فهرست مطالب

Solid Mechanics - Volume:10 Issue: 3, 2018
  • Volume:10 Issue: 3, 2018
  • تاریخ انتشار: 1397/06/02
  • تعداد عناوین: 16
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  • M.M Najafizadeh* , M Raki, P Yousefi Pages 464-475
    In present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based on two different models of power function and exponential function. All equations governing on the vibration of FG Nano-plate have been derived from Hamilton’s principle. It has been also obtained the analytical solution for natural frequencies and corresponding mode shapes of simply supported FG Nano-plates. In addition, the general form of stiffness and mass matrix elements has been expressed based on this theory. The effect of different parameters such as power and exponential indexes of targeted function , nonlocal parameter of Nano-plate, aspect ratio and thickness to length ratio of Nano-plate on non-dimensional natural frequencies of free vibration responses have been investigated. The obtained analytical results show an excellent agreement with other available solutions of previous studies. The formulation and analytical results obtained from proposed method can be used as a benchmark for further studies to develop this area of research.
    Keywords: Nano-plate, Functionally graded material (FGM), Nonlocal elasticity, Third order of shear deformation theory (TSDT), natural frequency
  • H Behzad, A.R Shaterzadeh *, M Shariyat Pages 476-488
    In this paper, mechanical buckling analysis of composite annular sector plates with bean shape cut out is studied. Composite material sector plate made of Glass-Epoxy and Graphite-Epoxy with eight layers with same thickness but different fiber angles for each layer. Mechanical loading to form of uniform pressure loading in radial, environmental and biaxial directions is assumed. The method used in this analysis is three dimensional (3D) finite elements based on the elasticity relations. With zero first and second variation of potential energy of the entire annular sector plate, we find stability equation. Green non-linear displacement strain relations to obtain geometric stiffness matrix is ​​used. Unlike many studies, in present work three dimensional finite elements method has been used with an eight node element and meshing in the thickness direction is done, too. The bean shaped cut out in the sector has increased the complexity of the analysis. The continuing, effect of different parameters including cut out dimensions, fiber angles of layers, loading direction and dimensions of the annular sector plate on the mechanical buckling load has been investigated and interesting results have been obtained.
    Keywords: Annular sector plate, Composite material, 3D finite elements method, Mechanical buckling
  • S.F Asbaghian Namin, R Pilafkan * Pages 489-501
    This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the most common nano-plates. On the other hand, governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different side lengths, boundary conditions, and nonlocal parameter are inspected for the aforementioned methods. The results obtained from the MD simulations are compared with those of nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. As a result, for the first time, the nonlocal parameter values are suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.
    Keywords: Nano-plates, Molecular dynamics simulations, Fundamental frequencies, Nonlocal elasticity theory, Nonlocal parameter
  • Gh Debkumar *, L Abhijit, R Kumar, R Surath Pages 502-521
    The present paper is devoted to the determination of displacement, stresses and temperature from three dimensional anisotropic half spaces due to presence of heat source. The normal mode analysis technique has been used to the basic equations of motion and generalized heat conduction equation proposed by Green-Naghdi model-II [1]. The resulting equation are written in the form of a vector –matrix differential equation and exact expression for displacement component, stresses, strains and temperature are obtained by using eigen value approach. Finally, temperature, stresses and strain are presented graphically and analyzed.
    Keywords: Eigenvalue, Generalized thermoelasticity, Normal mode analysis, vector-matrix, Differential equation
  • L Nourine *, A Sahli, S Sahli Pages 522-531
    This paper deals with the development of a numerical simulation methodology for estimating damages in laminate composite materials caused by a low-speed impact. Experimental tests were performed on laminate plates reinforced with woven carbon fibers and epoxy resin. Three thickness plates were evaluated. The impact loads were transversal and punctual. Two lamina failure criteria were evaluated. The first is the maximum stress. The second is a proposed modification of the Hashin failure criterion. Four lamina degradation criteria were evaluated too. The numerical contact loads between the plate and impactor were well represented. The numerical damaged areas and lengths were similar or greater than the experimental results.
    Keywords: Criterion damage, Failure criteria, Impact, Laminate composite materials, Damage strength
  • M.M Mohammadi *, M Hamedi, H Daneshpajooh Pages 532-546
    In this paper, the general case of an anisotropic thermo-electro elastic body subjected to static biasing fields is considered. The biasing fields may be introduced by heat flux, body forces, external surface tractions, and electric fields. By introducing proper thermodynamic functions and employing variational principle for a thermo-electro elastic body, the nonlinear constitutive relations and the nonlinear equation of motion are extracted. The equations have the advantage of employing the Lagrangian strain and second Piola-Kirchhoff stress tensor with symmetric characteristics. These equations are used to analyze the high frequency vibrations of piezoelectric resonators under finite biasing fields. A system of three dimensional equations is derived for initial and incremental fields on the body. Capability of the equations in numerical modelling of temperature-frequency and force-frequency effects in quartz crystal is demonstrated. The numerical results compare well with the data from experiments. These equations may be used in accurate modelling of piezoelectric devices subjected to thermo electro mechanical loads.
    Keywords: Nonlinear equations, Thermo-electro elasticity, Initial static bias, Resonators
  • F Farhadzadeh, M Tajdari *, M Salmani Tehrani Pages 547-560
    The current paper primarily aims to suggest a mathematical model for the shape-dependent term of Khan- Liu (KL) Yield/ fracture criterion as a function of Plastic Strain for DP590 steel alloy. The shape-dependent term in the mention criterion can generalize the application of this criterion in order to predict the behavior of other materials. Plane stress case and the first quarter of the stress plane have been specifically studied. Uniaxial stresses in rolling and transverse directions of sheet and also the tensions caused by equal-biaxial tension have been experimentally used. Then, material constants of KL yield/ fracture criterion and Khan- Huang- Liang (KHL) constitutive equation are calculated using genetic algorithm (GA) optimization and the value of the shape-dependent factor in KL criterion is extracted. The same has been repeated for various plastic strains and finally a polynomial mathematical model based on the plastic strain for the KL shape-dependent factor is suggested. Hence, material constants of KL criterion could be calculated using at least tests namely experimental uniaxial stress test, experimental equal-biaxial stress, and one of the optimization models such as GA. Using the given mathematical model based on the plastic strain, correction term can be calculated and the generalized form of KL criterion can be used for various ductile metallic materials.
    Keywords: Yield-fracture criterion, Constitutive equation, Shape-dependent term, Cruciform specimen, DP590 Steel alloy
  • Sh Dastjerdi *, L Yazdanparast Pages 561-570
    The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before has been used. By applying SAPM method, the nonlinear partial differential equations have been transformed to the nonlinear algebraic equations system. Then, the nonlinear algebraic equations have been solved by using Newton–Raphson method. The obtained results of this study have been compared with the results of other references and the accuracy of the results has been shown. The effect of some important parameters on the results such as the location of the circular hole, the ratio of major to minor radiuses of elliptical plate, the size of circular hole and boundary conditions have been studied. It is concluded that applying the presented method is very convenient and efficient. So, it can be used for analyzing the mechanical behavior of elliptical plates, instead of relatively complicated formulations in elliptic coordinates system.
    Keywords: Elliptical plate, Eccentric circular hole, First-order shear deformation theory, Semi-analytical polynomial method (SAPM)
  • K Seghir, M Bendaoui, R Benbouta * Pages 571-580
    The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of an isotropic elastic layer compressed by two rigid cylinders with flat ends. Hankel transformation and auxiliary functions with boundary conditions reduce the differential equation to an algebraic equations system, which can be solved in a numerical way. The contact efforts equations are established. From the general method, solutions of particular cases are also resolved. A particular case is studied, the contact zone pressure and stresses distribution curves are presented.
    Keywords: Contact problem, Elastic layer, Cylindrical punches, Flat ends
  • S Yadav*, S Sharma Pages 581-590
    In this paper, a numerical solution has been developed for hollow circular cylinders made up of orthotropic material which is subjected to twist using micro polar theory. The effect of twisting moment and material internal length on hollow thick-walled circular cylinder made up of micro polar orthotropic material is investigated. Finite difference method has been used to exhibit the influence of shear moduli and material internal length on shear stresses and couple stresses. It is found that the effect of small characteristic length on shear stresses is negligible and couple stresses present its significance when characteristic length is large in solid particle. The behavior of couple stresses are nonlinear for large internal length while for small internal length couple stresses are linear in nature except near the free boundaries. Torsion in hollow cylinder made up of micro polar orthotropic play vital role in the presence of cracks and holes. Therefore, torsional analysis of hollow cylinder plays important role in the field of biomechanics.
    Keywords: Elastic, Orthotropic, Micro polar, Characteristics length, Twist, Couple stress
  • R.M Prasad *, S Kundu Pages 591-602
    This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dispersion equation of Love wave has been deduced for existing geometry of the problem under suitable boundary conditions using variable separation method. It has also been observed that for a homogeneous layer with rigidity lying over a regular homogeneous isotropic half-space, the velocity equation coincides with the classical results of Love wave. The effect of the medium characteristics on the dispersion of Love waves has been discussed and the results are displayed with graphs by means of MATLAB programming to clear the physical significance. The study of Love wave dispersion with irregular interface helps civil engineers in building construction, analysis of earthquake in mountain roots, continental margins, and so on. It is also beneficial for the study of seismic waves generated by artificial explosions.
    Keywords: Fiber reinforcement, Rectangular irregularity, Heterogeneous half-space, Phase velocity
  • A.R Shahani *, G Rezazadeh, A Rahmani Pages 603-620
    In the present work the pull-in voltage of a micro cracked cantilever beam subjected to nonlinear electrostatic pressure was studied. Two mathematical models were employed for modeling the problem: a lumped mass model and a classical beam model. The effect of crack in the lumped mass model is the reduction of the effective stiffness of the beam and in the beam model; the crack is modeled as a massless rotational spring the compliance of which is related to the crack depth. Using these two models the pull-in voltage is extracted in the static and dynamic cases. Stability analysis is also accomplished. It has been observed that the pull-in voltage decreases as the crack depth increases and also when the crack approaches the clamped support of the beam. The finding of this research can further be used as a non-destructive test procedure for detecting cracks in micro-beams.
    Keywords: MEMS, Cracked micro-beam, Stability analysis
  • S Devi *, R Kumar Pages 621-636
    In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode analysis. The solutions for the free vibrations of plates under clamped-simply supported (CS) and clamped-free (CF) conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for couple stress generalized thermoelastic and coupled thermoelastic plates. A computer algorithm has been constructed to obtain the numerical results. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically in the absence and presence of couple stress for (i) clamped-simply supported, (ii) clamped-free boundary conditions. Some particular cases are also presented.
    Keywords: Modified couple stress theory, Thermoelasticity, Thermoelastic damping, Frequency shift
  • B Prasad *, P Chandra Pal, S Kundu Pages 637-654
    A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the corrugation. Further, closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). Numerical computations for this particular type of corrugated interface are performed and a number of graphs are plotted to illustrate the effect of different parameters of the both half-spaces on the reflection and transmission coefficients. It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave and are strongly influenced by the anisotropy, inhomogeneity and visco-elasticity of the half-spaces. Some special cases are also derived.
    Keywords: SH-waves, Visco-elastic, Inhomogeneity, Anisotropy, Corrugated boundary
  • V Kaliraman *, P.K Poonia Pages 655-671
    This paper deals with the reflection and transmission of elastic waves from imperfect interface separating a micropolar elastic solid half-space and a fluid saturated porous solid half-space. Longitudinal and transverse waves impinge obliquely at the interface. Amplitude ratios of various reflected and transmitted waves are obtained and computed numerically for a specific model and results obtained are depicted graphically with angle of incidence of incident waves. It is found that these amplitude ratios depend on angle of incidence of the incident wave, imperfect boundary and material properties of half-spaces. From the present study, a special case when fluid saturated porous half-space reduces to empty porous solid is also deduced and discussed graphically.
    Keywords: Porous solid, Micro polar elastic solid, Reflection, Transmission, Longitudinal wave, Transverse wave, Amplitude ratios, Stiffness
  • k.S Sai Ram* , K Pratyusha, P Kiranmayi Pages 672-687
    The free vibration analysis of the functionally graded cylindrical shell panels with and without cutout is carried out using the finite element method based on a higher-order shear deformation theory. A higher-order theory is used to properly account for transverse shear deformation. An eight noded degenerated isoparametric shell element with nine degrees of freedom at each node is considered. The stiffness and mass matrices are derived based on the principle of minimum potential energy. The stiffness and mass matrices of the element are evaluated by performing numerical integration using the Gaussian quadrature. The effect of volume fraction exponent on the fundamental natural frequency of simply supported and clamped functionally graded cylindrical shell panel without a cutout is studied for various aspect ratios and arc-length to thickness ratios. Results are presented for variation of the fundamental natural frequency of the cylindrical shell panel with cutout size for simply supported and clamped boundary conditions.
    Keywords: Functionally graded materials, Free vibration, Finite element method, Higher-order shear deformation theory, Cylindrical shell panel with a cutout