The present paper analyzes different integration schemes of solid dynamics in the frequency domain involving the so-called Proper Generalized Decomposition – PGD. The last framework assumes for the solution a parametric dependency with respect to frequency. This procedure allowed introducing other parametric dependences related to loading, geometry, and material properties. However, in these cases, affine decompositions are required for an efficient computation of separated representations. A possibility for circumventing such difficulty consists in combining modal and harmonic analysis for defining an hybrid integration scheme. Moreover, such a procedure, as proved in the present work, can be easily generalized to address nonlinear parametric dynamics, as well as to solve problems with non-symmetric stiffness matrices, always operating in the domain of low frequencies.
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@article{CRMECA_2019__347_5_445_0,
author = {Giacomo Quaranta and Clara Argerich Martin and Ruben Iba\~nez and Jean Louis Duval and Elias Cueto and Francisco Chinesta},
title = {From linear to nonlinear {PGD-based} parametric structural dynamics},
journal = {Comptes Rendus. M\'ecanique},
pages = {445--454},
publisher = {Elsevier},
volume = {347},
number = {5},
year = {2019},
doi = {10.1016/j.crme.2019.01.005},
language = {en},
}
TY - JOUR AU - Giacomo Quaranta AU - Clara Argerich Martin AU - Ruben Ibañez AU - Jean Louis Duval AU - Elias Cueto AU - Francisco Chinesta TI - From linear to nonlinear PGD-based parametric structural dynamics JO - Comptes Rendus. Mécanique PY - 2019 SP - 445 EP - 454 VL - 347 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2019.01.005 LA - en ID - CRMECA_2019__347_5_445_0 ER -
%0 Journal Article %A Giacomo Quaranta %A Clara Argerich Martin %A Ruben Ibañez %A Jean Louis Duval %A Elias Cueto %A Francisco Chinesta %T From linear to nonlinear PGD-based parametric structural dynamics %J Comptes Rendus. Mécanique %D 2019 %P 445-454 %V 347 %N 5 %I Elsevier %R 10.1016/j.crme.2019.01.005 %G en %F CRMECA_2019__347_5_445_0
Giacomo Quaranta; Clara Argerich Martin; Ruben Ibañez; Jean Louis Duval; Elias Cueto; Francisco Chinesta. From linear to nonlinear PGD-based parametric structural dynamics. Comptes Rendus. Mécanique, Volume 347 (2019) no. 5, pp. 445-454. doi : 10.1016/j.crme.2019.01.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.01.005/
[1] Dynamics of Structures, Civil Engineering Series, McGraw-Hill, New York, NY, 1993
[2] The large time increment method for the analyze of structures with nonlinear constitutive relation described by internal variables, C. R. Acad. Sci. Paris, Ser. IIb, Volume 309 (1989), pp. 1095-1099
[3] Nonlinear Computational Structural Mechanics, New Approaches and Non-incremental Methods of Calculation, Springer Verlag, 1999
[4] On the verification of model reduction methods based on the proper generalized decomposition, Comput. Methods Appl. Mech. Eng., Volume 200 (2011), pp. 2032-2047
[5] PGD-VTCR: a reduced order model technique to solve medium frequency broad band problems on complex acoustical systems, J. Mech. Eng., Volume 60 (2014) no. 5, pp. 307-314
[6] Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – application to transient elastodynamics in space–time domain, Comput. Methods Appl. Mech. Eng., Volume 273 (2014), pp. 56-76
[7] Fast simulation of the pantograph-catenary dynamic interaction, Finite Elem. Anal. Des., Volume 129 (2017), pp. 1-13
[8] Real-time direct integration of reduced solid dynamics equations, Int. J. Numer. Methods Eng., Volume 99 (2014) no. 9, pp. 633-653
[9] Proper Generalized Decompositions: An Introduction to Computer Implementation with Matlab, SpringerBriefs in Applied Sciences and Technology, Springer International Publishing, 2016
[10] The role of damping in vibration theory, J. Sound Vib., Volume 11 (1970) no. 1, pp. 3-18
[11] Efficient PGD-based dynamic calculation of non-linear soil behavior, C. R. Mecanique, Volume 344 (2016), pp. 24-41
[12] Inclusion of frequency dependent parameters in power transmission lines simulation using harmonic analysis and proper generalized decomposition, Int. J. Numer. Model. Electron. Netw., Devices Fields, Volume 31 (2018) no. 5
[13] Parametric PGD based computational vademecum for efficient design, optimization and control, Arch. Comput. Methods Eng., Volume 20 (2013) no. 1, pp. 31-59
[14] The Proper Generalized Decomposition for Advanced Numerical Simulations. A Primer, SpringerBriefs, Springer, 2014
[15] Real-time monitoring of thermal processes by reduced order modelling, Int. J. Numer. Methods Eng., Volume 102 (2015) no. 5, pp. 991-1017
[16] Advanced parametric space-frequency separated representations in structural dynamics: a harmonic-modal hybrid approach, C. R. Mecanique, Volume 346 (2018) no. 7, pp. 590-602
[17] An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004) no. 9, pp. 667-672
[18] Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput., Volume 32 (2010) no. 5, pp. 2737-2764
[19] A Simulation App based on reduced order modeling for manufacturing optimization of composite outlet guide vanes, Adv. Model. Simul. Eng. Sci., Volume 4 (2017), p. 1
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