Automation is conquering new fields on a daily basis. Aiming for faster and more reliable products, industrials as well as researchers are oriented into automation. Non-destructive testing as well as defect quantification is not an exception. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. In this work, we suggest a comprehensive method based on model order reduction techniques to judge if a structure shall be salvaged. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The PGD is a model order reduction technique that allows circumventing the curse of dimensionality by using domain decomposition. Therefore, the 6D simulation illustrated in this paper is performed within a few minutes on a standard laptop. Later on, a stress concentration manifold is built and used online for decision-making. The manifold is validated on a few selected solutions solved analytically using an analytical procedure. The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied.
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@article{CRMECA_2019__347_2_101_0,
author = {Chady Ghnatios and Ghazi Asmar and Elie Chakar and Charbel Bou Mosleh},
title = {A reduced-order model manifold technique for automated structural defects judging using the {PGD} with analytical validation},
journal = {Comptes Rendus. M\'ecanique},
pages = {101--113},
publisher = {Elsevier},
volume = {347},
number = {2},
year = {2019},
doi = {10.1016/j.crme.2018.11.003},
language = {en},
}
TY - JOUR AU - Chady Ghnatios AU - Ghazi Asmar AU - Elie Chakar AU - Charbel Bou Mosleh TI - A reduced-order model manifold technique for automated structural defects judging using the PGD with analytical validation JO - Comptes Rendus. Mécanique PY - 2019 SP - 101 EP - 113 VL - 347 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2018.11.003 LA - en ID - CRMECA_2019__347_2_101_0 ER -
%0 Journal Article %A Chady Ghnatios %A Ghazi Asmar %A Elie Chakar %A Charbel Bou Mosleh %T A reduced-order model manifold technique for automated structural defects judging using the PGD with analytical validation %J Comptes Rendus. Mécanique %D 2019 %P 101-113 %V 347 %N 2 %I Elsevier %R 10.1016/j.crme.2018.11.003 %G en %F CRMECA_2019__347_2_101_0
Chady Ghnatios; Ghazi Asmar; Elie Chakar; Charbel Bou Mosleh. A reduced-order model manifold technique for automated structural defects judging using the PGD with analytical validation. Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 101-113. doi : 10.1016/j.crme.2018.11.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.11.003/
[1] A Simulation App based on reduced order modeling for manufacturing optimization of composite outlet guide vanes, Adv. Model. Simul. Eng. Sci., Volume 4 (2017) no. 1, pp. 1-26
[2] Some unexpected results in the stress calculation around multiple holes in an isotropic plate under in-plane-loads, Copenhagen, Denmark (2014)
[3] Stratégie numériques avancées pour la simulation de modeles définis sur une géométrie de plaques et coques: solution 3D avec une complexité 2D, École centrale de Nantes, 2013 (PhD thesis)
[4] Parametric 3D elastic solutions of beams involved in frame structures, Adv. Aircr. Spacecr. Sci., Volume 2 (2015) no. 3, pp. 233-248
[5] On the use of model order reduction for simulating automated fibre placement processes, Adv. Model. Simul. Eng. Sci., Volume 3 (2016), pp. 1-18
[6] Recent advances in the use of the proper generalized decomposition for solving multidimensional models, Arch. Comput. Methods Eng., Volume 17 (2010) no. 4, pp. 327-350
[7] Improving computational efficiency in LCM by using computational geometry and model reduction techniques, Key Eng. Mater., Volume 611 (2014), pp. 339-343
[8] Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter, Comput. Fluids, Volume 32 (2003), pp. 3-29
[9] Aeroelastic dynamic analysis of a full F-16 configuration for various flight conditions, AIAA J., Volume 41 (2003), pp. 363-371
[10] Modélisation avancée des procédés thermiques rencontrés lors de la mise en forme des composites, École centrale de Nantes, October 2012 (PhD thesis)
[11] First steps in the space separated representation of models defined in complex domains, ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, American Society of Mechanical Engineers, 2012, pp. 37-42
[12] Poroelastic properties identification through micro indentation modeled by using the proper generalized decomposition, ACTEA, IEEE (2016), pp. 141-145
[13] Modeling soft permeable matter with the proper generalized decomposition (PGD) approach, and verification by means of nanoindentation, Soft Matter, Volume 13 (2017), pp. 4482-4493
[14] On the space separated representation when addressing the solution of PDE in complex domains, Discrete Contin. Dyn. Syst., Ser. S, Volume 9 (2016) no. 2, pp. 475-500
[15] kPCA-based parametric solutions with the PGD framework, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 69-86
[16] Stresses in an infinite plate with two unequal circular holes, Q. J. Mech. Appl. Math., Volume 20 (1967) no. 3, pp. 277-291
[17] Stresses in a plate containing an infinite row of holes, Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., Volume 148 (1935) no. 864, pp. 471-491
[18] A manifold learning approach to data driven computational elasticity and inelasticity, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 47-57
[19] Data-driven non-linear elasticity: constitutive manifold construction and problem discretization, Comput. Mech., Volume 60 (2017) no. 5, pp. 813-826
[20] Plane stress and plane strain in bipolar co-ordinates, Philos. Trans. R. Soc. Lond. Ser. A, Volume 221 (1921), pp. 265-293
[21] On the stresses in a plate containing two circular holes, J. Appl. Phys., Volume 19 (1948), pp. 77-82
[22] Some Basic Problems of the Mathematical Theory of Elasticity, Springer Science, 1977
[23] Nonlinear dimensionality reduction by locally linear embedding, Science, Volume 290 ( December 2000 ), pp. 2323-2326
[24] Non linear component analysis as a kernel eigenvalue problem, Neural Comput., Volume 10 ( March 2006 ) no. 5, pp. 1299-1319
[25] Applied alternating method to analyse the stress concentration around interacting multiple circular holes in an infinite domain, Int. J. Solids Struct., Volume 36 (1998), pp. 533-556
[26] Stress analysis of the multiple circular holes with the rhombic array using alternating method, Int. J. Press. Vessels Piping, Volume 76 (1999), pp. 503-514
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