eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
445
455
533175
Displacement Field Due to a Cylindrical Inclusion in a Thermoelastic Half-Space
K Singh
1
M Renu
renumuwal66@gmail.com
2
Department of Mathematics,Guru Jambheshwar ,University of Science & Technology, Hisar, Pin-125001, Haryana, India
Department of Mathematics,Guru Jambheshwar ,University of Science & Technology, Hisar, Pin-125001, Haryana, India
In this paper, the closed form analytical expressions for the displacement field due to a cylindrical inclusion in a thermoelastic half-space are obtained. These expressions are derived in the context of steady-state uncoupled thermoelasticity using thermoelastic displacement potential functions. The thermal displacement field is generated due to differences in the coefficients of linear thermal expansion between a subregion and the surrounding material. Further, comparison between displacement field in a half-space and in an infinite medium has been discussed. The variation of displacement field in a half-space and its comparison with an infinite medium is also shown graphically.
http://jsm.iau-arak.ac.ir/article_533175_006b677563ef21b6bd91ea5795994560.pdf
Displacement field
Thermoelastic half-space
Potential functions
Cylindrical inclusion, Uncoupled thermoelasticity
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
456
471
533178
Weight Optimum Design of Pressurized and Axially Loaded Stiffened Conical Shells to Prevent Stress and Buckling Failures
M Talebitooti
talebi@qut.ac.ir
1
M Fadaee
2
M.H Seyyedsharbati
3
M.M Shojaee
4
Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
An optimal design of internal pressurized stiffened conical shell is investigated using the genetic algorithm (GA) to minimize the structural weight and to prevent various types of stress and buckling failures. Axial compressive load is applied to the shell. Five stress and buckling failures as constraints are taken into account. Using the discrete elements method as well as the energy method, global buckling load and stress field in the stiffened shell are obtained. The stiffeners include rings and stringers. Seven design variables including shell thickness, number of rings and stringers, stiffeners width and height are considered. In addition, the upper and lower practical bounds are applied for the design variables. Finally, a graphical software package named as Optimal Sizer is developed to help the designers.
http://jsm.iau-arak.ac.ir/article_533178_5021ad9d9b35c2e7fe439369a8f2e80c.pdf
Weight optimum design
Internal pressurized stiffened conical shell
Failure Analysis
Genetic algorithm
Discrete elements method
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
472
489
533181
The Prediction of Forming Limit Diagram of Low Carbon Steel Sheets Using Adaptive Fuzzy Inference System Identifier
H Aleyasin
h.aleyasin.2011@gmail.com
1
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
The paper deals with devising the combination of fuzzy inference systems (FIS) and neural networks called the adaptive network fuzzy inference system (ANFIS) to determine the forming limit diagram (FLD). In this paper, FLDs are determined experimentally for two grades of low carbon steel sheets using out-of-plane (dome) formability test. The effect of different parameters such as work hardening exponent (<em>n</em>), anisotropy (<em>r</em>) and thickness on these diagrams were studied. The out-of-plane stretching test with hemispherical punch was simulated by finite element software Abaqus. The limit strains occurred with localized necking were specified by tracing the thickness strain and its first and second derivatives versus time at the thinnest element. In addition, to investigate the effect of different parameters such as work hardening exponent (<em>n</em>), anisotropy (<em>r</em>) and thickness on these diagrams, a machine learning algorithm is used to simulate a predictive framework. The method of learning algorithm uses the rudiments of neural computing through layering the FIS and using hybrid-learning optimization algorithm. In other words, for building the training database of ANFIS, the experimental work and finite element software Abaqus are used to obtain limit strains. Good agreement was achieved between the predicted data and the experimental results.
http://jsm.iau-arak.ac.ir/article_533181_1a1755c6cd9ee4c4d1f84f15b936ba6a.pdf
Forming Limit Diagram
Out-of-plane
Localized necking
Finite Element
Fuzzy Inference System
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
490
507
533182
Spectral Finite Element Method for Free Vibration of Axially Moving Plates Based on First-Order Shear Deformation Theory
M.R Bahrami
1
S Hatami
hatami@yu.ac.ir
2
Civil Engineering Department, Yasouj University, Yasouj, Iran
Civil Engineering Department, Yasouj University, Yasouj, Iran
In this paper, the free vibration analysis of moderately thick rectangular plates axially moving with constant velocity and subjected to uniform in-plane loads is investigated by the spectral finite element method. Two parallel edges of the plate are assumed to be simply supported and the remaining edges have any arbitrary boundary conditions. Using Hamilton’s principle, three equations of motion for the plate are developed based on first-order shear deformation theory. The equations are transformed from the time domain into the frequency domain by assuming harmonic solutions. Then, the frequency-dependent dynamic shape functions obtained from the exact solution of the governing differential equations is used to develop the spectral stiffness matrix. By solving a non-standard eigenvalue problem, the natural frequencies and the critical speeds of the moving plates are obtained. The exactness and validity of the results are verified by comparing them with the results in previous studies. By the developed method some examples for vibration of stationary and moving moderately thick plates with different boundary conditions are presented. The effects of some parameters such as the axially speed of plate motion, the in-plane forces, aspect ratio and length to thickness ratio on the natural frequencies and the critical speeds of the moving plate are investigated. These results can be used as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.
http://jsm.iau-arak.ac.ir/article_533182_d347218bd7c71ba7ae94f90277f505cd.pdf
First-order shear deformation theory
Spectral finite element method
Transverse vibration
Axially moving
Dynamic stiffness matrix
Free Vibration
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
508
526
533183
Reflection and Transmission of Plane Waves at Micropolar Piezothermoelastic Solids
R Kumar
rajneesh_kuk@rediffmail.com
1
M Kaur
mandeep1125@yahoo.com
2
Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India
Department of Mathematics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab 140118, India
The present investigation analysis a problem of reflection and transmission at an interface of two micropolar orthotropic piezothermoelastic media. The basic equations and constitutive relations for micropolar orthotropic piezothermoelastic media for G-L theory are derived. The expressions for amplitude ratios corresponding to reflected and transmitted waves are derived analytically. The effect of angle of incidence, frequency, micropolarity, thermopiezoelectric interactions on the reflected and transmitted waves are studied numerically for a specific model. Some special cases of interest one are also deduced.
http://jsm.iau-arak.ac.ir/article_533183_28d743399d3ac3cc0d5e3178e024a182.pdf
Orthotropic
Micropolar
Piezothermoelastic
Amplitude ratios
Angle of incidence
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
527
542
533184
Effects of Hall Current and Rotation in Modified Couple Stress Generalized Thermoelastic Half Space due to Ramp-Type Heating
R Kumar
rajneesh_kuk@rediffmail.com
1
Sh Devi
2
V Sharma
3
Department of Mathematics, Kurukshetra University, Kurukshetra, India
Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, India
Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, India
The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic rotating medium in the presence of Hall current and magnetic field due to a ramp-type thermal source. The generalized theories of thermoelasticity developed by Lord Shulman (L-S, 1967) and Green Lindsay (G-L, 1972) are used to investigate the problem. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacements, stress components, temperature change and mass concentration are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of Hall current and rotation are shown in a resulting quantities. Some special cases of interest are also deduced.
http://jsm.iau-arak.ac.ir/article_533184_d971b48920e8e74c07c6451e10c48d4d.pdf
Modified couple stress
Generalized thermoelasticity
Laplace and Fourier transforms
Ramp-Type heating
Hall current and magnetic effect
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
543
554
533185
Influence of the Vacancies on the Buckling Behavior of a Single–Layered Graphene Nanosheet
S.M.H Farrash
1
M Shariati
mshariati44@um.ac.ir
2
J Rezaeepazhand
jrezaeep@ferdowsi.um.ac.ir
3
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Graphene is a new class of two-dimensional carbon nanostructure, which holds great promise for the vast applications in many technological fields. It would be one of the prominent new materials for the next generation nano-electronic devices. In this paper the influence of various vacancy defects on the critical buckling load of a single-layered graphene nanosheet is investigated. The nanosheet is modeled on the base of structural mechanics approach which covalent bonds between atoms are modeled as equivalent beam elements in a finite element model. The mechanical properties of the nanosheet extracted from the model are in good agreement with those of other research works. Effect of the number of vacancies and their positions on the critical buckling load is investigated in the present work. Our results show that the location of the vacancy has a significant role in the amount of critical buckling load. Furthermore, as the density of the vacancies increases, the value of critical buckling load decreases and the relationship is approximately linear.
http://jsm.iau-arak.ac.ir/article_533185_558776aac77a4d9fae729d5fdd92ee64.pdf
graphene
Structural mechanics
Buckling
Vacancy defect
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
555
567
533186
Influence of Heterogeneity on Rayleigh Wave Propagation in an Incompressible Medium Bonded Between Two Half-Spaces
S.A Sahu
1
A Singhal
ism.abhinav@gmail.com
2
S Chaudhary
3
Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India
The present investigation deals with the propagation of Rayleigh wave in an incompressible medium bonded between two half-spaces. Variation in elastic parameters of the layer is taken linear form. The solution for layer and half-space are obtained analytically. Frequency equation for Rayleigh waves has been obtained. It is observed that the heterogeneity and width of the incompressible medium has significant effect on the phase velocity of Rayleigh waves. Some particular cases have been deduced. Results have been presented by the means of graph. Also the findings are exhibited through graphical representation and surface plot.
http://jsm.iau-arak.ac.ir/article_533186_1cdccd9cae74ea05661a9c074c476a64.pdf
Heterogeneity
Incompressibility
Frequency equation
Rayleigh waves
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
568
586
533187
Analysis of Rectangular Stiffened Plates Based on FSDT and Meshless Collocation Method
Sh Hosseini
1
B Soltani
bsoltani@kashanu.ac.ir
2
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, University of Kashan,Kashan,Iran
In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matrices of the plate and the beams were combined together using transformation equations to obtain a total stiffness matrix. Being independent of the mesh along with its simpler implementation process, compared to the other numerical methods, the meshless collocation method was used for analyzing the beam stiffened plate. In order to produce meshless shape functions, radial point interpolation method was used where moment matrix singularity problem of the polynomial interpolation method was fixed. Also, the Multiquadric radial basis function was used for point interpolations. Used to have solutions of increased accuracy and stability were polynomials with the radial basis functions. Several examples are presented to demonstrate the accuracy of the method used to analyze stiffened plates with the accuracy of the results showing acceptable accuracy that the employed method in analyzing concentric and eccentric beam stiffened square and rectangular plates.
http://jsm.iau-arak.ac.ir/article_533187_941593adfb53fefff6a1f1c465f734e1.pdf
Beam stiffened plate
Concentric and eccentric stiffener
Meshless collocation method
Radial point interpolation
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
587
598
533188
Predicting Depth and Path of Subsurface Crack Propagation at Gear Tooth Flank under Cyclic Contact Loading
H Heirani
1
Kh Farhangdoost
farhang@um.ac.ir
2
Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
<span>In this paper, a two-dimensional computational model is proposed for predicting the initiation position and propagation path of subsurface crack of spur gear tooth flank. In order to simulate the contact of teeth, an equivalent model of two contacting cylinders is used. The problem is assumed to be under linear elastic fracture mechanic conditions and finite element method is used for numerical study. An initial subsurface crack is considered in the model at different depths. For each position of the initial crack, moving contact loading is applied to the part and value of <em>∆K<sub>II</sub></em> is obtained for the crack tips. The position of maximum <em>∆K<sub>II</sub></em> is selected as the location of crack initiation. It is shown that the subsurface crack appears at the maximum shear stress point. The maximum tangential stress criterion is used to determine the crack growth angle. The crack is incrementally propagated until the crack tip reaches the part surface and a cavity is formed on the tooth surface. Analyzing the stress field and stress intensity factors are performed in ABAQUS software. The obtained results for the depth and shape of the spall are in good agreement with the experimental results reported in literature.</span>
http://jsm.iau-arak.ac.ir/article_533188_0da6d4d89d28bbf6c04d421746c407af.pdf
Spalling
Crack initiation and propagation
Gear
Finite Element
Fatigue
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
599
607
533189
A New Approach to Buckling Analysis of Lattice Composite Structures
S.A Galehdari
ali.galehdari@pmc.iaun.ac.ir
1
A.H Hashemian
2
J.E Jam
3
A Atrian
4
Department of Mechanical Engineering, Najafabad Branch ,Islamic Azad University, Najafabad, Iran---- Modern Manufacturing Technologies Research Center, Najafabad Branch ,Islamic Azad University, Najafabad, Iran
Mechanical and Aerospace Engineering Department, Science and Research Branch, Islamic Azad University ,Tehran, Iran
Composite Material & Technology, Malek Ashtar University of Technology, Tehran, Iran
Department of Mechanical Engineering, Najafabad Branch ,Islamic Azad University, Najafabad, Iran---- Modern Manufacturing Technologies Research Center, Najafabad Branch ,Islamic Azad University, Najafabad, Iran
Buckling strength of composite latticed cylindrical shells is one of the important parameters for studying the failure of these structures. In this paper, new governing differential equations are derived for latticed cylindrical shells and their critical buckling axial loads. The nested structure under compressive axial buckling load was analyzed. Finite Element Method (FEM) was applied to model the structure in order to verify the analytical results. The obtained results were validated based upon the results of previous case studies in literature. For the squared type of lattice composite shells, a new formula for the buckling load was developed and its value was compared to the critical load, using FEM with 3D beam elements. The processes were carried out for three different materials of Carbon/Epoxy, Kevlar/Epoxy and EGlass/Epoxy.
http://jsm.iau-arak.ac.ir/article_533189_5a662eaf70cff812d8599d9f6085ecfa.pdf
Lattice structures
Composite materials
Finite Element Method
Buckling loading
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
608
618
533190
An Upper Bound Analysis of Sandwich Sheet Rolling Process
H Haghighat
hhaghighat@razi.ac.ir
1
P Saadati
2
Mechanical Engineering Department, Razi University, Kermanshah, Iran
Mechanical Engineering Department, Razi University, Kermanshah, Iran
In this research, flat rolling process of bonded sandwich sheets is investigated by the method of upper bound. A kinematically admissible velocity field is developed for a single layer sheet and is extended into the rolling of the symmetrical sandwich sheets. The internal, shear and frictional power terms are derived and they are used in the upper bound model. Through the analysis, the rolling torque, the roll separating force and the thickness of each layer at the exit of deformation are determined. The validity of the proposed analytical method is discussed by comparing the theoretical predictions with the experimental data found in the literature and by the finite element method. It is shown that the accuracy of the newly developed analytical model is good.
http://jsm.iau-arak.ac.ir/article_533190_0b49a0ec0df0b72d8ae7877376cc3a09.pdf
Flat rolling
Sandwich sheet
Upper bound method
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
619
631
533191
Transference of SH-Waves in Fluid Saturated Porous Medium Sandwiched Between Heterogeneous Half-Spaces
S.A Sahu
1
S Chaudhary
soniya.ism14@gmail.com
2
P.K Saroj
pksaroj.ism@gmail.com
3
A Chattopadhyay
4
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, India
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, India
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, India
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, India
<span>A mathematical model is considered to investigate the behavior of horizontally polarized shear waves (SH-waves) in fluid saturated porous medium sandwiched between heterogeneous half-spaces. Heterogeneity in the upper half-space is due to linear variation of elastic parameters, whereas quadratic variation has been considered for lower half-space. The method of separation of variables and Whittaker’s function are used to get an analytical solution for the considered problem. Frequency equation of SH waves in considered model has been obtained. Also, frequency equations have been derived for several particular cases. It is observed that the heterogeneity and porosity have significant effect on the phase velocity of SH-waves. In particular, heterogeneity and porosity increases the phase velocity of SH-waves. Obtained result is matched with classical Love wave equation. Graphical representation is done efficiently to explain the findings. Also the surface plot is added to exhibit the velocity profile of SH-waves in different cases.</span>
http://jsm.iau-arak.ac.ir/article_533191_9ed9a6ad128a28b6a3fc003cde2300d8.pdf
Heterogeneity
SH-waves
Frequency equation
porosity
Fluid saturated medium
Whittaker function
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
632
649
533192
An Efficient Strain Based Cylindrical Shell Finite Element
M Bourezane
bourmess@yahoo.fr
1
Civil Engineering Department, University of Biskra, BP 145 RP, 07000 Biskra, Algeria
The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additional rotational degree of freedom. The resulting element has 24 degrees of freedom, six essential external degrees of freedom at each of the four nodes and thus, avoiding the difficulties associatedwithinternal degrees of freedom (the three translations and three rotations) and the displacement functions of the developed element satisfy the exact representation of the rigid body motion and constant strains (in so far as this allowed by compatibility equations). Numerical experiments analysis have been conducted to assess accuracy and reliability of the present element, this resulting element with the added degree of freedom is found to be numerically more efficient in practical problems than the corresponding Ashwell element [4].
http://jsm.iau-arak.ac.ir/article_533192_8ba272e8b3566205e647ed2654ad8d9b.pdf
Strain approach
Cylindrical finite element
Displacement functions
Rigid body modes
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
650
662
533193
Elastic Analysis of Functionally Graded Variable Thickness Rotating Disk by Element Based Material Grading
A.K Thawait
amkthawait@gmail.com
1
L Sondhi
2
Sh Sanyal
3
Sh Bhowmick
4
Department of Mechanical Engineering, Shri Shankaracharya Technical Campus, SSGI,Bhilai, (C.G.), India
Department of Mechanical Engineering, Shri Shankaracharya Technical Campus, SSGI,Bhilai, (C.G.), India
Department of Mechanical Engineering, NIT Raipur, 492010, India
Department of Mechanical Engineering, NIT Raipur, 492010, India
The present study deals with the elastic analysis of concave thickness rotating disks made of functionally graded materials (FGMs).The analysis is carried out using element based gradation of material properties in radial direction over the discretized domain. The resulting deformation and stresses are evaluated for free-free boundary condition and the effect of grading index on the deformation and stresses is investigated and presented. The results obtained show that there is a significant reduction of stresses in FGM disks as compared to homogeneous disks and the disks modeled by power law FGM have better strength.
http://jsm.iau-arak.ac.ir/article_533193_b892da5f865196adc445b53af0de8db0.pdf
Functionally graded material
Elastic analysis
Annular rotating disk
Concave thickness profile rotating disk
Element based material gradation
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2017-09-01
9
3
663
679
533194
Time-Dependent Hygro-Thermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field
A Bakhshizadeh
1
M Zamani Nejad
m_zamani@yu.ac.ir
2
M Davoudi Kashkoli
3
Mechanical Engineering Department, Yasouj University, Yasouj, Iran
Mechanical Engineering Department, Yasouj University,Yasouj,Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Time-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel, material creep behavior and the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of the problem considering linear elastic behavior of the material. Therefore, using equations of equilibrium, stress–strain and strain–displacement, a differential equation for displacement is obtained and subsequently the initial elastic stresses at a time equal to zero are calculated. Assuming that the Magneto-hygro-thermoelastic creep response of the material is governed by Norton’s law, using the rate form of constitutive differential equation, the displacement rate is obtained and then the stress rates are calculated. Once the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the plane strain condition. The pressure, inner radius and outer radius are considered to be constant and the magnetic field is uniform. Material properties are considered as power law function of the radius of the cylinder and the poisson’s ratio as constant. Following this, profiles are plotted for different values of material exponent for the radial, circumferential and effective stresses as a function of radial direction and time. The in-homogeneity exponent have significant influence on the distributions of the creep stresses.
http://jsm.iau-arak.ac.ir/article_533194_406239fd925fb8c07dde18088027e44a.pdf
Thick cylindrical pressure vessel
Magneto-hygro-thermoelastic-creep
Time-dependent
Functionally graded material (FGM)