scholarly journals Analytical Solutions of Functionally Graded Curved Beams under an Arbitrarily Directed Single Force

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Liangliang Zhang ◽  
Lange Shang ◽  
Yang Gao
Keyword(s):  
Analytical Solutions ◽  
Inverse Method ◽  
Radial Direction ◽  
Functionally Graded ◽  
Curved Beams ◽  
Dimensional Solution ◽  
Concentrated Force ◽  
Good Consistency ◽  
Single Force ◽  
Power Function Exponent

A functionally graded curved beam subjected to a shear tension force as well as a concentrated force at the free end is solved based on the inverse method, and a general two-dimensional solution is presented. The explicit expressions are derived by assuming that the elastic properties within curved beams vary in the radial direction according to a power law, i.e., E = E0rn, but are constant across the depth. After degenerating it into the isotropic homogeneous elastic cases, the results are in good consistency with existing analytical solutions. The stresses and displacements are firstly observed in different forms in terms of the different power function exponent n. These results will be useful as a guide for designing devices or as benchmark to assess other approximate methodologies.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Exact Radial Displacement Solutions of Curved Beams with Clamped-Clamped Ends

2012 ◽  
Vol 178-181 ◽  
pp. 2164-2167
Author(s):  
Xiao Fei Li ◽  
Zhe Fu Yu ◽  
Chun Yang Zhu ◽  
Chen Chen
Keyword(s):  
Cross Section ◽  
Analytical Solutions ◽  
Radial Displacement ◽  
Radial Direction ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Concentrated Load ◽  
Internal Forces ◽  
Scientific Base

Based on the principle of thermal expansion and theory of virtual work, a class of equations for in-plane displacements at radial direction and internal forces in the cross-section of statically indeterminate curved beams under radial concentrated load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Analytical Solutions for Large Deflections of Functionally Graded Beams Based on Layer-Graded Beam Model

2018 ◽  
Vol 10 (09) ◽  
pp. 1850098 ◽  
Author(s):  
Peng Zhou ◽  
Ying Liu ◽  
Xiaoyan Liang
Keyword(s):  
Intensity Factor ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Yield Criterion ◽  
Functionally Graded ◽  
Beam Model ◽  
Large Deflections ◽  
Transverse Loading ◽  
Functionally Graded Beam ◽  
Gradient Variation

The objective of this paper is to investigate the large deflection of a slender functionally graded beam under the transverse loading. Firstly, by modeling the functionally graded beam as a layered structure with graded yield strength, a unified yield criterion for a functionally graded metallic beam is established. Based on the proposed yielding criteria, analytical solutions (AS) for the large deflections of fully clamped functionally graded beams subjected to transverse loading are formulated. Comparisons between the present solutions with numerical results are made and good agreements are found. The effects of gradient profile and gradient intensity factor on the large deflections of functionally graded beams are discussed in detail. The reliability of the present analytical model is demonstrated, and the larger the gradient variation ratio near the loading surface is, the more accurate the layer-graded beam model will be.

Study on the Best Reinforcement Arrangement of Thick-Walled Cylinder

2011 ◽  
Vol 94-96 ◽  
pp. 2009-2014
Author(s):  
Yun Qian Xu ◽  
Ai Zhong Lu ◽  
Ning Zhang ◽  
Pan Cui
Keyword(s):  
Stress State ◽  
Bearing Capacity ◽  
Functionally Graded Material ◽  
Radial Direction ◽  
Plain Concrete ◽  
Functionally Graded ◽  
Reinforcement Ratio ◽  
Uniform Load ◽  
Graded Material ◽  
Walled Cylinder

In order to improve the ultimate bearing capacity, In this paper, the theory of functionally graded material is introduced. This paper simulate thick-walled cylinder with functionally graded characteristics through the analysis of using different reinforced ways along the radial direction. The author analyzes the stress state of the thick-walled cylinder with plain concrete and three different reinforced ways under the radical uniform load. Comparisons and evaluations are provided based on ANSYS results. The paper provide a reasonable reinforced way that is a larger reinforcement ratio near the outer and a smaller reinforcement ratio near the inner and is different with the traditional way. But the worst reinforcement arrangement is that a larger reinforcement ratio near the inner and a smaller reinforcement ratio near the outer. The conclusion shows that the principle that larger reinforcement ratio should be adopted where the tangential stress is larger is not suitable to the thick-walled cylinder.

Love Wave in an Isotropic Half-Space with a Graded Layer

2013 ◽  
Vol 325-326 ◽  
pp. 252-255
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Jian Wang
Keyword(s):  
Shear Modulus ◽  
Half Space ◽  
Analytical Solutions ◽  
Love Wave ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Vibration Model ◽  
General Dispersion ◽  
Functionally Graded Layer

This work addresses the dispersion of Love wave in an isotropic homogeneous elastic half-space covered with a functionally graded layer. First, the general dispersion equations are given. Then, the approximation analytical solutions of displacement, stress and the general dispersion relations of Love wave in both media are derived by the WKBJ approximation method. The solutions are checked against numerical calculations taking an example of functionally graded layer with exponentially varying shear modulus and density along the thickness direction. The dispersion curves obtained show that a cut-off frequency arises in the lowest order vibration model.

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