Journal of Solid Mechanics
Volume:9 Issue: 4, Autumn 2017

In this article, electro-thermo nonlocal nonlinear vibration and instability of viscous-fluid-conveying double–walled boron nitride nanotubes (DWBNNTs) embedded on Pasternak foundation are investigated. The DWBNNT is simulated as a Timoshenko beam (TB) which includes rotary inertia and transverse shear deformation in the formulation. Considering electro-mechanical coupling, the nonlinear governing equations are derived using Hamilton’s principle and discretized based on the differential quadrature method (DQM). The lowest four frequencies are determined for clamped-clamped boundary condition. The effects of dimensionless small scale parameter, elastic medium coefficient, flow velocity, fluid viscosity and temperature change on the imaginary and real components of frequency are also taken into account. Results indicate that the electric potential increases with decreasing nonlocal parameter. It is also worth mentioning that decreasing nonlocal parameter and existence of Winkler and Pasternak foundation can enlarge the stability region of DWBNNT.

Fracture analysis of glass/epoxy composites under different thermal cycling conditions is considered. Temperature difference, stacking sequence, fiber volume fraction and number of thermal cycles are selected as the experimental design factors. The Taguchi method is implemented to design of the experiment and an apparatus is developed for automatic thermal cycling tests. The tensile tests are done to study mechanical behavior of the specimens after the thermal cycling. The results show that the stacking sequence is the main effective factor on the fracture surface behavior of the specimens. Also, long splitting, lateral and angled breakage are the dominate failure mode of [0]8, [02/902]s and [0/±45/90]s layups, respectively. It’s found that the thermal cycling and temperature difference cause to increase the surface matrix loss significantly. This surface matrix loss can be an initial region to matrix debonding and crack propagation. Also, when the angle difference between lamina is increased the mechanical properties are reduced under the thermal cycling, significantly.

This paper presents the surface piezomagnetoelasticity theory for size-dependent buckling analysis of an embedded piezoelectric/magnetostrictive nanobeam (PMNB). It is assumed that the subjected forces from the surrounding medium contain both normal and shear components. Therefore, the surrounded elastic foundation is modeled by Pasternak foundation. The nonlocal piezomagnetoelasticity theory is applied so as to consider the small scale effects. Based on Timoshenko beam (TB) theory and using energy method and Hamilton’s principle the motion equations are obtained. By employing an analytical method, the critical magnetic, electrical and mechanical buckling loads of the nanobeam are yielded. Results are presented graphically to show the influences of small scale parameter, surrounding elastic medium, surface layers, and external electric and magnetic potentials on the buckling behaviors of PMNBs. Results delineate the significance of surface layers and external electric and magnetic potentials on the critical buckling loads of PMNBs. It is revealed that the critical magnetic, electrical and mechanical buckling loads decrease with increasing the small scale parameter. The results of this work is hoped to be of use in micro/nano electro mechanical systems (MEMS/NEMS) especially in designing and manufacturing electromagnetoelastic sensors and actuators. © 2017 IAU, Arak Branch.All rights reserved.

A Newtonian (vectorial) approach is used to develop the governing differential equations of motion for a three layer sandwich beam in which the uniform distribution of mass and stiffness is dealt with exactly. The model allows for each layer of material to be of unequal thickness and the effects of coupled bending and longitudinal motion are accounted for. This results in an eighth order ordinary differential equation whose closed form solution is developed into an exact dynamic member stiffness matrix (exact finite element) for the beam. Such beams can then be assembled to model a variety of structures in the usual manner. However, such a formulation necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm, whose implementation is discussed in detail. The algorithm enables any desired natural frequency to be converged upon to any required accuracy with the certain knowledge that none have been missed. The accuracy of the method is then confirmed by comparison with five sets of published results together with a further example that indicates its range of application. A number of further issues are considered that arise from the difference between sandwich beams and uniform single material beams, including the accuracy of the characteristic equation, co-ordinate transformations, modal coupling and the application of boundary conditions.

This research pertains to the three-dimensional (3D) finite element analysis (FEA) of the stress intensity factors (SIFs) along the crack front in a spherical pressure vessel coated with functionally graded material (FGM). The vessel is subjected to internal pressure and thermal gradient. The exponential function is adopted for property of FGMs. SIFs are obtained for a wide variety of crack shapes and layer thickness. The reported results clearly show that the material gradation of coating and the crack configuration can significantly affect the variation of SIFs along the crack front. The results are given which are applicable for fatigue life assessment and fracture endurance of FGM coating spherical pressure vessel and can be used in design purposes.

In this paper, an exact closed-form solution is presented for free vibration analysis of Euler-Bernoulli conical and tapered beams carrying any desired number of attached masses. The concentrated masses are modeled by Dirac’s delta functions which creates no need for implementation of compatibility conditions. The proposed technique explicitly provides frequency equation and corresponding mode as functions with only two integration constants which leads to solution of a two by two eigenvalue problem for any number of attached masses. Using Basic functions which are made of the appropriate linear composition of Bessel functions leads to make implementation of boundary conditions much easier. The proposed technique is employed to study effect of quantity, position and translational inertia of the concentrated masses on the natural frequencies and corresponding modes of conical and tapered beams for all standard boundary conditions. Unlike many of previous exact approaches, presented solution has no limitation in number of concentrated masses. In other words, by increase in number of attached masses, there is no considerable increase in computational effort.

In the present paper, we are contemplating the influences of heterogeneities and pre-stresses on the propagation of Love-type waves in an initially stressed heterogeneous transversely isotropic layer of finite thickness lying over an inhomogeneous half space. The material constants and pre-stress have been taken as space dependent and arbitrary functions of depth in the respective media. To simplify the problem, we have used Whittaker’s function and separation of variables method. We present a general dispersion relation to describe the impacts on the propagation of Love-type waves in the structure. The present dispersion relation is analyzed case wise and also validated by comparison of the standard Love wave equation. Further, numerical computations are demonstrated graphically for the set of dimensionless parameters between dimensionless phase velocity and dimensionless wave number of the wave.

Besides experimental methods, numerical simulations bring benefits and great opportunities to characterize and predict mechanical behaviors of materials especially at nanoscale. In this study, a nano-single crystal aluminum (Al) as a typical face centered cubic (FCC) metal was modeled based on molecular dynamics (MD) method and by applying tensile and compressive strain loadings its mechanical behaviors were investigated. Embedded atom method (EAM) was employed to represent the interatomic potential of the system described by a canonical ensemble. Stress-strain curves and mechanical properties including modulus of elasticity, Poisson’s ratio, and yield strength were determined. Furthermore, the effects of strain rate and system temperature on mechanical behavior were obtained. It was found that the mechanical properties exhibited a considerable dependency to temperature, but they hardly changed with increase of strain rate. Moreover, nucleation and propagation of dislocations along the plane of maximum shearing stress were the mechanisms of the nanocrystalline Al plastic deformation.

Buckling of imperfect thin shell tank which is subjected to uniform axial compression is analyzed. The effect of internal pressure on the stability of a shell tank filled with a homogeneous-heterogeneous liquid was considered. Investigation of the liquid nature effect on reduction of the shell buckling load is performed by using the finite elements method. Calculating results in terms of analytical formula give a good agreement with the numerical results given by Abaqus when using actual measurements. The obtained results show the influence of the physical characteristics of liquid especially in the case of heterogeneous liquid. The study of combination between compression load, lateral pressure and the mechanical properties of liquid filling the tank is recommended for dimensioning the shell tanks to avoid the buckling phenomenon.

In this paper, accumulation of plastic deformation of AISI 1045 steel plates with circular cutouts under cyclic axial loading is studied. Loading was applied under force-control conditions. Experimental tests were performed using a Zwick/Roell servo hydraulic machine. Under force-control loading with nonzero mean force, plastic strain was accumulated in continuous cycles called ratcheting. Numerical analysis was carried out by ABAQUS software using nonlinear isotropic/kinematic hardening model. The results of the numerical simulations were compared to experimental data. The results demonstrated that the ratcheting response of plates with circular cutouts could be numerically simulated with a reasonable accuracy. It was observed that the local and global plastic deformation increase with increasing the notch diameter. Also, maximum principal stress was the main parameter for initiation of crack around the notch. Based on numerical results, at notch root, both ratcheting strain and local mean stress relaxation was occur simultaneously and due to relaxation of local mean stress, plastic shakedown was occurred.

In this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined through numerical examples. Effect of FGM power law index, plate aspect ratio, elastic foundation stiffness and metal core thickness on critical buckling load is investigated. The accuracy of this approach is verified by comparing its results to those obtained in another work, which is performed using Fourier series expansion.

This article has studied the effect of ratio of stiffness and thickness between piezoelectric actuators and host plat has been explored on optimal pattern for placement of piezoelectric work pieces around a hole in thin isotropic plate under static loading to reduce stress concentration. The piezoelectric actuators reduce directly or indirectly the stress concentration by applying positive and negative strains on the host plate. For this purpose, various modes as the thickness/stiffness ratios of the plate to the piezoelectric patches as ≥1 or ≤1 were considered. Then, a Python code was developed using particle swarm optimization algorithm in order to achieve the best model of piezoelectric actuators around the hole for maximum reduction in stress concentration factor. Also, the maximum stress concentration on the top and bottom of the hole was moved to another point around the edge by changing the location of piezoelectric patches. The results obtained from software solutions were confirmed by experimental tests.

In this paper, semi-analytical method for asymmetrical eccentrically stiffened FGM cylindrical shells under external pressure and surrounded by a linear and non-linear elastic foundation is presented. The proposed linear model is based on two parameter elastic foundation Winkler and Pasternak. According to the von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method, used for solving nonlinear problem. To finding the nonlinear dynamic response of fourth order Runge-Kutta method is used. The effect of parameters asymmetrical eccentrically stiffened on the nonlinear dynamic buckling response of FGM cylindrical shells have been investigated.

The present study aims at investigating stress and deformation behavior of rotating thick truncated conical shells subjected to variable internal pressure. Material prpperties of the shells are graded along the axial direction by Mori-tanaka scheme, which is achieved by elemental gradation of the properties.Governing equations are derived using principle of stsionary total potential (PSTP) and shells are subjected to clamped- clamped boundary conditions. Aluminum-zirconia, metal-ceramic and ceramic-metal FGM is considered and effects of grading index of material properties and pressure distribution are analyzed. Distribution of Radial displacement and circumferential stress in both radial and axial direction is presented. Further a comparison of behaviors of different FGM shells and homogeneous shells are made which shows, a significant reduction in stresses and deformations of FGM shells as compared to homogeneous shell. FGM shell having value of grading parameter n = 2 is most suitable for the purpose of rotating conical shells having variable pressure distribution as compared to homogeneous shell and shell having other values of grading parameter n.

In this article the influence of welding parameters such as electrical current, feed rate and stick out on crack growth energy was investigated. Therefore, prepared specimens were welded in various conditions. Using the Minitab software, 18 states of 36 possible states were chosen and applied. Then a crack was crated on the weld metal and the force-displacement diagram was plotted. Comparison of results shows that in high electricity current, the extra heat flux is the dominant factor, which causes coarse grains of microstructures. On the other hand, in low electricity current, lack of fusion and penetration reduce the crack propagation energy. Furthermore, the neural network could predict the amount of energy with high accuracy.

In automotive industry fixtures have a direct effect on product manufacturing quality, productivity and cost, as a result fixtures, particularly welding fixture, play a crucial role in the auto industry. The fixture is a special tool for holding a work piece in proper position during manufacturing operation, so in the phase of the fixture design process positioning pins and surfaces are used to make sure that the work piece is positioned correctly and remain in the same position throughout the operation. The less positioning surfaces leads to the less work piece deformation. The aim of this paper is to find optimal number of positioning surfaces using VIKOR method with Shanon entropy concept to extract and utilize objective weights. VIKOR, means multi-criteria optimization and compromise solution, is a modern approach that has preference over other MCDM methods. An empirical example is presented to demonstrate an application of mentioned method.