Monolithic and Staggered Strategies Using Solid-Shell Formulations for Nonlinear Coupled Thermoelasticity
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
In this work, monolithic and staggered schemes using a locking-free solid-shell element are proposed to analyze the behavior of thin-walled structural components subjected to combined thermal and mechanical loads. The enhanced assumed strain method, assumed natural strain method, and reduced integration with hourglass control are incorporated into the formulation of the eight-node solid-shell element to seek accurate predictions of the structural response of the elastodynamic systems. The thermal field (the solution of the heat conduction problem) is obtained using a standard eight-node solid-element formulation with full integration. Element formulations for monolithic, isothermal, and isentropic staggered schemes are presented. The use of different element formulations in the structural and thermal fields brings difficulties in implementing the isentropic scheme; hence, special efforts are made to preserve its convergence properties and numerical stability. Numerical examples demonstrate the accuracy and efficiency of the present locking-free solid-shell element in conducting large-deformation thermoelastic analyses of thin-walled structures. In particular, the isentropic scheme with only a one-pass strategy presents equal robustness but superior efficiency to the monolithic element in simulations considering weak, as well as strong, couplings.
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Acknowledgments
The authors greatly appreciate the Air Force Office of Scientific Research support (Grant No. FA9550-121-1-0130).
References
Alinaghizadeh, F., and M. Kadkhodayan. 2013. “Investigation of nonlinear bending analysis of moderately thick functionally graded material sector plates subjected to thermomechanical loads by the GDQ method.” J. Eng. Mech. 140 (5): 04014012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000715.
Alves de Sousa, R. J., R. P. Cardoso, R. A. Fontes Valente, J.-W. Yoon, J. J. Grácio, and R. M. Natal Jorge. 2005. “A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness—Part I: Geometrically linear applications.” Int. J. Numer. Methods Eng. 62 (7): 952–977. https://doi.org/10.1002/nme.1226.
Alves de Sousa, R. J., R. P. Cardoso, R. A. Fontes Valente, J.-W. Yoon, J. J. Grácio, and R. M. Natal Jorge. 2006. “A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness—Part II: Nonlinear applications.” Int. J. Numer. Methods Eng. 67 (2): 160–188. https://doi.org/10.1002/nme.1609.
Armero, F., and J. Simo. 1992. “A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems.” Int. J. Numer. Methods Eng. 35 (4): 737–766. https://doi.org/10.1002/nme.1620350408.
Boley, B. A. 1956. “Thermally induced vibrations of beams.” J. Aeronaut. Sci. 23 (2): 179–181.
Bonet, J., and R. D. Wood. 1997. Nonlinear continuum mechanics for finite element analysis. Cambridge, UK: Cambridge University Press.
Cardoso, R. P., J. W. Yoon, M. Mahardika, S. Choudhry, R. Alves de Sousa, and R. Fontes Valente. 2008. “Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements.” Int. J. Numer. Methods Eng. 75 (2): 156–187. https://doi.org/10.1002/nme.2250.
Chandra, Y., I. Stanciulescu, T. Eason, and M. Spottswood. 2012. “Numerical pathologies in snap-through simulations.” Eng. Struct. 34 (Jan): 495–504. https://doi.org/10.1016/j.engstruct.2011.10.013.
Danilovskaya, V. 1952. “On a dynamic problem of thermoelasticity.” Prikladnaya Matematicka i Mekhanika 16 (4): 341–344.
Danowski, C., V. Gravemeier, L. Yoshihara, and W. A. Wall. 2013. “A monolithic computational approach to thermo-structure interaction.” Int. J. Numer. Methods Eng. 95 (13): 1053–1078. https://doi.org/10.1002/nme.4530.
Erbts, P., and A. Düster. 2012. “Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains.” Comput. Math. Appl. 64 (8): 2408–2430. https://doi.org/10.1016/j.camwa.2012.05.010.
Girish, J., and L. Ramachandra. 2006. “Thermomechanical postbuckling analysis of cross-ply laminated cylindrical shell panels.” J. Eng. Mech. 132 (2): 133–140. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:2(133).
Hauptmann, R., K. Schweizerhof, and S. Doll. 2000. “Extension of the ‘solid-shell’ concept for application to large elastic and large elastoplastic deformations.” Int. J. Numer. Methods Eng. 49 (9): 1121–1141. https://doi.org/10.1002/1097-0207(20001130)49:9%3C1121::AID-NME130%3E3.0.CO;2-F.
Holzapfel, G., and J. Simo. 1996. “Entropy elasticity of isotropic rubber-like solids at finite strains.” Comput. Methods Appl. Mech. Eng. 132 (1–2): 17–44. https://doi.org/10.1016/0045-7825(96)01001-8.
Ibrahimbegovic, A. 2009. Nonlinear solid mechanics: Theoretical formulations and finite element solution methods. New York: Springer.
Jog, C., and G. Gautam. 2017. “A monolithic hybrid finite element strategy for nonlinear thermoelasticity.” Int. J. Numer. Methods Eng. 112 (1): 26–57. https://doi.org/10.1002/nme.5500.
Klinkel, S., and S. Govindjee. 2002. “Using finite strain 3D-material models in beam and shell elements.” Eng. Comput. 19 (3): 254–271. https://doi.org/10.1108/02644400210423918.
Klinkel, S., and W. Wagner. 1997. “A geometrical non-linear brick element based on the EAS-method.” Int. J. Numer. Methods Eng. 40 (24): 4529–4545. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24%3C4529::AID-NME271%3E3.0.CO;2-I.
Lee, C.-Y., and J.-H. Kim. 2013. “Thermo-mechanical characteristics and stability boundaries of antenna structures in supersonic flows.” Compos. Struct. 97 (Mar): 363–369. https://doi.org/10.1016/j.compstruct.2012.09.048.
Martins, J., D. Neto, J. Alves, M. Oliveira, H. Laurent, A. Andrade-Campos, and L. Menezes. 2017. “A new staggered algorithm for thermomechanical coupled problems.” Int. J. Solids Struct. 122 (Sep): 42–58. https://doi.org/10.1016/j.ijsolstr.2017.06.002.
Miehe, C. 1995. “Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation.” Comput. Methods Appl. Mech. Eng. 120 (3–4): 243–269. https://doi.org/10.1016/0045-7825(94)00057-T.
Nali, P., E. Carrera, and A. Calvi. 2011. “Advanced fully coupled thermo-mechanical plate elements for multilayered structures subjected to mechanical and thermal loading.” Int. J. Numer. Methods Eng. 85 (7): 896–919. https://doi.org/10.1002/nme.3006.
Nguyen, N. H. 2009. “Development of solid-shell elements for large deformation simulation and springback prediction.” Ph.D. thesis, Dept. of Mechanical Engineering, Université de Liège.
Schwarze, M., and S. Reese. 2009. “A reduced integration solid-shell finite element based on the EAS and the ANS concept-Geometrically linear problems.” Int. J. Numer. Methods Eng. 80 (10): 1322–1355. https://doi.org/10.1002/nme.2653.
Schwarze, M., and S. Reese. 2011. “A reduced integration solid-shell finite element based on the EAS and the ANS concept—Large deformation problems.” Int. J. Numer. Methods Eng. 85 (3): 289–329. https://doi.org/10.1002/nme.2966.
Simo, J. C., F. Armero, and R. L. Taylor. 1993. “Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems.” Comput. Methods Appl. Mech. Eng. 110 (3–4): 359–386. https://doi.org/10.1016/0045-7825(93)90215-J.
Stanciulescu, I., T. Mitchell, Y. Chandra, T. Eason, and M. Spottswood. 2012. “A lower bound on snap-through instability of curved beams under thermomechanical loads.” Int. J. Non Linear Mech. 47 (5): 561–575. https://doi.org/10.1016/j.ijnonlinmec.2011.10.004.
Tanaka, M., T. Matsumoto, and M. Moradi. 1995. “Application of boundary element method to 3-D problems of coupled thermoelasticity.” Eng. Anal. Boundary Elem. 16 (4): 297–303. https://doi.org/10.1016/0955-7997(95)00074-7.
Taylor, R. L., and S. Govindjee. 2017. “Finite element analysis program, FEAP 8.5.” Accessed May 2017. https://www.ce.berkeley.edu/projects/feap/.
Vu-Quoc, L., and X. Tan. 2003. “Optimal solid shells for non-linear analyses of multilayer composites. I. Statics.” Comput. Methods Appl. Mech. Eng. 192 (9): 975–1016. https://doi.org/10.1016/S0045-7825(02)00435-8.
Zhou, Y., I. Stanciulescu, T. Eason, and M. Spottswood. 2015. “Nonlinear elastic buckling and postbuckling analysis of cylindrical panels.” Finite Elem. Anal. Des. 96 (Apr): 41–50. https://doi.org/10.1016/j.finel.2014.12.001.
Zuchowski, B. 2010. Predictive capability for hypersonic structural response and life prediction phase 1-Identification of knowledge gaps. Air Vehicles Integration and Technology Research (AVIATR) Task Order 0015. Palmdale, CA: Lockheed Martin Aeronautics.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Sep 10, 2018
Accepted: Mar 21, 2019
Published online: Sep 20, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 20, 2020
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