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Advances in Mechanical Problems of Functionally Graded Materials and Structures

A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (31 December 2018) | Viewed by 51071

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Special Issue Editors

Department of Civil and Environmental Engineering, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Interests: computational mechanics; fracture mechanics; composites; functionally graded materials; numerical methods; computational inelasticity; structures
Special Issues, Collections and Topics in MDPI journals
Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan
Interests: multifunctional materials; smart materials; fracture mechanics; multiphysics properties
Department of Engineering Mechanics, Hohai University, Nanjing, China
Interests: functionally graded materials; composites; computational mechanics; numerical methods; structures; mechanics of materials
Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India
Interests: computational mechanics; functionally graded materials; failure analysis; fatigue; numerical method

Special Issue Information

Dear Colleagues,

Functionally-graded materials (FGMs) are an advanced class of composite materials that exhibit continuous variations of properties, arising from spatial gradation in composition. Engineering FGM structures, thus, integrates the advantageous properties of constituent compounds. Research and development in the area of mechanics of FGMs have made great leaps towards the application of FGM structures in various engineering fields, such as aerospace, aircrafts, engine combustion chambers, fusion reactors, and biomedical devices. In addition, recent developments in material science and computational technology have enabled us to make further advancements in the research area of FGM structures, and the enthusiasm of numerous research teams is still far from being exhausted.

This Special Issue aims to collect recent studies and developments associated with mechanical problems of FGMs and FGM structures. Manuscripts are invited from various researchers/investigators, to contribute to this Special Issue with their original research articles, short communications, and review articles.

Prof. Dr. Tinh Quoc Bui
Dr. Le Van Lich
Prof. Dr. Tiantang Yu
Dr. Indra Vir Singh
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Materials is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Functionally Graded Materials (FGM)
  • FGM structures
  • Thermal/Mechanical Properties
  • Fracture Mechanics of FGM
  • Mechanical Design

Published Papers (14 papers)

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Research

17 pages, 1343 KiB  
Article
A Theory of Elastic/Plastic Plane Strain Pure Bending of FGM Sheets at Large Strain
by Sergey Alexandrov, Yun-Che Wang and Lihui Lang
Materials 2019, 12(3), 456; https://doi.org/10.3390/ma12030456 - 01 Feb 2019
Cited by 6 | Viewed by 3131
Abstract
An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. [...] Read more.
An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. The study is concentrated on a power law through thickness distribution of material properties. However, the general method can be used in conjunction with any other through thickness distributions assuming that plastic yielding initiates at one of the surfaces of the sheet. Effects of material properties on the distribution of residual stresses are investigated. Full article
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14 pages, 3031 KiB  
Article
Description of Residual Stress and Strain Fields in FGM Hollow Disc Subject to External Pressure
by Stanislav Strashnov, Sergei Alexandrov and Lihui Lang
Materials 2019, 12(3), 440; https://doi.org/10.3390/ma12030440 - 31 Jan 2019
Cited by 6 | Viewed by 2663
Abstract
Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s [...] Read more.
Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions. Full article
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14 pages, 6839 KiB  
Article
Stress Concentration and Damage Factor Due to Central Elliptical Hole in Functionally Graded Panels Subjected to Uniform Tensile Traction
by Wenshuai Wang, Hongting Yuan, Xing Li and Pengpeng Shi
Materials 2019, 12(3), 422; https://doi.org/10.3390/ma12030422 - 30 Jan 2019
Cited by 19 | Viewed by 4241
Abstract
Functionally graded material (FGM) can optimize the mechanical properties of composites by designing the spatial variation of material properties. In this paper, the stress distribution of functionally graded panel with a central elliptical hole under uniaxial tensile load is analyzed. Based on the [...] Read more.
Functionally graded material (FGM) can optimize the mechanical properties of composites by designing the spatial variation of material properties. In this paper, the stress distribution of functionally graded panel with a central elliptical hole under uniaxial tensile load is analyzed. Based on the inhomogeneity variation and three different gradient directions, the effects of the inhomogeneity on the stress concentration factor and damage factor are discussed. The study results show that when Young’s modulus increases with the distance from the hole, the stress concentration factor decreases compared with that of homogeneous material, and the optimal design of r-FGM is better than that of x-FGM and y-FGM when the tensile load. In addition, when the associated variation of ultimate stress is considered, the choice of scheme to reduce the failure index is related to the strength-modulus exponent ratio. When the strength-modulus exponent ratio is small, the failure index changes with the index of power-law, which means there is an optimal FGM design. But when the strength-modulus exponent ratio is large, the optimal design modulus design is to select a uniform material that maximizes the modulus at each point. These research results have a certain reference value for further in-depth understanding of the inhomogeneous design for FGM. Full article
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14 pages, 1755 KiB  
Article
On the Finite Element Implementation of Functionally Graded Materials
by Emilio Martínez-Pañeda
Materials 2019, 12(2), 287; https://doi.org/10.3390/ma12020287 - 17 Jan 2019
Cited by 37 | Viewed by 6508
Abstract
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the element level by means of the two most commonly used [...] Read more.
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the element level by means of the two most commonly used schemes: (i) nodal based gradation, often via an auxiliary (non-physical) temperature-dependence, and (ii) Gauss integration point based gradation. These formulations are extensively compared by solving a number of paradigmatic boundary value problems for which analytical solutions can be obtained. The nature of the notable differences revealed by the results is investigated in detail. We provide a user subroutine for the finite element package ABAQUS to overcome the limitations of the most popular approach for implementing FGMs in commercial software. The use of reliable, element-based formulations to define the material property variation could be key in fracture assessment of FGMs and other non-homogeneous materials. Full article
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16 pages, 6587 KiB  
Article
Asymptotic Solution and Numerical Simulation of Lamb Waves in Functionally Graded Viscoelastic Film
by Xiaoshan Cao, Haining Jiang, Yan Ru and Junping Shi
Materials 2019, 12(2), 268; https://doi.org/10.3390/ma12020268 - 15 Jan 2019
Cited by 9 | Viewed by 2719
Abstract
To investigate Lamb waves in thin films made of functionally graded viscoelastic material, we deduce the governing equation with respect to the displacement component and solve these partial differential equations with complex variable coefficients based on a power series method. To solve the [...] Read more.
To investigate Lamb waves in thin films made of functionally graded viscoelastic material, we deduce the governing equation with respect to the displacement component and solve these partial differential equations with complex variable coefficients based on a power series method. To solve the transcendental equations in the form of a series with complex coefficients, we propose and optimize the minimum module approximation (MMA) method. The power series solution agrees well with the exact analytical solution when the material varies along its thickness following the same exponential function. When material parameters vary with thickness with the same function, the effect of the gradient properties on the wave velocity is limited and that on the wave structure is obvious. The influence of the gradient parameter on the dispersion property and the damping coefficient are discussed. The results should provide nondestructive evaluation for viscoelastic material and the MMA method is suggested for obtaining numerical results of the asymptotic solution for attenuated waves, including waves in viscoelastic structures, piezoelectric semiconductor structures, and so on. Full article
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21 pages, 5436 KiB  
Article
Application of First-Order Shear Deformation Theory on Vibration Analysis of Stepped Functionally Graded Paraboloidal Shell with General Edge Constraints
by Fuzhen Pang, Haichao Li, Fengmei Jing and Yuan Du
Materials 2019, 12(1), 69; https://doi.org/10.3390/ma12010069 - 25 Dec 2018
Cited by 22 | Viewed by 3378
Abstract
The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction [...] Read more.
The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction are represented by Jacobi polynomials, and the Fourier series are utilized to express displacement components in circumferential direction. Based on penalty method about spring stiffness technique, the general edge conditions of doubly curved paraboloidal shell can be easily simulated. The solutions about doubly curved paraboloidal shell were solved by approach of Rayleigh–Ritz. Convergence study about boundary parameters, Jacobi parameters et al. are carried out, respectively. The comparison with published literatures, FEM and experiment results show that the present method has good convergence ability and excellent accuracy. Full article
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24 pages, 4195 KiB  
Article
New Shape Function for the Bending Analysis of Functionally Graded Plate
by Dragan Čukanović, Aleksandar Radaković, Gordana Bogdanović, Milivoje Milanović, Halit Redžović and Danilo Dragović
Materials 2018, 11(12), 2381; https://doi.org/10.3390/ma11122381 - 26 Nov 2018
Cited by 6 | Viewed by 4107
Abstract
The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through [...] Read more.
The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. This paper presents the methodology of the application of the high order shear deformation theory based on the shape functions. A new shape function has been developed and the obtained results are compared to the results obtained with 13 different shape functions presented in the literature. Also, the validity and accuracy of the developed theory was verified by comparing those results with the results obtained using the third order shear deformation theory and 3D theories. In order to determine the procedure for the analysis and the prediction of behavior of functionally graded plates, the new program code in the software package MATLAB has been developed based on the theories studied in this paper. The effects of transversal shear deformation, side-to-thickness ratio, and volume fraction distributions are studied and appropriate conclusions are given. Full article
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27 pages, 5528 KiB  
Article
Nonlinear Stability Analysis of Eccentrically Stiffened Functionally Graded Truncated Conical Sandwich Shells with Porosity
by Duc-Kien Thai, Tran Minh Tu, Le Kha Hoa, Dang Xuan Hung and Nguyen Ngọc Linh
Materials 2018, 11(11), 2200; https://doi.org/10.3390/ma11112200 - 06 Nov 2018
Cited by 20 | Viewed by 3325
Abstract
This paper analyzes the nonlinear buckling and post-buckling characteristics of the porous eccentrically stiffened functionally graded sandwich truncated conical shells resting on the Pasternak elastic foundation subjected to axial compressive loads. The core layer is made of a porous material (metal foam) characterized [...] Read more.
This paper analyzes the nonlinear buckling and post-buckling characteristics of the porous eccentrically stiffened functionally graded sandwich truncated conical shells resting on the Pasternak elastic foundation subjected to axial compressive loads. The core layer is made of a porous material (metal foam) characterized by a porosity coefficient which influences the physical properties of the shells in the form of a harmonic function in the shell’s thickness direction. The physical properties of the functionally graded (FG) coatings and stiffeners depend on the volume fractions of the constituents which play the role of the exponent in the exponential function of the thickness direction coordinate axis. The classical shell theory and the smeared stiffeners technique are applied to derive the governing equations taking the von Kármán geometrical nonlinearity into account. Based on the displacement approach, the explicit expressions of the critical buckling load and the post-buckling load-deflection curves for the sandwich truncated conical shells with simply supported edge conditions are obtained by applying the Galerkin method. The effects of material properties, core layer thickness, number of stiffeners, dimensional parameters, semi vertex angle and elastic foundation on buckling and post-buckling behaviors of the shell are investigated. The obtained results are validated by comparing with those in the literature. Full article
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8 pages, 1684 KiB  
Article
Properties of Love Waves in Functional Graded Saturated Material
by Zhen Qu, Xiaoshan Cao and Xiaoqin Shen
Materials 2018, 11(11), 2165; https://doi.org/10.3390/ma11112165 - 02 Nov 2018
Cited by 4 | Viewed by 2419
Abstract
In the present study, the propagation of Love waves is investigated in a layered structure with two different homogeneity saturated materials based on Biot’s theory. The upper layer is a transversely isotropic functional graded saturated layer, and the substrate is a saturated semi-space. [...] Read more.
In the present study, the propagation of Love waves is investigated in a layered structure with two different homogeneity saturated materials based on Biot’s theory. The upper layer is a transversely isotropic functional graded saturated layer, and the substrate is a saturated semi-space. The inhomogeneity of the functional graded layer is taken into account. Furthermore, the gradient coefficient is employed as the representation of the relation with the layer thickness and the material parameters, and the power series method is applied to solve the variable coefficients governing the equations. In this regard, the influence of the gradient coefficients of saturated material on the dispersion relations, and the attenuation of Love waves in this structure are explored, and the results of the present study can provide theoretical guidance for the non-destructive evaluation of functional graded saturated material. Full article
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16 pages, 4366 KiB  
Article
The Computation of Complex Dispersion and Properties of Evanescent Lamb Wave in Functionally Graded Piezoelectric-Piezomagnetic Plates
by Xiaoming Zhang, Zhi Li and Jiangong Yu
Materials 2018, 11(7), 1186; https://doi.org/10.3390/ma11071186 - 10 Jul 2018
Cited by 12 | Viewed by 3374
Abstract
Functionally graded piezoelectric-piezomagnetic material (FGPPM), with a gradual variation of the material properties in the desired direction(s), can improve the conversion of energy among mechanical, electric, and magnetic fields. Full dispersion relations and wave mode shapes are vital to understanding dynamic behaviors of [...] Read more.
Functionally graded piezoelectric-piezomagnetic material (FGPPM), with a gradual variation of the material properties in the desired direction(s), can improve the conversion of energy among mechanical, electric, and magnetic fields. Full dispersion relations and wave mode shapes are vital to understanding dynamic behaviors of structures made of FGPPM. In this paper, an analytic method based on polynomial expansions is proposed to investigate the complex-valued dispersion and the evanescent Lamb wave in FGPPM plates. Comparisons with other related studies are conducted to validate the correctness of the presented method. Characteristics of the guided wave, including propagating modes and evanescent modes, in various FGPPM plates are studied, and three-dimensional full dispersion and attenuation curves are plotted to gain a deeper insight into the nature of the evanescent wave. The influences of the gradient variation on the dispersion and the magneto-electromechanical coupling factor are illustrated. The displacement amplitude and electric potential and magnetic potential distributions are also discussed in detail. The obtained numerical results could be useful to design and optimize different sensors and transducers made of smart piezoelectric and piezomagnetic materials with high performance by adjusting the gradient property. Full article
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21 pages, 8681 KiB  
Article
Neuro-Fuzzy Modelling of the Metallic Surface Characterization on Linear Dry Contact between Plastic Material Reinforced with SGF and Alloyed Steel
by Victor Vlădăreanu, Lucian Căpitanu and Luige Vlădăreanu
Materials 2018, 11(7), 1181; https://doi.org/10.3390/ma11071181 - 10 Jul 2018
Cited by 6 | Viewed by 3216
Abstract
This paper presents the modelling of wear data resulting from linear dry contact using artificial neural networks (ANN) and adaptive neuro-fuzzy inference systems (ANFIS) with the aim of constructing predictor models for the depth and volume of the wear scar, with great impact [...] Read more.
This paper presents the modelling of wear data resulting from linear dry contact using artificial neural networks (ANN) and adaptive neuro-fuzzy inference systems (ANFIS) with the aim of constructing predictor models for the depth and volume of the wear scar, with great impact in the characterization of new industrial processes utilizing existing materials. The dataset is the result of laboratory testing, presenting both numerical and categorical variables whose inclusion into the model allows for a number of possibilities. The width of the wear scar was measured on a microscope, and its depth was calculated. A multitude of experimental tests was performed with normal loads and different speeds, which led to some conclusive results, but in some cases, with relatively high variance. Various options for the automatic generation of fuzzy inference systems were also approached (genfis2). The innovative approach was compared with a baseline model featuring multivariate linear regression optimized using gradient descent, drawing on previous experimentation on the same dataset. The models developed can be implemented in future research and in practical applications under similar conditions, aiming to optimize performance by applying Computer Science. The obtained results lead to highly accurate prediction models which are further integrated into various metallic surface characterizations in the wear process for tribological and robotics research in new industrial processes using short glass fiber reinforced polymers. Full article
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22 pages, 2614 KiB  
Article
An Electroelastic Solution for Functionally Graded Piezoelectric Circular Plates under the Action of Combined Mechanical Loads
by Zhi-xin Yang, Xiao-ting He, Xue Li, Yong-sheng Lian and Jun-yi Sun
Materials 2018, 11(7), 1168; https://doi.org/10.3390/ma11071168 - 09 Jul 2018
Cited by 5 | Viewed by 2705
Abstract
In this study, we obtained an electroelastic solution for functionally graded piezoelectric circular plates under the action of combined mechanical loads which include the uniformly distributed loads on the upper surface of the plate and the radial force and bending moment at the [...] Read more.
In this study, we obtained an electroelastic solution for functionally graded piezoelectric circular plates under the action of combined mechanical loads which include the uniformly distributed loads on the upper surface of the plate and the radial force and bending moment at the periphery of the plate. All electroelastic materials parameters are assumed to vary according to the same gradient function along the thickness direction. The influence of different functionally graded parameters on the elastic displacement and elastic stress, as well as the electric displacement and electric potential, was discussed by a numerical example. The solution presented in this study is not only applicable to the case of combined loads, but also to the case of a single mechanical load. In addition, this solution reflects the influence of the function gradient on the pure piezoelectric plate, which is helpful to the refined analysis and optimization design of similar structures. Full article
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15 pages, 5295 KiB  
Article
Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates
by Hocine Chalal and Farid Abed-Meraim
Materials 2018, 11(6), 1046; https://doi.org/10.3390/ma11061046 - 20 Jun 2018
Cited by 7 | Viewed by 4320
Abstract
In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as [...] Read more.
In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates. Full article
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20 pages, 2553 KiB  
Article
One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in Tension and Compression
by Xue Li, Jun-yi Sun, Jiao Dong and Xiao-ting He
Materials 2018, 11(5), 830; https://doi.org/10.3390/ma11050830 - 17 May 2018
Cited by 13 | Viewed by 3300
Abstract
The material considered in this study not only has a functionally graded characteristic but also exhibits different tensile and compressive moduli of elasticity. One-dimensional and two-dimensional mechanical models for a functionally graded beam with a bimodular effect were established first. By taking the [...] Read more.
The material considered in this study not only has a functionally graded characteristic but also exhibits different tensile and compressive moduli of elasticity. One-dimensional and two-dimensional mechanical models for a functionally graded beam with a bimodular effect were established first. By taking the grade function as an exponential expression, the analytical solutions of a bimodular functionally graded beam under pure bending and lateral-force bending were obtained. The regression from a two-dimensional solution to a one-dimensional solution is verified. The physical quantities in a bimodular functionally graded beam are compared with their counterparts in a classical problem and a functionally graded beam without a bimodular effect. The validity of the plane section assumption under pure bending and lateral-force bending is analyzed. Three typical cases that the tensile modulus is greater than, equal to, or less than the compressive modulus are discussed. The result indicates that due to the introduction of the bimodular functionally graded effect of the materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam. The real location at which the maximum bending stress takes place is determined via the extreme condition for the analytical solution. Full article
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