Islamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Vibration Analysis of Functionally Graded Spinning Cylindrical Shells Using Higher Order Shear Deformation Theory159170514299ENM MehrparvarDepartment of Mechanical Engineering, Islamic Azad University, Khomeinishahr BranchJournal Article20090719In this paper the vibration of a spinning cylindrical shell made of functional graded material is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. Next, governing differential equation of spinning cylindrical shell is obtained through utilizing energy method and Hamilton’s principle. Making use of the principle of minimum potential energy, the characteristic equation of natural frequencies is derived. After verification of the results, the effect of changing different parameters such as material grade, geometry of shell and spinning velocity on the natural frequency are examined.http://jsm.iau-arak.ac.ir/article_514299_d1c9c6d32a376e918fc7e81151bb7034.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Thermal Stability of Thin Rectangular Plates with Variable Thickness Made of Functionally Graded Materials171189514300ENM PouladvandFaculty of Engineering, University of Applied Science and Technology, Borojerd BranchJournal Article20090729In this research, thermal buckling of thin rectangular plate made of Functionally Graded Materials (FGMs) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The supporting condition of all edges of such a plate is simply supported. The equilibrium and stability equations of a FGM rectangular plate (FGRP) under thermal loads derived based on classical plate theory (CPT) via variational formulation, and are used to determine the pre-buckling forces and the governing differential equation of the plate. The buckling analysis of a functionally graded plate is conducted using; the uniform temperature rise, having temperature gradient through-the-thickness, and linear temperature variation in the thickness and closed-form solutions are obtained. The buckling load is defined in a weighted residual approach. In a special case the obtained results are compared by the results of functionally graded plates with uniform thickness. The influences of the plate thickness variation and the edge ratio on the critical loads are investigated. Finally, different plots indicating the variation of buckling load vs. different gradient exponent k, different geometries and loading conditions were obtained.http://jsm.iau-arak.ac.ir/article_514300_e4eea9f70232d2c12dcd93657abc9fe3.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Comparison of Two Kinds of Functionally Graded Cylindrical Shells with Various Volume Fraction Laws for Vibration Analysis190200514301ENM.R IsvandzibaeiDepartment of Mechanical Engineering, Sinhgad College of Engineering, University of PuneP.J AwasareDepartment of Mechanical Engineering, Sinhgad College of Engineering, University of PuneJournal Article20090801In this paper, a study on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are taken into account by studying the frequencies of two FG cylindrical shells. Type I FG cylindrical shell has nickel on its inner surface and stainless steel on its outer surface and Type II FG cylindrical shell has stainless steel on its inner surface and nickel on its outer surface. The study is carried out based on third order shear deformation shell theory (TSDT). The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. The analysis is carried out with strains-displacement relations from Love's shell theory. The governing equations are obtained using energy functional with the Rayleigh-Ritz method. Results are presented on the frequency characteristics and the influences of constituent various volume fractions for Type I and II FG cylindrical shells and simply supported boundary conditions on the frequencies.http://jsm.iau-arak.ac.ir/article_514301_00418f871ecfbc997728f4c0b12f27c6.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Buckling Analysis of FG Plate with Smart Sensor/Actuator201212514302ENN.S VilianiDepartment of Mechanical Engineering, Islamic Azad University, Abhar BranchS.M.R KhaliliFaculty of Mechanical Engineering, K.N. Toosi University of Technology-Faculty of Engineering, Kingston UniversityH PorrostamiDepartment of Mechanical Engineering, Islamic Azad University, Abhar BranchJournal Article20091111In this paper, the active buckling control of smart functionally graded (FG) plates using piezoelectric sensor/actuator patches is studied. A simply supported FG rectangular plate which is bonded with piezoelectric rectangular patches on the top and/or the bottom surface(s) as actuators/sensors is considered. When a constant electric charge is imposed, the governing differential equations of motion are derived using the classical laminated plate theory (CLPT). The solution for the equation of motion is obtained using a Fourier series method and the effect of feedback gain on the critical buckling load for PZT-4 is studied .The buckling behavior of smart plate subjected to compressive load is also investigated. The sensor output is used to determine the input to the actuator using the feedback control algorithm. The forces induced by the piezoelectric actuators under the applied voltage field, enhance the critical buckling loadhttp://jsm.iau-arak.ac.ir/article_514302_53aeedb6d24774db870bd3d23ddca30f.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Buckling Analysis of Simply-supported Functionally Graded Rectangular Plates under Non-uniform In-plane Compressive Loading213225514303ENM MahdavianDepartment of Mechanical Engineering, Islamic Azad University, Arak BranchJournal Article20091105In this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling loads have been presented for non-uniformly compressed rectangular plates based on a rigorous superposition fourier solution for the in-plane Airy stress field and Galerkin’s approach for stability analysis. The results for isotropic case will be compared with reference articles and finite element method (FEM) solution. Finally, the results will be achieved for a sample of FGM material as well as the research on the effect of power law index on buckling coefficient.http://jsm.iau-arak.ac.ir/article_514303_028dbf316f86a1389bbc37303e6ede01.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Effect of Stress Triaxiality on Yielding of Anisotropic Materials under Plane Stress Condition226232514304ENS.S BhadauriaDepartment of Applied Mechanics, Maulana Azad National Institute of TechnologyM.S HoraDepartment of Applied Mechanics, Maulana Azad National Institute of TechnologyK.K PathakScientist, Advanced Materials Processes Research Institute (CSIR)Journal Article20091110The triaxiality of the stress state is known to greatly influence the amount of plastic strain which a material may undergo before ductile failure occurs. It is defined as the ratio of hydrostatic pressure, or mean stress, to the von Mises equivalent stress. This paper discusses the effects of stress triaxiality on yielding behavior of anisotropic materials. Hill-von Mises’s criteria for anisotropic material have been used with triaxiality factor (TF). Mathematical model that combines the yield stress and anisotropic ratio R (ratio of width strain to thickness strain) along with triaxiality have been formulated. This model is considered as an objective function subjected to inequality constraint. Constrained optimization is solved using genetic algorithm. The results obtained give the set of principal stresses along with corresponding critical triaxiality which is the maximum value at which the material can sustain without failure. If triaxiality extends further more the material will go to plastic deformation and may prone to failure. In this way, the critical triaxiality of materials can be determined to avoid fracture and failure of materials. This article is important from the industrial application point of view by considering triaxiality as a design parameter while designing the component.http://jsm.iau-arak.ac.ir/article_514304_dcda506fa21c2b73d3cc128c5e00b93c.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930Photoelastic Determination of Mixed Mode Stress Intensity Factors233244514305ENV.K SinghDepartment of Mechanical Engineering, College of Technology, G.B. Pant University of Agriculture & TechnologyP.C GopeDepartment of Mechanical Engineering, College of Technology, G.B. Pant University of Agriculture & TechnologyJournal Article20091117A two dimensional finite model with inclined crack at different crack angles are being analyzed in mixed mode condition using photo elasticity method for the determination of Stress Intensity Factors. The well-known Sih’s equation and three points deterministic approach is used for the determination of stress intensity factors. The effects of biaxial load factor, crack angle, size factors were studied and a regression model was developed for geometry correction to predict Stress Intensity Factors. The results give a good compromise to the theoretical one. The experimental result also gives significant data for the two dimensional mixed mode loading conditions.http://jsm.iau-arak.ac.ir/article_514305_274ae607db76de3d3acde0926ffd29ad.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-35051320090930hp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates245259514306ENR RanjanAdvanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College StationJ.N ReddyAdvanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College StationJournal Article20091125There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized displacements have suffered from shear locking, which has been alleviated with the help of primarily reduced/selective integration techniques to obtain acceptable solutions [1-4]. These kinds of 'fixes' have come into existence because the element stiffness matrix becomes excessively stiff with low-order interpolation functions. In this study we propose an alternative spectrally accurate <em>hp</em>/spectral method to model the Timoshenko beam theory and first order shear deformation theory of plates (FSDT) to eliminate shear and membrane locking. Beams and isotropic and orthotropic plates with clamped and simply supported boundary conditions are analyzed to illustrate the accuracy and robustness of the developed elements. Full integration scheme is employed for all cases. The results are found to be in excellent agreement with those published in literature.http://jsm.iau-arak.ac.ir/article_514306_a40298440af92ed1a8c376d79729afed.pdf