Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Effect of Compressive Residual Stress on the Corner Crack Growth
324
335
EN
M.H
Gozin
Department of Mechanical Engineering, K.N. Toosi University of Technology
M
Aghaie-Khafri
Department of Mechanical Engineering, K.N. Toosi University of Technology
maghaei@kntu.ac.ir
In the present study, plasticity induced crack closure (PICC) concept and three dimensional (3D) finite element methods (FEM) are used to study the effect of compressive residual stress field on the fatigue crack growth from a hole. To investigate the effect of compressive residual stress on crack opening levels and crack shape evolution, Carlson’s experiments were simulated. Crack shape evolution is investigated by employing an automatic remeshing technique using MATLAB-ABAQUS code. The effect of mesh element size is considered by using element sizes of 0.025mm and 0.0125mm. Crack opening level results indicate that the applied residual stress increases the opening levels with an average of 45%. The higher opening levels results in higher number of fatigue cycles by a ratio of 3.07 for 1.9mm surface crack growth increment. Comparing the result obtained with Carlson’s experiments indicates that the crack closure method employed in the present analysis is in good agreement. Comparing the results with Jones’ supeposition method, moreover, illustrates that present paper method is more accurate.
Residual stress,Crack Closure,FEM
http://jsm.iau-arak.ac.ir/article_514575.html
http://jsm.iau-arak.ac.ir/article_514575_c5cfd907e831e20311514e1022e130e0.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Vibration Analysis of Multi-Step Bernoulli-Euler and Timoshenko Beams Carrying Concentrated Masses
336
349
EN
K
Torabi
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan
kvntrb@kashanu.ac.ir
H
Afshari
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan
H
Najafi
Department of Solid Mechanics, Faculty of Mechanical Engineering, Politecnico di Milano, Milan, Italy
In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinuity in geometrical and natural parameters; these changes are shown by transfer matrices depended on the geometry of each step or value of the translational and rotational inertias of each attached element. First, natural frequencies and corresponding normal mode shapes are obtained by implementation of the compatibility conditions and external boundary conditions; Then, the precision of the proposed method is checked by comparison of the results with other exact solutions; Finally, the effect of the translational and rotational inertias and position of the attached elements on the natural frequencies of multi-stepped beams are investigated for various boundary conditions.
Bernoulli-Euler beam,Timoshenko beam,Multi-Step beam,Concentrated mass,Rotary inertia
http://jsm.iau-arak.ac.ir/article_514576.html
http://jsm.iau-arak.ac.ir/article_514576_9cd1f57a3ffe712a16997adc00d7bce5.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Analytical Solution for Response of Piezoelectric Cylinder Under Electro-Thermo-Mechanical Fields
350
370
EN
S
Golabi
Department of Mechanical Engineering, University of Kashan
golabi-s@kashanu.ac.ir
J
Jafari Fesharaki
Department of Mechanical Engineering, University of Kashan
This paper presents an analytical solution for response of a piezoelectric hollow cylinder under two-dimensional electro thermo mechanical fields. The solution is based on a direct method and the Navier equations were solved using the complex Fourier series. The advantage of this method is its generality and from mathematical point of view, any type of the thermo mechanical and electrical boundary conditions can be considered without any restrictions. The thermo mechanical and electrical displacements are assumed that vary in radial and circumferential directions. Finally, three examples were considered to confirm the results and investigate the effect of in-phase and opposite-phase electro thermo mechanical boundary loads on two-dimensional electro thermo mechanical behavior of piezoelectric hollow cylinder. The results are compared with the previous work and FEM analysis. The main result of this study is that, by applying a proper distribution of thermal, electrical and mechanical fields, the distributions of electric and mechanical displacement, thermal and mechanical stresses can be controlled.
Two-Dimensional,Piezoelectric,Thermo elasticity,Cylinder,Analytical solution,Fourier series
http://jsm.iau-arak.ac.ir/article_514577.html
http://jsm.iau-arak.ac.ir/article_514577_b509eacad2b172699a7ef3fd93a4ef6c.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
A New Mathematical Model for Permeability of Composites
371
379
EN
M.M
Shahmardan
Department of Mechanical Engineering, Shahrood University of Technology
M
Nazari
Department of Mechanical Engineering, Shahrood University of Technology
nazari_me@yahoo.com
M
Khaksar
Department of Mechanical Engineering, Shahrood University of Technology
M
Khatib
Department of Mechanical Engineering, Shahrood University of Technology
Study of permeability of Fibrous Composites is important in several natural and industrial processes in mechanical engineering. In this study, a comprehensive mathematical model is presented for calculation of normal permeability of ordered elliptical fibrous media. An innovative scale-analysis technique is employed for determining the normal permeability of elliptical fibrous media. In this technique, the permeability is related to the porosity, elliptical fiber diameters, and tortuosity of the medium. In other word, the normal permeability of the circular fibrous structures, which presented in the literature, is extended to the general case of elliptical fibrous media. The composite material is represented by a “unit cell” which is assumed to be repeated throughout the media. A closed-form relation is obtained for non-dimensional permeability using scale analysis approach. Due to lack of experimental data for permeability of fibrous porous media (composite media), with elliptical cross section, a numerical analysis is also employed. The governing equations are solved numerically in the unit cells using finite volume method. The results obtained by numerical solution are compared with those presented by scale analysis method. The presented relation for normal permeability can suitably cover the case of fibrous media with circular cross section. The results are also compared with those presented in the literature for the case of cylindrical fibers. The developed compact relationships are successfully verified through comparison with the present experimental results and the data reported by others.
mathematical model,permeability,Elliptical,Composite,Scale analysis
http://jsm.iau-arak.ac.ir/article_514578.html
http://jsm.iau-arak.ac.ir/article_514578_7c11b67e061361a2f727da58690c25aa.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Isogeometric-Based Modeling and Analysis of Laminated Composite Plates Under Transverse Loading
380
390
EN
A
Behshad
Faculty of Engineering, University of Sistan and Baluchestan, Zahedan
ambehshad@yahoo.com
M.R
Ghasemi
Faculty of Engineering, University of Sistan and Baluchestan, Zahedan
Analysis of the laminated composite plates under transverse loading is considered using the new method of Isogeometric Analysis (IGA). Non-Uniform Rational B-Splines(NURBS)are used as shape functions for modeling the geometry of the structure and also are used as shape functions in the analysis process. To show robustness of the new technique, some examples are represented and are compared with the theoretical method at the end. The obtained results show the efficiency of the method.
Isogeometric analysis,Nun-Uniform rational B-Splines,Composite plates,Genetic Algorithm
http://jsm.iau-arak.ac.ir/article_514579.html
http://jsm.iau-arak.ac.ir/article_514579_af6e1f751330cfc7a4ea74724a7bb09f.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Response Determination of a Beam with Moderately Large Deflection Under Transverse Dynamic Load Using First Order Shear Deformation Theory
391
401
EN
F
Sohani
Mechanical Engineering Faculty, Shahrood University
H.R
Eipakchi
Mechanical Engineering Faculty, Shahrood University
web2-eipakchi@shahroodut.ac.ir
In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive equation. These equations which are a system of nonlinear partial differential equations with constant coefficients are derived by using the Hamilton’s principle. The eigenfunction expansion method and the perturbation technique are applied to obtain the response. The results are compared with the finite elements method.
First-order shear deformation theory,Response determination,Perturbation technique,Eigenfunction expansion,Moderately large deflection
http://jsm.iau-arak.ac.ir/article_514580.html
http://jsm.iau-arak.ac.ir/article_514580_3fc0e5a0a278723055ad4812cd4a53ef.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Mechanical Stresses in a Linear Plastic FGM Hollow and Solid Rotational Disk
402
417
EN
M
Jabbari
South Tehran Branch, Islamic Azad University
mohsen.jabbari@gmail.com
A
Hatefkia
South Tehran Branch, Islamic Azad University
M
Shokouhfar
South Tehran Branch, Islamic Azad University
miladshokouhfar@gmail.com
In this paper, an analytical solution for computing the plastic & linear plastic stresses and critical angular velocity in a FGM hollow & solid rotating disk is developed. It has been assumed that the modulus of elasticity and yield strength were varying through thickness of the FGM material according to a power law relationship. The Poisson's ratio were considered constant throughout the thickness. In the analysis presented here the effect of non-homogeneity in FGM rotating disk was implemented by choosing a dimensionless parameter, named m, which could be assigned an arbitrary value affecting the stresses in the rotating disk. Distribution of stresses in radial and circumferential directions for FGM rotating disk under the influence of angular velocity were obtained. Graphs of variations of stress, critical angular velocity versus radius of the rotating disk were plotted. The direct method is used to solve the Navier equations.
Hollow & solid disk,Non-Homogenous,Axisymmetric,FGM,Elastic-plastic analysis
http://jsm.iau-arak.ac.ir/article_514581.html
http://jsm.iau-arak.ac.ir/article_514581_d92932d8bb75a507b0ed10b1701a7f70.pdf
Islamic Azad University - Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
5
4
2013
12
30
Plane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space
418
435
EN
A
Miglani
Department of Mathematics, Ch. Devi Lal University
N
Kumari
Department of Mathematics, Ch. Devi Lal University
neelamkumaricdlu@gmail.com
The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained conditions in high frequency limit. The undrained displacements, stresses and pore pressure in poroelastic medium are plotted and discussed to draw the conclusions.
Poroelastic,Line load,Undrained state,Displacements,Stresses
http://jsm.iau-arak.ac.ir/article_514582.html
http://jsm.iau-arak.ac.ir/article_514582_24a43e127a6c477c39ecedd06ec3cadd.pdf