Islamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Multiscale Analysis of Transverse Cracking in Cross-Ply Laminated Beams Using the Layerwise Theory118514315ENWJin NaDepartment of Mechanical Engineering, Texas A&M University, College StationJ.NReddyDepartment of Mechanical Engineering, Texas A&M University, College StationJournal Article20091225A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numerical solutions with the elasticity solutions available in the literature; an excellent agreement is found. The layerwise beam model is then used to investigate the influence of transverse cracks on material properties and the response in cross-ply laminates using a multiscale approach. The multiscale analysis consists of numerical simulations at two different length scales. In the first scale, a mesoscale, a systematic procedure to quantify the stiffness reduction in the cracked ply is proposed exploiting the laminate theory. In the second scale, a macroscale, continuum damage mechanics approach is used to compute homogenized material properties for a unit cell, and the effective material properties of the cracked ply are extracted by the laminate theory. In the macroscale analysis, a beam structure under a bending load is simulated using the homogenized material properties in the layerwise finite element beam model. The stress redistribution in the beam according to the multiplication of transverse cracks is taken into account and a prediction of sequential matrix cracking is presented.http://jsm.iau-arak.ac.ir/article_514315_168593bf8c9067ae1cc6d2eaa6ab27ad.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Elastic Buckling of Moderately Thick Homogeneous Circular Plates of Variable Thickness1927514353ENS.KJalaliFaculty of Mechanical Engineering, College of Engineering, University of TehranM.HNaeiFaculty of Mechanical Engineering, College of Engineering, University of TehranJournal Article20100108In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the thickness variation profile and aspect ratio on the buckling behavior is examined. The comparison shows that the results derived, using the current method, compare very well with those available in the literature.http://jsm.iau-arak.ac.ir/article_514353_67468b8beb7629452bbf84bdef2dd781.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Effect of Rotation and Stiffness on Surface Wave Propagation in a Elastic Layer Lying Over a Generalized Thermodiffusive Elastic Half-Space with Imperfect Boundary2842514354ENRKumarDepartment of Mathematics, Kurukshetra UniversityVChawlaDepartment of Mathematics, Kurukshetra UniversityJournal Article20091217The present investigation is to study the surface waves propagation with imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of Green-Lindsay (G-L model) theory. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed at the free plane boundary. Specific loss of energy is obtained and presented graphically. The effects of rotation on phase velocity, attenuation coefficient and amplitudes of displacements, temperature change and concentration are depicted graphically. Some Special cases of interest are also deduced and compared with known results.http://jsm.iau-arak.ac.ir/article_514354_5611efd0659aa849e2c3d0d9c8d4c2ba.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Rubber/Carbon Nanotube Nanocomposite with Hyperelastic Matrix4349514355ENMMotamediDepartment of Mechanical Engineering, University of TehranMMoosavi MashhadiDepartment of Mechanical Engineering, University of TehranJournal Article20100302An elastomer is a polymer with the property of viscoelasticity, generally having notably low Young's modulus and high yield strain compared with other materials. Elastomers, in particular rubbers, are used in a wide variety of products ranging from rubber hoses, isolation bearings, and shock absorbers to tires. Rubber has good properties and is thermal and electrical resistant. We used carbon nanotube in rubber and modeled this composite with ABAQUS software. Because of hyperelastic behavior of rubber we had to use a strain energy function for nanocomposites modeling. A sample of rubber was tested and gained uniaxial, biaxial and planar test data and then the data used to get a good strain energy function. Mooney-Rivlin form, Neo-Hookean form, Ogden form, Polynomial form, reduced polynomial form, Van der Waals form etc, are some methods to get strain function energy. Modulus of elasticity and Poisson ratio and some other mechanical properties gained for a representative volume element (RVE) of composite in this work. We also considered rubber as an elastic material and gained mechanical properties of composite and then compared result for elastic and hyperelastic rubber matrix together.http://jsm.iau-arak.ac.ir/article_514355_0b7ef48df0f22d51ec32eed0ab7ba7f4.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Effect of Initial Stress on Propagation of Love Waves in an Anisotropic Porous Layer5062514356ENSGuptaDepartment of Applied Mathematics, Indian School of MinesAChattopadhyayDepartment of Applied Mathematics, Indian School of MinesD.KMajhiDepartment of Applied Mathematics, Indian School of MinesJournal Article20100116In the present paper, effect of initial stresses on the propagation of Love waves has been investigated in a fluid saturated, anisotropic, porous layer lying in welded contact over a prestressed, non-homogeneous elastic half space. The dispersion equation of phase velocity has been derived. It has been found that the phase velocity of Love waves is considerably influenced by porosity and anisotropy of the porous layer, inhomogeneity of the half-space and prestressing present in the media, the layer and the half-space. The effect of the medium characteristics on the propagation of Love waves has been discussed and results of numerical calculations have been presented graphically.http://jsm.iau-arak.ac.ir/article_514356_23e90f1972ca5b958896fac6bf66c418.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330A Semi-Analytical Solution for Free Vibration and Modal Stress Analyses of Circular Plates Resting on Two-Parameter Elastic Foundations6378514357ENM.MAlipourFaculty of Mechanical Engineering, K.N. Toosi University of TechnologyMShariyatFaculty of Mechanical Engineering, K.N. Toosi University of TechnologyMShabanFaculty of Mechanical Engineering, K.N. Toosi University of TechnologyJournal Article20100302In the present research, free vibration and modal stress analyses of thin circular plates with arbitrary edge conditions, resting on two-parameter elastic foundations are investigated. Both Pasternak and Winkler parameters are adopted to model the elastic foundation. The differential transform method (DTM) is used to solve the eigenvalue equation yielding the natural frequencies and mode shapes of the circular plates. Accuracy of obtained results is evaluated by comparing the results with those available in the well-known references. Furthermore, effects of the foundation stiffness parameters and the edge conditions on the natural frequencies, mode shapes, and distribution of the maximum in-plane modal stresses are investigated.http://jsm.iau-arak.ac.ir/article_514357_3df1d88c2abfd64c2940fe58dbcfa42c.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330A Static Flexure of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory7990514358ENY.MGhugalDepartment of Applied Mechanics, Government Engineering CollegeA.SSayyadDepartment of Applied Mechanics, Government Engineering CollegeJournal Article20100125A Trigonometric Shear Deformation Theory (TSDT) for the analysis of isotropic plate, taking into account transverse shear deformation effect as well as transverse normal strain effect, is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, trigonometric shear deformation theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. It accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free surface conditions at the top and bottom surfaces of the plate. The theory obviates the need of shear correction factor like other higher order or equivalent shear deformation theories. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexural analysis of simply supported thick isotropic plates for various loading cases are compared with those of other refined theories and exact solution from theory of elasticity.http://jsm.iau-arak.ac.ir/article_514358_a4a2b358aec70795b97288a810b365c3.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35052120100330Study of Wave Motion in an Anisotropic Fiber-Reinforced Thermoelastic Solid91100514359ENRKumarDepartment of Mathematics, Kurukshetra UniversityR.RGuptaDepartment of Mathematics, Maharishi Markandeshwar UniversityJournal Article20091215The present investigation deals with the propagation of waves in the layer of an anisotropic fibre reinforced thermoelastic solid. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitude of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for Cobalt material and the dispersion curves, amplitude of displacements and temperature distribution for symmetric and skew-symmetric wave modes to examine the effect of anisotropy. Some particular cases are also deduced.http://jsm.iau-arak.ac.ir/article_514359_c11d02a3c00cf7e1e9f3ac41ac2c6788.pdf