Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T22:04:40.195Z Has data issue: false hasContentIssue false
  • English
  • Français

Second-Order Two-Scale Computational Method for Nonlinear Dynamic Thermo-Mechanical Problems of Composites with Cylindrical Periodicity

Part of: Homogenization, determination of effective properties Partial differential equations, initial value and time-dependent initial-boundary value problems Approximations and expansions Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  08 March 2017

Hao Dong ,
Junzhi Cui ,
Yufeng Nie  and
Zihao Yang
Hao Dong*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
Junzhi Cui*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China
Yufeng Nie*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
Zihao Yang*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
*
*Corresponding author. Email addresses:[email protected] (H. Dong), [email protected] (J. Cui), [email protected] (Y. Nie), [email protected] (Z. Yang)
*Corresponding author. Email addresses:[email protected] (H. Dong), [email protected] (J. Cui), [email protected] (Y. Nie), [email protected] (Z. Yang)
*Corresponding author. Email addresses:[email protected] (H. Dong), [email protected] (J. Cui), [email protected] (Y. Nie), [email protected] (Z. Yang)
*Corresponding author. Email addresses:[email protected] (H. Dong), [email protected] (J. Cui), [email protected] (Y. Nie), [email protected] (Z. Yang)
Get access

Abstract

In this paper, a novel second-order two-scale (SOTS) computational method is developed for nonlinear dynamic thermo-mechanical problems of composites with cylindrical periodicity. The non-linearities of these multi-scale problems were caused by the temperature-dependent properties of the composites. Firstly, the formal SOTS solutions for these problems are constructed by the multiscale asymptotic analysis. Then we theoretically explain the importance of the SOTS solutions by the error analysis in the pointwise sense. In addition, a SOTS numerical algorithm is proposed in detail to effectively solve these problems. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

Keywords

Second-order two-scalenonlinear dynamic thermo-mechanical problemstemperature-dependent propertiescylindrical periodicity

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 35Q74: PDEs in connection with mechanics of deformable solids 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 74Q10: Homogenization and oscillations in dynamical problems
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1173 - 1206
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Matsumoto, T., Guzik, A., Tanaka, M., A boundary elementmethod for analysis of thermoelastic deformations in materials with temperature dependent properties, International Journal for Numerical Methods in Engineering, 64 (2005), 1432–1458.Google Scholar
[2] Zhang, H. W., Yang, D. S., Zhang, S., Zheng, Y. G., Multiscale nonlinear thermoelastic analysis of heterogeneous multiphase materials with temperature-dependent properties, Finite Elements in Analysis and Design, 88 (2014), 97–117.CrossRefGoogle Scholar
[3] Reddy, J. N., Chin, C. D., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21 (1998), 593–626.Google Scholar
[4] Nasution, M. R. E., Watanabe, N., Kondo, A., Yudhanto, A., Thermo-mechanical properties and stress analysis of 3-d textile composites by asymptotic expansion homogenization method, Composites Part B-Engineering, 60 (2014), 378–391.Google Scholar
[5] Yang, Z. Q., Cui, J. Z., Sun, Y., Ge, J. R., Multiscale computation for transient heat conduction problemwith radiation boundary condition in porousmaterials, Finite Elements in Analysis and Design, 102-103 (2015), 7–18.Google Scholar
[6] Hetnarski, R. B., Eslami, M. R., Thermal Stresses: Advanced Theory and Applications, Springer Verlag, Berlin, 2008.Google Scholar
[7] Wu, L. H., Jiang, Z. Q., Liu, J., Thermoelastic stability of functionally graded cylindrical shells, Composite Structures, 70 (2005), 60–68.CrossRefGoogle Scholar
[8] Chatzigeorgiou, G., Charalambakis, N., Murat, F., Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties, International Journal of Solids and Structures, 45 (2008), 5165–5180.CrossRefGoogle Scholar
[9] Charalambakis, N., Chatzigeorgiou, G., Efendiev, Y., Lagoudas, D., Effective behavior of composite structures made of thermoelastic constituents with cylindrical periodicity, volume 10 of Procedia Engineering, 2011, pp. 3602-3607.Google Scholar
[10] Chatzigeorgiou, G., Efendiev, Y., Charalambakis, N., Lagoudas, D. C., Effective thermoelastic properties of composites with periodicity in cylindrical coordinates, International Journal of Solids and Structures, 49 (2012), 2590–2603.CrossRefGoogle Scholar
[11] Wan, J. J., Multi-scale Analysis Method for Dynamic Coupled Thermoelasticity of Composite Structures, Ph.D. thesis, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, 2007.Google Scholar
[12] Yang, Z. H., Cui, J. Z., Wu, Y. T., Wang, Z. Q., Wan, J. J., Second-order two-scale analysis method for dynamic thermo-mechanical problems in periodic structure, International Journal of Numerical Analysis and Modeling, 12 (2015), 144–161.Google Scholar
[13] Yang, Z. Q., Cui, J. Z., Sun, Y., Liang, J., Yang, Z. H., Multiscale analysis method for thermo-mechanical performance of periodic porous materials with interior surface radiation, International Journal for Numerical Methods in Engineering, 105 (2016), 323–350.Google Scholar
[14] Wang, X., Cao, L. Q., Wong, Y. S., Multiscale computation and convergence for coupled thermoelastic system in composite materials, Multiscale Modeling & Simulation, 13 (2015), 661–690.Google Scholar
[15] Nečas, J., Hlaváček, I., Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier Academic Press, New York, 1981.Google Scholar
[16] Yang, Z. Q., Cui, J. Z., Zhou, S., Thermo-mechanical analysis of periodic porous materials with microscale heat transfer by multiscale asymptotic expansion method, International Journal of Heat and Mass Transfer, 92 (2016), 904–919.Google Scholar
[17] Ma, Q., Cui, J. Z., Second-order two-scale analysis method for the heat conductive problem with radiation boundary condition in periodical porous domain, Communications in Computational Physics, 14 (2013), 1027–1057.Google Scholar
[18] Cioranescu, D., Donato, P., An Introduction to Homogenization 1nd ed., Oxford University Press, London, 1999.CrossRefGoogle Scholar
[19] Ciarlet, Philippe G., Mathematical Elasticity Volume III: Theory of Shells 1nd ed., North-Holland Publishing Company, Amsterdam, 2000.Google Scholar
[20] Cui, J. Z., Multiscale computational method for unified design of structure, components and their materials, in: Proceedings on Computational Mechanics in Science and Engineering, CCCM-2001, Guangzhou, 5-8 December, Peking University Press, 2001, pp. 33–43.Google Scholar
[21] Cao, L. Q., Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains, Numerische Mathematik, 103 (2006), 11–45.Google Scholar
[22] Dong, Q. L., Cao, L. Q., Multiscale asymptotic expansions methods and numerical algorithms for the wave equations in perforated domains, Applied Mathematics and Computation, 232 (2014), 872–887.Google Scholar
[23] Zhang, Q. F., Cui, J. Z., Existence theory for rosseland equation and its homogenized equation, Applied Mathematics and Mechanics-English Edition, 33 (2012), 1595–1612.Google Scholar
[24] Ma, Q., Cui, J. Z., Li, Z. H., Second-order two-scale asymptotic analysis for axisymmetric and spherical symmetric structure with periodic configurations, International Journal of Solids and Structures, 78-79 (2016), 77–100.Google Scholar
[25] Lin, Q., Zhu, Q. D., The Preprocessing and Postprocessing for the Finite Element Method, Shanghai Scientific & Technical Publishers, Shanghai, 1994.Google Scholar
[26] Duc, N. D., Quan, T. Q., Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment, European Journal of Mechanics a-Solids, 47 (2014), 101–123.Google Scholar
[27] Wang, Y. Z., Liu, D., Wang, Q., Shu, C., Thermoelastic response of thin plate with variable material properties under transient thermal shock, International Journal of Mechanical Sciences, 104 (2015), 200–206.Google Scholar
[28] Kolahchi, R., Safari, M., Esmailpour, M., Dynamic stability analysis of temperature-dependent functionally graded cnt-reinforced visco-plates resting on orthotropic elastomeric medium, Composite Structures, 150 (2016), 255–265.Google Scholar
[29] Wu, Y. T., Nie, Y. F., Yang, Z. H., Comparison of four multiscale methods for elliptic problems, Cmes-Computer Modeling in Engineering & Sciences, 99 (2014), 297–325.Google Scholar
[30] Mierzwiczak, M., Chen, W., Fu, Z. J., The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity, International Journal of Heat and Mass Transfer, 91 (2015), 205–217.Google Scholar
[31] Chatzigeorgiou, G., Charalambakis, N., Chemisky, Y., Meraghni, F., Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials, International Journal of Plasticity, 81 (2016), 18–39.CrossRefGoogle Scholar
[32] Han, F., Cui, J. Z., Nie, Y. F., The two-order and two-scale method in cylindrical coordinates for mechanical properties of laminated composite cylindrical structure. 8th. World Congress on Computational Mechanics (WCCM8)& 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 2008, Venice, Italy.Google Scholar
[33] Han, F., Cui, J. Z., Yu, Y., The statistical second-order two-scale method for thermomechanical properties of statistically inhomogeneous materials, Computational Materials Science, 46 (2009), 654–659.CrossRefGoogle Scholar
[34] Yu, Y., Cui, J. Z., Han, F., The statistical second-order two-scale analysis method for heat conduction performances of the composite structure with inconsistent random distribution, Computational Materials Science, 46 (2009), 151–161.CrossRefGoogle Scholar