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One-Dimensional And Two-Dimensional Analytical Solutions For Functionally Graded Beams With Different Moduli In Tension And Compression

Xue Li, Jun-Yi Sun, J. Dong, X. He
Published 2018 · Materials Science, Medicine

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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.
This paper references
10.1115/1.1751184
A Combined Fourier Series–Galerkin Method for the Analysis of Functionally Graded Beams
H. Zhu (2004)
10.1007/BF02439863
Analytical solution for bending beam subject to lateral force with different modulus
Yao Wen-juan (2004)
Modulus of elasticity in shear and accelerate convergence of different extension-compression elastic modulus finite element method
X. B. Liu (2000)
10.1016/J.COMPSCITECH.2006.08.023
Analytical solution of a cantilever functionally graded beam
Z. Zhong (2007)
10.1080/15376494.2012.736053
Analytical Solutions for Bending Curved Beams with Different Moduli in Tension and Compression
Xiao-Ting He (2015)
10.1016/S0263-8223(01)00048-4
Damage evolution in bimodular laminated composites under cyclic loading
R. Zinno (2001)
10.3390/ma10101194
The Dynamic Response and Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) Truncated Conical Shells Resting on Elastic Foundations
D. Nguyen Dinh (2017)
10.1007/s10443-011-9243-6
Elasticity Solution of a Cantilever Functionally Graded Beam
T. H. Daouadji (2012)
10.1016/J.COMPSCITECH.2007.11.016
Nacre : An orthotropic and bimodular elastic material
K. Bertoldi (2008)
PROGRESSES IN ELASTICITY THEORY WITH DIFFERENT MODULI IN TENSION AND COMPRESSION AND RELATED FEM
Yao Wen-juan (2004)
10.1177/002199838301700505
Analysis of Curved Laminated Beams of Bimodulus Composite Materials
P.V. Ramana Murthy (1983)
10.3390/ma11020273
Free Vibration Analysis of Moderately Thick Orthotropic Functionally Graded Plates with General Boundary Restraints
Yu Fu (2018)
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license
10.1007/S12206-010-0601-3
A review on the research of mechanical problems with different moduli in tension and compression
J. Sun (2010)
10.2514/2.6853
ELASTICITY SOLUTION FOR STRESSES IN A SANDWICH BEAM WITH FUNCTIONALLY GRADED CORE
S. Venkataraman (2003)
10.1007/S10483-015-1922-9
Analytic elasticity solution of bi-modulus beams under combined loads
Huiling Zhao (2015)
10.1007/s10999-014-9265-y
Numerical analysis of quasi-static fracture in functionally graded materials
E. Martínez-Pañeda (2015)
10.2140/JOMMS.2010.5.755
Application of the Kirchhoff hypothesis to bending thin plates with different moduli in tension and compression
Xiao-Ting He (2010)
10.2514/2.1775
Thermal Stresses in Functionally Graded Beams
B. Sankar (2002)
10.1080/15376494.2016.1255808
An elasticity solution of functionally graded beams with different moduli in tension and compression
Xiao-Ting He (2018)
Basic equations and relations in the theory of anisotropic bodies with different moduli in tension and compression
S. A. Ambartsumyan (1969)
10.2514/3.7297
Stress-strain relations for materials with different moduli in tension and compression
R. Jones (1977)
10.1016/J.COMPOSITESB.2012.05.029
Analytical solution for a functionally graded beam with arbitrary graded material properties
G. Nie (2013)
10.1177/002199838201600205
Transient Response of Laminated, Bimodular-Material, Composite Rectangular Plates
J. Reddy (1982)
10.1142/S0219455418500712
Vibration Analysis of Third-Order Shear Deformable FGM Beams with Elastic Support by Chebyshev Collocation Method
N. Wattanasakulpong (2017)
10.1016/J.IJSOLSTR.2016.07.009
A new computational framework for materials with different mechanical responses in tension and compression and its applications
Zongliang Du (2016)
10.1177/002199838301700401
Transverse Shear Effects in Bimodular Composite Laminates
C. Bert (1983)
10.1016/S0045-7949(82)80003-5
Bending of thick beams of bimodulus materials
A. Tran (1982)
Modulus of elasticity in shear and accelerate convergence of different extensioncompression elastic modulus finite element method
X. B. Liu (2000)
ELASTICITY SOLUTION OF SIMPLE BEAMS WITH DIFFERENT MODULUS UNDER UNIFORMLY DISTRIBUTED LOAD
He Xiao-ting (2007)
10.1016/0961-9526(93)90079-Y
Nonlinear analysis of doubly curved composite shells of bimodular material
D. Bruno (1993)
10.1016/S0266-3538(01)00007-0
AN ELASTICITY SOLUTION FOR FUNCTIONALLY GRADED BEAMS
B. Sankar (2001)



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