSI 7910, in certain cases, an overly conservative safety prediction is obtained when applied to the operation of pressure vessel containing surface fatigue crack growth. By using improved analytical techniques as well as nonlinear finite element methods critical cracks lengths may be derived more accurately thus reducing conservatism. In this paper, a specific pressure vessel analyzed for fitness for service, which sees fatigue crack growth rate, is assessed using analytical and numerical stress intensity factors. The estimated fatigue life is compared with both methods. It is found that both approaches give similar predictions within a range of scatter assuming that the fatigue properties used are the same in both cases. However, it can be said that the numerical approach gave the more conservative predictions suggesting a detailed analysis is always preferable in FFS examinations.

Vibration analysis of vessels conveying blood flow embedded in viscous fluid is studied based on the modified strain gradient theory. The viscoelastic vessels are simulated as a non-classical EulerBernoulli beam theory. Employing Hamilton’s principle, the governing equations for size-dependent vessels are derived. The Galerkin method is used in order to transform the resulting equations into general eigenvalue equations. The effects of the blood flow profile and its modification factors, red blood cells (RBCs) and hematocrit are considered in the blood flow. Besides, the influences of the constitutional material gradient scale, blood flow, internal pressure, structural damping coefficient, viscous fluid substrate and various boundary conditions on the natural frequencies and critical buckling velocities are studied. It is revealed that as the hematocrit, fluid viscosity of substrate, internal pressure and mass ratio increase, the natural frequencies and critical buckling velocities decrease. Furthermore, the results indicated that the strain gradient theory predicts the highest natural frequencies and critical buckling velocities among others. The results are compared with those available in the literature and good agreement has been observed.

In this paper, semi-exact methods are introduced for estimating the distribution of tangential displacement and shear stress in nonuniform rotating disks. At high variable angular velocities, the effect of shear stress on Von Mises stress is important and must be considered in calculations. Therefore, He’s homotopic perturbation method (HPM) and Adomian’s decomposition method (ADM) is implemented for solving equilibrium equation of rotating disk in tangential direction under variable mechanical loading. The results obtained by these methods are then verified by the exact solution and finite difference method. The comparison among HPM and ADM results shows that although the numerical results are the same approximately but HPM is much easier, straighter and efficient than ADM. Numerical calculations for different ranges of thickness parameters, boundary conditions and angular accelerations are carried out. It is shown that with considering disk profile variable, level of displacement and stress in tangential direction are not always reduced and type of changing the thickness along the radius of disk and boundary condition are an important factor in this case. Finally, the optimum disk profile is selected based on the tangential displacement-shear stress distribution. The presented algorithm is useful for the analysis of rotating disk with any arbitrary function form of thickness and density that it is impossible to find exact solutions.

In the present article, the free vibration analysis of a multi-layer rectangular plate with two magneto-rheological (MR) fluid layers and a flexible core is investigated based on exponential shear deformation theory for the first time. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The displacement of the flexible core is modeled using Frostig’s second order model which contains a polynomial with unknown coefficients. MR fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they have the capability to change the stiffness and damping of a structure. The governing equations of motion have been derived using Hamilton`s principle. The Navier technique is employed to solve derived equations. To validate the accuracy of the derived equations, the results in a specific case are compared with available results in the literature, and a good agreement will be observed. Then, the effect of variation of some parameters such as magnetic field intensity, core thickness to panel thickness ratio hc h ( ) and MR layer thickness to panel thickness ratio hMR h ( ) on natural frequency of the sandwich panel is investigated.

This paper investigates the nonlinear-coupled radial-axial vibration of single-walled carbon nanotubes (SWCNTs) based on numerical methods. Two coupled partial differential equations that govern the nonlinearcoupled radial-axial vibration for such nanotube are derived using nonlocal doublet mechanics (DM) theory. To obtain the nonlinear natural frequencies in coupled radial-axial vibration mode, these equations are solved using Homotopic perturbation method (HPM). It is found that the coupled radial-axial vibrational frequencies are complicated due to coupling between two vibration modes. The influences of some commonly used boundary conditions, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear-coupled radial-axial vibration characteristics of SWCNTs are discussed. It was shown that boundary conditions and maximum vibration velocity play significant roles in the nonlinear-coupled radial-axial vibration response of SWCNTs. It was shown that unlike the linear one, the nonlinear natural frequencies are dependent to maximum vibration velocity. Increasing the maximum vibration velocity increases the natural frequency of vibration compared to the prediction of the linear model. However, with increase in tube length, the effect of the maximum vibration velocity on the natural frequencies decreases. It was also shown that the amount and variation of nonlinear natural frequencies are more apparent in higher vibration modes and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein are compared with the fourth order Runge-Kuta numerical results and also with the other available results and good agreement is observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

This paper deals with the mathematical approach to discuss the radially varying transient temperature distribution in a multilayer composite hollow sphere subjected to the time independent volumetric generation of heat in each layer. Initially the layers are at arbitrary temperature and the analysis assumes all the layers of the body are thermally isotropic and having a perfect thermal contact. It is novel to obtain the exact solution for temperature field by the separation of variables by splitting the problem into two parts homogeneous transient and non-homogeneous steady state. The set of equations obtained are solved by using the rigorous applications of analytic techniques with the help of eigen value expansion method. The thermoelastic response is studied in the context of uncoupled Thermoelasticity. The results obtained pointed out that the magnitude and distribution of the temperature and thermal stresses are greatly influenced by the layered heat generation parameter. The accuracy and feasibility of the proposed model is demonstrated by an example of three layered hollow sphere of Aluminium, Copper and Iron subjected to given conditions. The results presented in this article could be found hardly in an open literature despite of extensive search.

The effect of cyclic loading on fatigue crack growth in plastically compressible solids is investigated at negative stress ratio under plane strain and small scale yielding conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The plastic crack growth, crack tip opening displacement (CTOD) and near crack tip stress fields are presented using finite element method. Material hardening/ softening has a major relevance on crack growth, CTOD and the evolution of stress distribution. It is revealed here that the negative stress ratio can significantly influence the loading conditions at the crack tip and thereby increase the crack growth for tension–compression loading for hardening material whereas the fatigue crack growth of plastically compressible hardening-softening-hardening material is only slightly affected by the negative stress ratio albeit it is accepted in literature that compressive loads contribute to fatigue crack growth significantly. In the present studies, the CTOD variation with applied load and the near stress distribution are also very unusual in nature.

Present work is concerned with the analysis of transient wave phenomena in a piezo-thermoelastic medium with diffusion, fiber reinforcement and two-temperature, when an elastic wave is made incident obliquely at the traction free plane boundary of the considered medium. The formulation is applied under the purview of generalized theory of thermoelasticity with one relaxation time. The problem is solved analytically and it is found that there exists four coupled quasi waves: qP (quasi-P ), qMD (quasi mass diffusion), qT (quasi thermal) and qSV (quasi-SV ) waves propagating with different speeds in a two-dimensional model of the solid. The amplitude ratios, phase velocities and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. Effect of presence of diffusion is analyzed theoretically, numerically and graphically. The number of reflected waves reduce to three in the absence of diffusion as qMD wave will disappear in that case which is physically admissible. Influence of piezoelectric effect, two temperature and anisotropy is discussed on different characteristics of reflected waves such as phase velocity and reflection coefficients. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Thus, the energy conservation law holds at the surface. Finally, all the reflection coefficients are represented graphically through 3D plots to estimate and highlight the effects of frequency and angle of incidence.

To investigate static and free vibration for thin plate bending structures, a four-node quadrilateral finite element is proposed in this research paper. This element has been formulated by using both the assumptions of thin plates theory (Kirchhoff plate theory) and strain approach. The suggested element which possesses only three degrees of freedom (one transverse displacement and two normal rotations) at each of four corner nodes is based on assumed higher-order functions for the various components of strain field that satisfies the compatibility equation. The displacement functions of the developed element are obtained by integrating the assumed strains functions and satisfy the exact representation of the rigid body modes. Several numerical tests in both static and free vibration analysis are presented to assess the performance of the new element. The obtained results show high solution accuracy, especially for coarse meshes, of the developed element compared with analytical and other numerical solutions available in the literature.

In this article a two-dimensional problem of generalized thermoelasticity has been formulated with state space approach. In this formulation, the governing equations are transformed into a matrix differential equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to an isotropic half space problem under Green-Naghdi type-III model i.e., with energy dissipation theory of thermoelasticity in the presence of a magnetic field. The bounding surface is traction free and subjected to a time dependent thermal shock. The solution for temperature distribution, displacements and stress components are obtained and presented graphically. The effect of magnetic field, electric field and phase velocity on the considered parameters is observed in the figures.

Characteristics of creep deformation for 2.25Cr -1Mo were studied using the Monkman–Grant relation. A series of creep tests were conducted on 2.25Cr -1Mo at low-stress levels and at different temperatures ranging from 655 0C to 6850C . The analysis of creep data indicates that 2.25Cr -1Mo is practically supported by Monkman-Grant relationship. Yet, this paper highlights the foremost difficulties associated with the parametric fitting techniques. The damage tolerance factor has been estimated to demonstrate its reliance on the loading conditions and to categorize the material strain concentration. It has been shown that at 55MPa and T=6850C , the tertiary creep stage is not well characterized. Also, this paper identifies a need to provide a serious consideration for an appropriate creep strength factor that would be applied to pressure vessels and to improve the criteria related to design against creep and the prevention of failure.