Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

doi:10.1007/s10483-018-2372-8

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (10): 1485-1498.doi: https://doi.org/10.1007/s10483-018-2372-8

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

Libiao XIN^1,2, Yanbin LI³, Dongmei PAN⁴, Guansuo DUI⁵, Chengjian JU⁵

1. Shanxi Key Laboratory of Material Strength & Structural Impact, College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China;
2. National Demonstration Center for Experimental Mechanics Education, College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China;
3. Applied Mechanics of Materials Laboratory, Department of Mechanical Engineering, Temple University, Philadelphia, Pennsylvania 19122, U. S. A;
4. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas 77204, U. S. A;
5. Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China

收稿日期:2018-04-14 修回日期:2018-06-18 出版日期:2018-10-01 发布日期:2018-10-01
通讯作者: Libiao XIN E-mail:xinlibiao@tyut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11772041)

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

Libiao XIN^1,2, Yanbin LI³, Dongmei PAN⁴, Guansuo DUI⁵, Chengjian JU⁵

1. Shanxi Key Laboratory of Material Strength & Structural Impact, College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China;
2. National Demonstration Center for Experimental Mechanics Education, College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China;
3. Applied Mechanics of Materials Laboratory, Department of Mechanical Engineering, Temple University, Philadelphia, Pennsylvania 19122, U. S. A;
4. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas 77204, U. S. A;
5. Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China

Received:2018-04-14 Revised:2018-06-18 Online:2018-10-01 Published:2018-10-01
Contact: Libiao XIN E-mail:xinlibiao@tyut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11772041)

摘要/Abstract

摘要： In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material (FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

关键词: thick-walled tube, discrete type, absolute stability, necessary and sufficientcondition, Lune problem, functionally graded material (FGM), magnetic field, elasticity solution, perturbation of magnetic field vector

Abstract: In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material (FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

Key words: discrete type, absolute stability, necessary and sufficientcondition, Lune problem, functionally graded material (FGM), thick-walled tube, elasticity solution, magnetic field, perturbation of magnetic field vector

中图分类号:

74E30
74M25

Libiao XIN, Yanbin LI, Dongmei PAN, Guansuo DUI, Chengjian JU. Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(10): 1485-1498.

参考文献

[1] MIYAMOTO, Y., KAYSSER, W., RABIN, B., KAWASAKI, A., and FORD, R. G. Functionally Graded Materials:Design, Processing and Applications, Springer Science and Business Media, United States (2013)
[2] DAI, H. L., RAO, Y. N., and DAI, T. A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000-2015. Composite Structures, 152, 199-225(2016)
[3] YANG, S. and CHEN, Y. C. Wrinkle surface instability of an inhomogeneous elastic block with graded stiffness. Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 473, 20160882(2017)
[4] JHA, D., KANT, T., and SINGH, R. A critical review of recent research on functionally graded plates. Composite Structures, 96, 833-849(2013)
[5] GUPTA, A. and TALHA, M. Recent development in modeling and analysis of functionally graded materials and structures. Progress in Aerospace Sciences, 79, 1-14(2015)
[6] ZHENG, G., PANG, T., SUN, G., WU, S., and LI, Q. Theoretical, numerical, and experimental study on laterally variable thickness (LVT) multi-cell tubes for crashworthiness. International Journal of Mechanical Sciences, 118, 283-297(2016)
[7] SUN, G., PANG, T., XU, C., ZHENG, G., and SONG, J. Energy absorption mechanics for variable thickness thin-walled structures. Thin-Walled Structures, 118, 214-228(2017)
[8] SUN, G., TIAN, J., LIU, T., YAN, X., and HUANG, X. Crashworthiness optimization of automotive parts with tailor rolled blank. Engineering Structures, 169, 201-215(2018)
[9] YOU, L., ZHANG, J., and YOU, X. Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials. International Journal of Pressure Vessels and Piping, 82, 347-354(2005)
[10] TUTUNCU, N. and OZTURK, M. Exact solutions for stresses in functionally graded pressure vessels. Composites Part B:Engineering, 32, 683-686(2001)
[11] SHI, Z., ZHANG, T., and XIANG, H. Exact solutions of heterogeneous elastic hollow cylinders. Composite Structures, 79, 140-147(2007)
[12] CHEN, Y. and LIN, X. Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials. Computational Materials Science, 44, 581-587(2008)
[13] LI, X. F. and PENG, X. L. A pressurized functionally graded hollow cylinder with arbitrarily varying material properties. Journal of Elasticity, 96, 81-95(2009)
[14] SOFIYEV, A. H. and SCHNACK, E. The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading. Engineering Structures, 26, 1321-1331(2004)
[15] SBURLATI, R. Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings. Composite Structures, 94, 3592-3600(2012)
[16] ODENBACH, S. Recent progress in magnetic fluid research. Journal of Physics Condensed Matter, 16, 1135-1150(2004)
[17] RAMANUJAN, R. V. and LAO, L. L. The mechanical behavior of smart magnet-hydrogel composites. Smart Materials & Structures, 15, 952-956(2006)
[18] CHERTOVICH, A. V., STEPANOV, G. V., KRAMARENKO, E. Y., and KHOKHLOV, A. R. New composite elastomers with giant magnetic response. Macromolecular Materials & Engineering, 295, 336-341(2010)
[19] BICA, I. The influence of the magnetic field on the elastic properties of anisotropic magnetorheological elastomers. Journal of Industrial & Engineering Chemistry, 18, 1666-1669(2012)
[20] REDDY, S. K., SURI, A., and MISRA, A. Influence of magnetic field on the compressive behavior of carbon nanotube with magnetic nanoparticles. Applied Physics Letters, 102, 241919(2013)
[21] PONNUSAMY, P. and AMUTHALAKSHMI, A. Influence of thermal and longitudinal magnetic field on vibration response of a fluid conveying double walled carbon nanotube embedded in an elastic medium. Journal of Computational & Theoretical Nanoscience, 11, 2570-2577(2014)
[22] ANSARI, R., HASRATI, E., GHOLAMI, R., and SADEGHI, F. Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams. Composites Part B:Engineering, 83, 226-241(2015)
[23] EBRAHIMI, F. and REZA, M. Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams. European Physical Journal Plus, 131(7), 238(2016)
[24] ESPINOSA-ALMEYDA, Y., CAMACHO-MONTES, H., RODRÍGUEZ-RAMOS, R., GUINOVART-DÍAZ, R., LÓPEZ-REALPOZO, J. C., BRAVO-CASTILLERO, J., and SABINA, F. J. Influence of imperfect interface and fiber distribution on the antiplane effective magneto-electro-elastic properties for fiber reinforced composites. International Journal of Solids and Structures, 112, 155-168(2017)
[25] DANIEL, L., HUBERT, O., BUIRON, N., and BILLARDON, R. Reversible magneto-elastic behavior:a multiscale approach. Journal of the Mechanics & Physics of Solids, 56, 1018-1042(2008)
[26] YANG, S., ZHAO, X., and SHARMA, P. Revisiting the instability and bifurcation behavior of soft dielectrics. Journal of Applied Mechanics, 84(3), 031008(2017)
[27] YANG, S., ZHAO, X., and SHARMA, P. Avoiding the pull-in instability of a dielectric elastomer film and the potential for increased actuation and energy harvesting. Soft Matter, 13, 4552-4558(2017)
[28] ALAMEH, Z., YANG, S., DENG, Q., and SHARMA, P. Emergent magnetoelectricity in soft materials, instability, and wireless energy harvesting. Soft Matter (2018) DOI:10.1039/C8SM00587G
[29] VARGA, Z., FILIPCSEI, G., and ZRÍNYI, M. Magnetic field sensitive functional elastomers with tuneable elastic modulus. Polymer, 47, 227-233(2006)
[30] STEPANOV, G. V., ABRAMCHUK, S. S., GRISHIN, D. A., NIKITIN, L. V., KRAMARENKO, E. Y., and KHOKHLOV, A. R. Effect of a homogeneous magnetic field on the viscoelastic behavior of magnetic elastomers. Polymer, 48, 488-495(2007)
[31] KRAMARENKO, E. Y., CHERTOVICH, A. V., STEPANOV, G. V., SEMISALOVA, A. S., MAKAROVA, L. A., PEROV, N. S., and KHOKHLOV, A. R. Magnetic and viscoelastic response of elastomers with hard magnetic filler. Smart Materials and Structures, 24, 035002(2015)
[32] DAI, H. and WANG, X. Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field. International Journal of Solids and Structures, 41, 5231-5246(2004)
[33] DAI, H. and WANG, X. Magneto-thermo-electro-elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings. International Journal of Solids and Structures, 43, 5628-5646(2006)
[34] DAI, H. and WANG, X. The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads. International Journal of Pressure Vessels and Piping, 83, 55-62(2006)
[35] AREFI, M., RAHIMI, G., and KHOSHGOFTAR, M. Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field. Smart Structures and Systems, 9, 427-439(2012)
[36] DAI, H., FU, Y., and YANG, J. Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere. Acta Mechanica Sinica, 23, 55-63(2007)
[37] DAI, H. and FU, Y. Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads. International Journal of Pressure Vessels and Piping, 84, 132-138(2007)
[38] BAYAT, M., RAHIMI, M., SALEEM, M., MOHAZZAB, A., WUDTKE, I., and TALEBI, H. Onedimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk. Applied Mathematical Modelling, 38, 4625-4639(2014)
[39] DAI, H. L., HONG, L., FU, Y. M., and XIAO, X. Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder. Applied Mathematical Modelling, 34, 343-357(2010)
[40] DAI, H. L., RAO, Y. N., and JIANG, H. J. An analytical method for magnetothermoelastic analysis of functionally graded hollow cylinders. Applied and Computational Mathematics, 218, 1467-1477(2011)
[41] DAI, H., FU, Y., and DONG, Z. Exact solutions for functionally graded pressure vessels in a uniform magnetic field. International Journal of Solids and Structures, 43, 5570-5580(2006)
[42] AKBARI, M. and GHANBARI, J. Discussion on "Exact solutions for functionally graded pressure vessels in a uniform magnetic field". International Journal of Solids and Structures, 78, 216-218(2016)
[43] ARANI, A. G., LOGHMAN, A., SHAJARI, A., and AMIR, S. Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks. Journal of Mechanical Science and Technology, 24, 2107-2118(2010)
[44] ARANI, A. G., AZAMIA, M., and SEPIANI, H. Magneto-thermo-elastic stresses and perturbation of the magnetic field vector in an EGM rotating disk. Journal of Solid Mechanics, 2, 168-178(2010)
[45] ARANI, A. G. and AMIR, S. Magneto-thermo-elastic stresses and perturbation of magnetic field vector in a thin functionally graded rotating disk. Journal of Solid Mechanics, 3, 392-407(2011)
[46] SAADATFAR, M. and AGHAIE, M. Thermoelastic analysis of a rotating functionally graded cylindrical shell with functionally graded sensor and actuator layers on an elastic foundation placed in a constant magnetic field. Journal of Intelligent Material Systems and Structures, 27, 512-527(2016)
[47] XIN, L., LU, W., YANG, S., JU, C., and DUI, G. Influence of linear work hardening on the elastic-plastic behavior of a functionally graded thick-walled tube. Acta Mechanica, 227, 2305-2321(2016)
[48] XIN, L., DUI, G., YANG, S., and ZHANG, J. An elasticity solution for functionally graded thick-walled tube subjected to internal pressure. International Journal of Mechanical Sciences, 89, 344-349(2014)
[49] XIN, L., YANG, S., ZHOU, D., and DUI, G. An approximate analytical solution based on the Mori-Tanaka method for functionally graded thick-walled tube subjected to internal pressure. Composite Structures, 135, 74-82(2016)
[50] XIN, L., DUI, G., YANG, S., and ZHOU, D. Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads. International Journal of Mechanical Sciences, 98, 70-79(2015)
[51] QU, J. M. and CHERKAOUI, M. Fundamentals of Micromechanics of Solids, John Wiley & Sons, New Jersey (2006)
[52] LI, S. and GAO, X. L. Handbook of Micromechanics and Nanomechanics, CRC Press, Singapore (2013)
[53] LI, S. and WANG, G. Introduction to Micromechanics and Nanomechanics, World Scientific Publishing Company, New Jersey (2008)
[54] KAMKE, E. Manual of Ordinary Differential Equations, Science Press, Beijing (1978)
[55] TIMOSHENKO, S. P. and GOODIER, J. N. Theory of Elasticity, 3rd ed., McGraw-Hill, New York (1970)

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

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