Abstract
For the rapid analysis methods, on the one hand, it is usually required to reduce the calculation intensity substantially, while on the other hand, it is expected to maintain the physical properties of the original structure to ensure the reliability of the analysis results.
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References
Maday, Y., Patera, A. T., & Turinici, G. (2002). A priori convergence theory for reduced basis approximations of single-parameter elliptic partial differential equations. Journal of Scientific Computing, 17(1–4), 437–446.
Veroy, K., & Patera, A. T. (2005). Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds. International Journal for Numerical Methods in Fluids, 47(8–9), 773–788.
Liu, G. R., Zaw, K., Wang, Y. Y., et al. (2008). A novel reduced basis method with upper and lower bounds for real-time computation of linear elasticity problems. Computer Methods in Applied Mechanics and Engineering, 198(2), 269–279.
Deraemaeker, A., Ladeveze, P., & Leconte, P. (2002). Reduced basis for model updating in structural dynamics based on constitutive relation error. Computer Methods in Applied Mechanics and Engineering, 191, 2427–2444.
Krysl, P., Lall, S., & Marsden, J. E. (2001). Dimensional model reduction in non-linear finite element dynamics of solids and structures. International Journal for Numerical Methods in Engineering, 51, 479–504.
Buffa, A., Maday, Y., Patera, A. T., et al. (2012). A priori convergence of the greedy algorithm for the parametrized reduced basis method. ESAIM: Mathematical Modelling and Numerical Analysis, 46(03), 595–603.
Rozza, G., Huynh, D. B. P., & Patera, A. T. (2008). Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives of Computational Methods in Engineering, 15(3), 229–275.
Lei, F., Ma, Y. L., Bai, Y. C., et al. (2012). A reduced basis approach for rapid and reliable computation of structural linear elasticity problems using mixed interpolation of tensorial components element. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227(5), 905–918.
Lei, F. (2009). A vehicle body design oriented rapid computational method of large-scale problems. Ph.D. Thesis, Hunan University, Changsha.
Zhang, Z., Han, X., & Jiang, C. (2011). An efficient technique for recovering responses of parameterized structural dynamic problems. Acta Mechanica Sinica, 27(5), 757–766.
Zhang, Z. (2012). Investigation on the rapid computation of structural mechanical responses based on the reduced basis method. Ph.D. Thesis, Hunan University, Changsha.
Zhang, Z., Han, X., & Jiang, C. (2011). A novel efficient method for real-time computation of parameterized dynamic equations with large-scale dimension. Acta Mechanica, 219(3–4), 337–356.
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Han, X., Liu, J. (2020). Rapid Structural Analysis Based on Reduced Basis Method. In: Numerical Simulation-based Design. Springer, Singapore. https://doi.org/10.1007/978-981-10-3090-1_7
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DOI: https://doi.org/10.1007/978-981-10-3090-1_7
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