Journal of Solid Mechanics
Volume:11 Issue: 4, Autumn 2019

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation.

The study of surface waves in a layered media has their viable application in geophysical prospecting. This paper presents an analytical study on the dispersion of torsional surface wave in a pre-stressed heterogeneous layer sandwiched between a pre-stressed anisotropic porous semi-infinite medium and gravitating anisotropic porous half-space. The non-homogeneity within the intermediate layer and upper semi-infinite medium is assumed to rise up, because of quadratic variation and exponential variation in directional rigidity, pre-stress, and density respectively. The displacement dispersion equation for the torsional wave velocity has been expressed in the term of Whitaker function and their derivatives. Dispersion relation and the closed-form solutions have been obtained analytically for the displacement in the layer and the half-spaces. It is determined that the existing geometry allows torsional surface waves to propagate and the observe exhibits that the layer width, layer inhomogeneity, frequency of heterogeneity in the heterogeneous medium has a great impact on the propagation of the torsional surface wave. The influence of inhomogeneities on torsional wave velocity is also mentioned graphically by means plotting the dimensionless phase velocity against non-dimensional wave number for distinct values of inhomogeneity parameters.

The present article deals with the analysis of thermal-bending stresses in a heated thin annular sector plate with simply supported boundary condition under transient temperature distribution using Berger’s approximate methods. The sectional heat supply is on the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the solution of heat conduction is obtained by the classical method. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using thermally induce resultant moment and resultant forces. The numerical calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the results for temperature, deflection, resultant bending moments and thermal stresses have been illustrated graphically with the help of MATHEMATICA software.

Although a few models have been proposed for 3D simulation of different welding processes, 2D models are still more effective in design goals, thus more popular due to the short-time analysis. In this research, replacing "time" by the "third dimension of place", the gas tungsten arc welding process was simulated by the finite element method in two dimensions and in a short time with acceptable accuracy in two steps (non-coupled thermal and mechanical analysis). A new method was proposed for applying initial conditions using temperature values calculated in the preceding step of the solution; this trick reduces nonlinear effects of birth of elements and considerably reduces analysis time. A new parameter was defined for determining thermal boundary conditions to determine the contribution of the imposed surface and volumetric thermal loads. The effect of weld joint geometry on residual stresses and distortion was studied based on a validated simulation program. Results suggest that changing the joint geometry from V</em>-into X</em>-groove, the maximum values of residual stress and distortion are reduced by 20% and 15%, respectively.

One of the best vibration control methods using smart actuators are semi-active approaches which are as strong as active methods and need no external energy supply such as passive ones. Compared with piezoelectric-based, magnetostrictive-based control methods have higher coupling efficiency, higher Curie temperature, higher flexibility to be integrated with curved structures and no depolarization problems. Semi-active methods are well-developed for piezoelectrics but magnetostrictive-based approaches are not as efficient, powerful and well-known as piezoelectric-based methods.  The aim of this work is to propose a powerful semi-active control method using magnetostrictive actuators. In this paper a new type of semi-active suppression methods using magnetostrictive materials is introduced which contains an equipped vibrating structure with magnetostrictive patches wound by a pick-up coil connected to an electronic switch and a capacitor. The novelty of the proposed damping method is switching on the coil current signal using mentioned switch and capacitor which is briefly named SSDC (synchronized switch damping on capacitor). In this paper the characteristics of the semi-active pulse-switching damping technique with magnetostrictive materials are studied and numerical results show significant damping for almost all types of excitations.

In this paper, the pull-in instability of piezoelectric polymeric nanocomposite plates reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) based on modified strain gradient theory (MSGT) is investigated. Various types of SWCNTs are distributed in piezoelectric polymeric plate and also surface stress effect is considered in this research. The piezoelectric polymeric nanocomposite plate is subjected to electro-magneto-mechanical loadings. The nonlinear governing equations are derived from Hamilton's principle. Then, pull-in voltage and natural frequency of the piezoelectric polymeric nanocomposite plates are calculated by Newton-Raphson method. There is a good agreement between the obtained and other researcher results. The results show that the pull-in voltage and natural frequency increase with increasing of applied voltage, magnetic field, FG-SWCNTs orientation angle and small scale parameters and decrease with increasing of van der Waals and Casimir forces, residual surface stress constant. Furthermore, highest and lowest pull-in voltages are belonging to FG-X and FG-O distribution types of SWCNTs.

Reflection and transmission of plane waves between two initially stressed thermoelastic half-spaces with orthotropic type of anisotropy is studied. Incidence of a SV-type wave from the lower half-space is considered and the amplitude ratios of the reflected and transmitted SV-wave, P-wave and thermal wave are obtained by using appropriate boundary conditions. Numerical computation for a particular model is performed and graphs are plotted to study the effect of angle of incidence of the wave and the initial stress parameters of the half-spaces. From the graphical results, it is found that the modulus of reflection and transmission coefficients of the thermal wave is very less in comparison to reflection and transmission coefficients of P- and SV-waves. It is also observed that for vertical incidence of SV-wave we have only reflected and refracted SV-waves and there is no reflected or refracted P and thermal waves, whereas for horizontal incidence of SV-wave there exists only reflected SV-wave and no other reflected or transmitted wave exists. Moreover, it is found that all the reflection and transmission coefficients are strongly affected by the initial stress parameters of the both half-spaces.

The dynamic performance of structures under traveling loads should be exactly analyzed to have a safe and reasonable structural design. Different higher-order shear deformation theories are proposed in this paper to analyze the dynamic stability of thick elastic plates carrying a moving mass. The displacement fields of different theories are chosen based upon variations along the thickness as cubic, sinusoidal, hyperbolic and exponential. The well-known Hamilton’s principle is utilized to derive equations of motion and then they are solved using the Galerkin method. The energy-rate method is used as a numerical method to calculate the boundary curves separating the stable and unstable regions in the moving mass parameters plane. Effects of the relative plate thickness, trajectories radii and the Winkler foundation stiffness on the system stability are examined. The results obtained in this research are compared, in a special case, with those of the Kirchhoff’s plate model for the validation.

The current study presents a mathematical modeling for sandwich panels with foam filled orthogonally rib-stiffened core using Heaviside distribution functions. The governing equations of the static problem have been derived based on classical lamination theory. The present model contains three displacement variables considering all of the stiffness coefficients. A closed form solution using Galerkin’s method is presented for simply supported sandwich panels with foam filled orthogonally rib-stiffened core subjected to uniform lateral static pressure. Compared to previous researches, the present work is comprehensive enough to be used for symmetric, unsymmetric, laminated or filament wound panels with orthogrid stiffeners. The accuracy of the solution is checked both through comparisons with previous works, and the results of simulation with ABAQUS software.

The single point incremental forming (SPIF) is one of the dieless forming processes which is widely used in the sheet metal forming. The correct selection of the SPIF parameters influences the formability and quality of the product. In the present study, the Gurson-Tvergaard Needleman (GTN) damage model was used for the fracture prediction in the numerical simulation of the SPIF process of aluminum alloy 1050. The GTN parameters of AA 1050 sheet were firstly identified by the numerical simulation of tensile test and comparison of the experimental and numerical stress-strain curves. The identified parameters of the GTN damage model were used for fracture prediction in the SPIF process. The numerical results of the fracture position, thickness variation across the sample and forming height were compared with the experimental results. The numerical results had good agreement with the experimental ones. The effect of SPIF main parameters was investigated on the formability of samples by the verified numerical model. These parameters were tool rotation speed, tool feed rate, tool diameter, wall angle of the sample, vertical pitch, and friction between the tool and the blank.

The coupled damage/plasticity model for meso-level which is ply-level in case of Uni-Directional (UD) Fiber Reinforced Polymers (FRPs) is implemented. The mathematical formulations, particularly the plasticity part, are discussed in a comprehensive manner. The plastic potential is defined in effective stress space and the damage evolution is based on the theory of irreversible thermodynamics. The model which is illustrated here has been implemented by different authors previously but, the complete pre-requisite algorithm ingredients used in the implicit scheme implementation are not available in the literature. This leads to the complexity in its implementation. Furthermore, this model is not available as a built-in material constitutive law in the commercial Finite Element Method (FEM) softwares. To facilitate the implementation and understanding, all the mathematical formulations are presented in great detail. In addition, the elastoplastic consistent operator needed for implementation in the implicit solution scheme is also derived. The model is formularized in incremental form to be used in the Return Mapping Algorithm (RMA). The quasi-static load carrying capability and non-linearity caused by the collaborative effect of damage and plasticity is predicted with User MATerial (UMAT) subroutine which solves the FEM problem with implicit techniques in ABAQUS.

The main aim of this paper is to study the material removal phenomenon using the finite element method (FEM) analysis for orthogonal cutting, and the impact of cutting speed variation on the chip formation, stress and plastic deformation. We have explored different constitutive models describing the tool-workpiece interaction. The Johnson-Cook constitutive model with damage initiation and damage evolution has been used to simulate chip formation. Chip morphology, Stress and equivalent plastic deformation has been presented in this paper as results of chip formation process simulation using Abaqus explicit Software. According to simulation results, the variation of cutting speeds is an influential factor in chip formation, therefore with the increasing of cutting speed the chip type tends to become more segmented. Additionally to the chip formation and morphology obtained from the finite element simulation results, some other mechanical parameters; which are very difficult to measure on the experimental test, can be obtained through finite element modeling of chip formation process.

We study the thermoelastic deformation of an elastic layer. The upper surface of the medium is subjected to a uniform thermal field along a circular area while the layer is resting on a rigid smooth circular base. The doubly mixed boundary value problem is reduced to a pair of systems of dual integral equations. The both system of the heat conduction and the mechanical problems are calculated by solving a dual integral equation systems which are reduced to an infinite algebraic one using a Gegenbauer’s formulas.  The stresses and displacements are then obtained as Bessel function series. To get the unknown coefficients, the infinite systems are solved by the truncation method. A closed form solution is given for the displacements, stresses and the stress singularity factors. The effects of the radius of the punch with the rigid base and the layer thickness on the stress field are discussed. A numerical application is also considered with some concluding results.

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen that the phase velocity is strongly influenced by the wave number, the depth of the irregularity, homogeneity parameter and the rigid boundary. The dimensionless phase velocity is plotted against dimensionless wave number graphically for different size of rectangular irregularities and homogeneity parameter with the help of MATLAB graphical routines for both free and rigid boundaries for several cases. The numerical analysis of dispersion equation indicates that the phase velocity of surface waves decreases with the increase in dimensionless wave number.  The obtained results can be useful to the study of geophysical prospecting and understanding the cause and estimating of damage due to earthquakes.

Discovering the mechanical properties of biological composite structures at the Nano-scale is much interesting today. Top Neck mollusk shells are amongst biomaterials Nano-Composite that their layered structures are composed of organic and inorganic materials. Since the Nano indentation process is known as an efficient method to determine mechanical properties like elastic modulus and hardness in small-scale, so, due to some limitation of considering all peripheral parameters; particular simulations of temperature effect on the atomic scale are considerable. The present paper provides a molecular dynamics approach for modeling the Nano-Indentation mechanism with three types of pyramids, cubic and spherical indenters at different temperatures of 173, 273, 300 and 373K</em>. Based on load-indentation depth diagrams and Oliver-Far equations, the findings of the study indicate that results in the weakening bond among the bilateral atoms lead to reduced corresponding harnesses. Whenever, the temperature increases the elastic modulus decrease as well as the related hardness. Moreover, within determining the elastic modulus and hardness, the results obtained from the spherical indenter will have the better consistency with experimental data. This study can be regarded as a novel benchmark study for further researches which tend to consider structural responses of the various Bio-inspired Nano-Composites.

A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP</em> wave generates three types of reflected waves namely quasi-P</em> (qP</em>), quasi-SV</em> (qSV</em>) and quasi-SH</em> (qSH</em>) waves in the triclinic medium and one refracted P</em> wave in the isotropic liquid medium. Expression of phase velocities of all the three quasi waves have been calculated. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation in anisotropic medium. Some specific relations have been established between directions of motion and propagation. The expressions for reflection coefficients of qP, qSV, qSH</em> and refracted P</em> waves with respect to incident qP wave are obtained. Numerical computation and graphical representations have been performed for the reflection coefficient of reflected qP</em>, reflected qSV</em>, reflected qSH</em> and refraction coefficient of refracted P</em> wave with incident qP</em> wave.