Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-24T10:24:54.471Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Element Algorithm for Dynamic Thermoelasticity Coupling Problems and Application to Transient Response of Structure with Strong Aerothermodynamic Environment

Part of: Thermodynamics and heat transfer Computer aspects of numerical algorithms Numerical methods Hypersonic flows

Published online by Cambridge University Press:  31 August 2016

Zhihui Li ,
Qiang Ma  and
Junzhi Cui
Zhihui Li*
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang 621000, China National Laboratory for Computational Fluid Dynamics, BUAA, No.37 Xueyuan Road, Beijing 100191, China
Qiang Ma*
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang 621000, China National Laboratory for Computational Fluid Dynamics, BUAA, No.37 Xueyuan Road, Beijing 100191, China
Junzhi Cui*
Affiliation:
LSEC, ICMSEC, The Academy of Mathematics and Systems Science, CAS, Beijing 100190, China
*
*Corresponding author. Email addresses:zhli0097@x263.net (Z. Li), maqiang@lsec.cc.ac.cn (Q. Ma), cjz@lsec.cc.ac.cn (J. Cui)
*Corresponding author. Email addresses:zhli0097@x263.net (Z. Li), maqiang@lsec.cc.ac.cn (Q. Ma), cjz@lsec.cc.ac.cn (J. Cui)
*Corresponding author. Email addresses:zhli0097@x263.net (Z. Li), maqiang@lsec.cc.ac.cn (Q. Ma), cjz@lsec.cc.ac.cn (J. Cui)
Get access

Abstract

As an exploratory study for structural deformation and thermodynamic response induced by spacecraft reentry aerodynamic force and thermal environment, a finite element algorithm is presented on the basis of the classic Fourier heat conductive law to simulate the dynamic thermoelasticity coupling performance of the material. The Newmark method and Crank-Nicolson scheme are utilized to discretize the dynamic thermoelasticity equation and heat conductive equation in the time domain, respectively, and the unconditionally stable implicit algorithm is constructed. Four types of finite-element computing schemes are devised and discussed to solve the thermodynamic coupling equation, all of which are implemented and compared in the computational examples including the one-dimensional transient heat conduction in considering and not considering the vibration, the transient heat flow for the infinite cylinder, and the dynamic coupling thermoelasticity around re-entry flat plate from hypersonic aerothermodynamic environment. The computational results show that the transient responses of temperature and displacement field generate lag phenomenon in case of considering the deformation effect on temperature field. Propagation, rebounding, attenuation and stabilized phenomena of elastic wave are also observed by the finite-element calculation of thermodynamic coupling problem considering vibration and damping, and the oscillation of the temperature field is simultaneously induced. As a result, the computational method and its application research platform have been founded to solve the transient thermodynamic coupling response problem of the structure in strong aerodynamic heating and force environment. By comparing various coupling calculations, it is demonstrated that the present algorithm could give a correct and reliable description of transient thermodynamic responses of structure, the rationality of the sequentially coupling method in engineering calculation is discussed, and the bending deformation mechanism produced by the thermodynamic coupling response from windward and leeward sides of flying body is revealed, which lays the foundation in developing the numerical method to solve material internal temperature distribution, structural deformation, and thermal damage induced by spacecraft dynamic thermoelasticity coupling response under uncontrolled reentry aerothermodynamic condition.

Keywords

Dynamic thermoelasticityfinite element algorithmNewmark methodCrank-Nicolson schemefluid-structure interactionstructural deformation

MSC classification

Secondary: 65Y10: Algorithms for specific classes of architectures 65Z05: Applications to physics 74S05: Finite element methods 76K99: None of the above, but in this section 80A10: Classical thermodynamics, including relativistic
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 773 - 810
Copyright
Copyright © Global-Science Press 2016 

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] Hoyt, R.P., Forward, R.L., Performance of the Terminator Tether for autonomous deorbit of LEO spacecraft, AIAA 99-2839, 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, June 20~24, 1999.CrossRefGoogle Scholar
[2] Reynerson, C.M., Reentry Debris EnvelopeModel for a Disintegrating, Deorbiting Spacecraft Without Heat Shields, AIAA 2005-5916, AIAA Atmospheric Flight Mechanics Conference and Exhibit, Aug. 15~18, 2005, 10.2514/6.2005-5916.CrossRefGoogle Scholar
[3] Prevereaud, Y., Vérant, J.L., Moschetta, J.M., Sourgen, F., Blanchard, M., ebris Aerodynamic Interactions during Uncontrolled Atmospheric Reentry, AIAA Atmospheric Flight Mechanics Conference, 2012, 10.2514/6.2012-4582.Google Scholar
[4] Reyhanoglu, M., Alvarado, J., Estimation of debris dispersion due to a space vehicle breakup during reentry, Acta Astronautica 86 (2013) 211–218.CrossRefGoogle Scholar
[5] Balakrishnan, D., Kurian, J., Material thermal degradation under reentry aerodynamic heating, J. Spacecraft & Rockets 51 (2014) 1–10.CrossRefGoogle Scholar
[6] Thuruthimattam, B.J., Friedmann, P. P., McNamara, J. J., Powell, K. G., Modeling approaches to hypersonic aerothermoelasticity with application to reusable launch vehicles, 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 7-10 April 2003, Norfolk, Virginia.Google Scholar
[7] Friedmann, P. P., McNamara, J. J., Thuruthimattam, B. J., Powell, K. G., Hypersonic aerothermoelasticity with application to reusable launch vehicles, 12th AIAA International Space Planes and Hypersonic Systems and Thechnologies, 15-19 December 2003, Norfolk, Virginia.CrossRefGoogle Scholar
[8] McNamara, J. J., Thuruthimattam, B. J., Friedmann, P. P., Powell, K. G., Hypersonic Aerothermoelastic Studies For Resuable Launch Vehicles, 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & Material Converence, 19-22 April 2004, Palm Springs, California.Google Scholar
[9] Hung, C.I., Chen, C.K., Lee, Z.Y., Thermoelastic transient response of multilayered hollow cylinder with initial interface pressure, J. of Thermal Stresses 24(10) (2001) 987–1006.CrossRefGoogle Scholar
[10] Armero, F., Ehrlich, D., Numerical modeling of softening hinges in thin Euler-Bernoulli beams, Comput. Struct. 84 (2006) 641–656.CrossRefGoogle Scholar
[11] Dujc, J., Brank, B., Ibrahimbegovic, A., Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1371–1385.Google Scholar
[12] Caggiano, A., Etse, G., Coupled thermo-mechanical interface model for concrete failure analysis under high temperature. Comput. Methods Appl. Mech. Engrg., 289 (2015) 498–516.CrossRefGoogle Scholar
[13] Javili, A., McBride, A., Steinmann, P., Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces, Computational Materials Science, 65 (2012) 542–551.Google Scholar
[14] E, W.N., Palffy-Muhoray, P., Dynamics of filaments during the isotropic-smectic A phase transition, J. Nonlin. Sci., 9 (1999) 417–437.CrossRefGoogle Scholar
[15] Samanta, A., Tuckerman, M.E., Yu, T.Q., E, W.N., Microscopic mechanism of equilibrium melting of a solid, Science, 346(6210) (2014) 729–732.Google Scholar
[16] Fan, H. T., Thermal Structures Analysis and Applications of High speed Vehicles, National Defense Industry Press (in Chinese), Beijing, 2009.Google Scholar
[17] Hou, G., Wang, J., Layton, A., Numerical methods for fluid-structure interaction – A review, Commun. Comput. Phys., 12 (2012) 337–377.Google Scholar
[18] Fung, Y. C., Tong, P.. Classical and Computational Solid Mechanics, World Scientific Pub. Co. Inc., 2001.CrossRefGoogle Scholar
[19] Chandrasekharalah, D. S., Thermo elasticity with second sound: A review, Appl. Mech. Rev. 39 (3) (1986) 355–376.CrossRefGoogle Scholar
[20] Hashiguchi, K., General description of elastoplastic deformation/sliding phenomena of solids in high accuracy and numerical efficiency: subloading surface concept, Arch. Comput. Methods Eng., 20 (2013) 361–417.Google Scholar
[21] Verdugo, F., Parés, N., Díez, P., Error Assessment in Structural Transient Dynamics, Arch. Comput. Methods Eng. 21 (2014) 59–90.CrossRefGoogle Scholar
[22] Lord, H.W., Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15 (1967) 299–309.CrossRefGoogle Scholar
[23] Green, A.E., Lindsay, K. E., Thermoelasticity, Elasticity 2 (1972) 1–7.Google Scholar
[24] Hetnarski, R. B., Eslami, M. R., Thermal Stress – Advanced Theory and Applications, Springer 2009.Google Scholar
[25] Nowacki, W., Thermoelasticity: 2nd Edition, Pergamon Press 1896.Google Scholar
[26] Carter, J. P. and Booker, J. R., Finite element analysis of coupled thermoelasticity, Comput. Struct. 31 (1) (1989) 73–80.Google Scholar
[27] Prevost, J. H. and Tao, D., Finite element analysis of dynamic coupled thermoelasticity problems with relaxation time, ASME, J. Appl. Mech. 50 (1983) 817–822.CrossRefGoogle Scholar
[28] Sherief, H. H. and Anwar, M. N., A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials, J. Thermal Stresses 12 (1989) 529–543.CrossRefGoogle Scholar
[29] Yang, Y. C., Chen, C. K., Thermoelastic transient response of an infinitely long annular cylinder composed of two different materials, Int. J. Eng. Sci. 24 (1986) 569–581.Google Scholar
[30] Osamah, F., Abdulateef, F., Investigation of thermal stress distribution in laser spot welding process, Al-Khwarizmi Eng. J. 5 (1) (2009) 33–41.Google Scholar
[31] Akbari Alashti, R., Khorsand, M., Tarahhomi, M.H., Asymmetric thermo-elastic analysis of long cylindrical shells of functionally graded materials by differential quadrature method, Proc. Inst. Mech. Eng. Part C: J. Mech. Engg. Sci. 226 (5) (2012) 1133–1147.Google Scholar
[32] Z˘eníšek, A., Finite element methods for coupled thermoelasticity and coupled consolidation of clay. RA. IRO Analyse numerique 18 (2) (1984) 183–205.CrossRefGoogle Scholar
[33] Hosseini, S. M., Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation), Mater. Design 30 (2009) 2011–2023.Google Scholar
[34] Strunin, D.V., Melnik, R.V.N., Roberts, A.J., Coupled thermomechanical waves in hyperbolic thermoelasticity, J. Thermal Stresses 24 (2001) 121–140.Google Scholar
[35] Ibrahim, A., Abbas, A., Youssef, H.M., A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method, Int. J. Thermophys. 33 (2012) 1302–1313.Google Scholar
[36] Serra, E., Bonaldi, M., A finite element formulation for thermoelastic damping analysis, Int. J. Num. Methods. Eng. 78 (6) (2009) 671–691.CrossRefGoogle Scholar
[37] Lutz, J. D., Alien, D. H., Haisler, W. E., Finite-element model for the thermoelastic analysis of large composite space structures, J. Spacecraft 24 (5) (1986) 430–436.CrossRefGoogle Scholar
[38] Li, Z.H., Zhang, H.X., Study on gas kinetic unified algorithmfor flows from rarefied transition to continuum, J. Comput. Phys. 193 (2004) 708–738.Google Scholar
[39] Li, Z.H., Zhang, H.X., Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry, J. Comput. Phys. 228 (2009) 1116–1138.Google Scholar
[40] Li, Z.H., Bi, L., Zhang, H.X., Li, L., Gas-kinetic numerical study of complex flow problems covering various flowregimes, Computers and Mathematics with Application, 61 (12) (2011) 3653–3667.CrossRefGoogle Scholar
[41] Li, Z.H., Wu, J.L., Jiang, X.Y., Zhang, H.X., The unified algorithm for various flow regimes solving Boltzmann model equation in rotational non-equilibrium, Acta Aerodynamica Sinica 32(2) (2014) 137–145.Google Scholar
[42] Li, Z.H., Peng, A.P., Zhang, H.X., Yang, J.Y., Rarefied gas flow simulations using high-order sas-kinetic unified algorithms for Boltzmann model equations, Progress in Aerospace Sciences, 74(2015) 81–113.CrossRefGoogle Scholar
[43] Lewis, R.W., Nithiarasu, P. and Seetharamu, K. N., Fundamentals of the Finite Element Method for Heat and Fluid flow, John Wiley & Sons. Ltd, England, 2004.Google Scholar
[44] Zienkiewicz, O.C. and Taylor, R.L. and Zhu, J.Z., The Finite Element Method: Its Basis and fundamentals. Elsevier, 6th edition, 2005.Google Scholar
[45] Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method For Solid and Structural Mechanics, Elsevier, 6th edition, 2005.Google Scholar
[46] Larson, M. G., Bengzon, F., The Finite Element Method: Theory, Implementation, and Applications, Springer, 2013.Google Scholar
[47] Frischkorn, J., Reese, S., Solid-beam finite element analysis of Nitinol stents, Comput. Methods Appl. Mech. Engrg. 291 (2015) 42–63.Google Scholar
[48] Daniel, W. J. T., The subcycled Newmark algorithm, Computational Mechanics 20(3) (1997) 272–281.CrossRefGoogle Scholar
[49] Sun, Z.Z., The numerical methods for partial equations, Science Press, Beijing, China, 2005 (in Chinese).Google Scholar
[50] Song, L.J., Wu, Y.J., A modified Crank-Nicolson scheme with incremental unknowns for convection dominated diffusion equations, Applied Mathematics and Computation, 215(9) (2010) 3293–3301.CrossRefGoogle Scholar
[51] Gu, W., Wang, P., A Crank-Nicolson difference scheme for solving a type of variable coefficient delay partial differential equations, Journal of Applied Mathematics, 2(2014) 1–6.Google Scholar
[52] Li, Z.H., Wu, Z.Y., DSMC simulation of hypersonic rarefied flow past Apollo-CM, Acta Aerodynamic Sinica 14 (2) (1996) 230–233.Google Scholar
[53] Huang, J.C., Xu, K., Yu, P.B., A unified gas-kinetic scheme for continuum and rarefied flows II: multi-dimensional cases, Commun. Comput. Phys. 12(3) (2012) 662–690.CrossRefGoogle Scholar
[54] Li, H.Y., Li, Z.H., Luo, W.Q., Li, M., Application and numerical method of chemical non-equilibrium flow for Teflon ablative flow fields in near-space flying condition, Sci. Sin.-Phys. Mech. Astron. 44(2) (2014) 194–202.Google Scholar