Optimal variable support size for mesh-free approaches using genetic algorithm

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dc.citation.epage690
dc.citation.issue4
dc.citation.spage678
dc.contributor.affiliationУніверситет Хасана II Касабланки
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorГассуна, С.
dc.contributor.authorТаймслі, А.
dc.contributor.authorHassouna, S.
dc.contributor.authorTimesli, A.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-11-01T07:49:17Z
dc.date.available2023-11-01T07:49:17Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractОсновна складність безсіткових методів пов’язана з підтримкою форми функцій. Ці методи стають стабільними, коли використовується достатньо велика підтримка. Значно більший розмір підтримки призводить до більших обчислень та значно гіршої якості. Неперервне регулювання розміру підтримки для апроксимації функцій форми під час моделювання може усунути цю проблему, але вибір розміру підтримки відносно локальної щільності не є простою проблемою. У даній роботі досліджується розумний розмір домену впливу, використовуючи генетичний алгоритм у поєднанні з безсітковими алгоритмами високого порядку, оптимальне значення яких залежить від точності та стабільності результатів. Пропонована стратегія забезпечує гарантії щодо зростання похибок наближення, контроль рівня похибки, а також адаптацію стратегії оцінки для досягнення необхідного рівня точності. Це дозволяє адаптувати запропонований алгоритм до необхідної складності задачі. Запропонована стратегія у безсіткових підходах випробовується на деяких прикладах структурного аналізу.
dc.description.abstractThe main difficulty of the meshless methods is related to the support of shape functions. These methods become stable when sufficiently large support is used. Rather larger support size leads to higher calculation costs and greatly degraded quality. The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem. In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with high order mesh-free algorithms which the optimal value depends on the accuracy and stability of the results. The proposed strategy provides guarantees about the growth of approximation errors, monitor the level of error, and adapt the evaluation strategy to reach the required level of accuracy. This allows the adaptation of the proposed algorithm with problem complexity. This new strategy in meshless approaches are tested on some examples of structural analysis.
dc.format.extent678-690
dc.format.pages13
dc.identifier.citationHassouna S. Optimal variable support size for mesh-free approaches using genetic algorithm / S. Hassouna, A. Timesli // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 678–690.
dc.identifier.citationenHassouna S. Optimal variable support size for mesh-free approaches using genetic algorithm / S. Hassouna, A. Timesli // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 678–690.
dc.identifier.doi10.23939/mmc2021.04.678
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60433
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 4 (8), 2021
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dc.relation.references[2] Kargarnovin M. H., Toussi H. E., Fariborz S. J. Elasto-plastic element-free galerkin method. Computational Mechanics. 33, 206–214 (2004).
dc.relation.references[3] Belinha J., Dinis L. M. Elastoplastic analysis of plates by the element free Galerkin method. International Journal of Computer Aided Engineering and Software. 23, 525–551 (2006).
dc.relation.references[4] Belinha J., Dinis L. M. Nonlinear analysis of plates and laminates using the element free Galerkin method. Composite Structures. 78, 337–350 (2007).
dc.relation.references[5] Chen S. S., Liu Y. H., Cen Z. Z. Lower bound shakedown analysis by using the element free Galerkin method and non linear programming. Computer Methods in Applied Mechanics and Engineering. 197, 3911–3921 (2008).
dc.relation.references[6] Belaasilia Y, Timesli A, Braikat B., Jamal M. A numerical mesh-free model for elasto-plastic contact problems. Engineering Analysis with Boundary Elements. 82, 68–78 (2017).
dc.relation.references[7] Alfaro I., Racineux G., Poitou A., Cueto E., Chinesta F. Numerical Simulation of Friction Stir Welding by Natural Element Methods. International Journal of Material Forming. 1, 1079–1082 (2008).
dc.relation.references[8] Timesli A., Braikat B., Lahmam H., Zahrouni H. An implicit algorithm based on continuous moving least square to simulate material mixing in friction stir welding process. Modelling and Simulation in Engineering. 2013, 1–14 (2013).
dc.relation.references[9] Timesli A., Braikat B., Lahmam H., Zahrouni H. A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding. Engineering Analysis with Boundary Elements. 50, 372–380 (2015).
dc.relation.references[10] Mesmoudi S., Timesli A., Braikat B., Lahmam H., Zahrouni H. A 2D mechanical-thermal coupled model to simulate material mixing observed in Friction Stir Welding process. Engineering with Computers. 33, 885–895 (2017).
dc.relation.references[11] Rao B. N., Rahman S. An enriched meshless method for non-linear fracture mechanics. International Journal for Numerical Methods in Engineering. 59, 197–223 (2004).
dc.relation.references[12] Xu Y., Saigal S. Element free Galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials. Computational Mechanics. 22, 255–265 (1998).
dc.relation.references[13] Xu Y., Saigal S. An element-free galerkin analysis of steady dynamic growth of a mode i crack in elasticplastic materials. International Journal of Solids and Structures. 36, 1045–1079 (1999).
dc.relation.references[14] Liu T., Liu G., Wang Q. An element-free Galerkin-finite element coupling method for elasto-plastic contact problems. Journal of Tribology. 128, 1–9 (2005).
dc.relation.references[15] Rabczuk T., Areias P., Belytschko T. A meshfree thin shell method for nonlinear dynamic fracture. International Journal for Numerical Methods in Engineering. 72, 524–548 (2007).
dc.relation.references[16] Alfaro I., Yvonnet J., Cueto E., Chinesta F., Doblar´e M. Meshless Methods with Application to Metal Forming. Computer Methods in Applied Mechanics and Engineering. 195, 6661–6675 (2006).
dc.relation.references[17] Li S., Hao W., Liu W. K. Mesh-free simulations of shear banding in large deformation. International Journal of solids and structures. 37, 7183–7206 (2000).
dc.relation.references[18] Martinez M. A., Cueto E., Alfaro I., Doblar´e M., Chinesta F. Updated lagrangian free surface flow simulations with Natural Neighbour Galerkin methods. International Journal for Numerical Methods in Engineering. 60, 2105–2129 (2004).
dc.relation.references[19] Li S., Liu W. K. Reproducing kernel hierarchical partition of unity part I: formulation and theory. International Journal for Numerical Methods in Engineering. 45, 1285–1309 (1999).
dc.relation.references[20] Li S., Liu W. K., Rosakis A., Belytschko T., Hao W. Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. International Journal of solids and structures. 39, 1213–1240 (2002).
dc.relation.references[21] Liu W. K., Junn S., Li S., Adee J. Reproducing Kernel Particle Methods for structural dynamics. International Journal for Numerical Methods in Engineering. 38, 1655–1679 (1995).
dc.relation.references[22] Liu W. K., Jun S., Zhang Y. F. Reproducing Kernel Particle Methods. International Journal for Numerical Methods Fluids. 21, 1081–1106 (1995).
dc.relation.references[23] Liu W. K., Li S., Belytschko T. Moving least square reproducing kernel method (I) methodology and convergence. Computer Methods in Applied Mechanics and Engineering. 143, 113–154 (1997).
dc.relation.references[24] Dolbow J., Belytschko T. Volumetric locking in the finite element free Galerkin method. International Journal for Numerical Methods in Engineering. 46, 925–942 (1999).
dc.relation.references[25] De S., Bathe K. J. Displacement/pressure mixed interpolation in the method of finite spheres. International Journal for Numerical Methodsin Engineering. 51, 275–292 (2001).
dc.relation.references[26] Liu W. K., Chen Y., Jun S., Chen J. S., Belytschko T. Advances in multiple scale kernel particle methods. Computational Mechanics. 18, 73–111 (1996).
dc.relation.references[27] El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S. A coupled Meshless-FEM method based on strongform of Radial Point Interpolation Method (RPIM). Journal of Physics: Conference Series. 1743, 012039 (2021).
dc.relation.references[28] El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S. Meshless approach based on MLS with additional constraints for large deformation analysis. Journal of Physics: Conference Series. 1743, 012015 (2021).
dc.relation.references[29] Timesli A. Optimized radius of influence domain in meshless approach for modeling of large deformation problems. Iranian Journal of Science and Technology-Transactions of Mechanical Engineering. (2021).
dc.relation.references[30] Cochelin B. A path-following technique via an asymptotic-numerical method. Computer and Structures. 53, 1181–1192 (1994).
dc.relation.references[31] Mitchell M. An Introduction to Genetic Algorithms. Cambridge, MA, MIT Press (1996).
dc.relation.references[32] Saffah Z., Timesli A., Lahmam H., Azouani A., Amdi M. New collocation path-following approach for the optimal shape parameter using Kernel method. SN Applied Sciences. 3, 249 (2021).
dc.relation.references[33] Dolbow J., Belytschko T. An introduction to programming the meshless element free Galerkin method. Archives of Computational Methods in Engineering. 5, 207–241 (1998).
dc.relation.referencesen[1] Chen J. S., Pan C., Wu C. T., Liu W. K. Reproducing kernel particle methods for large deformation analysis of non linear structures. Computer Methods in Applied Mechanics and Engineering. 139, 195–227 (1996).
dc.relation.referencesen[2] Kargarnovin M. H., Toussi H. E., Fariborz S. J. Elasto-plastic element-free galerkin method. Computational Mechanics. 33, 206–214 (2004).
dc.relation.referencesen[3] Belinha J., Dinis L. M. Elastoplastic analysis of plates by the element free Galerkin method. International Journal of Computer Aided Engineering and Software. 23, 525–551 (2006).
dc.relation.referencesen[4] Belinha J., Dinis L. M. Nonlinear analysis of plates and laminates using the element free Galerkin method. Composite Structures. 78, 337–350 (2007).
dc.relation.referencesen[5] Chen S. S., Liu Y. H., Cen Z. Z. Lower bound shakedown analysis by using the element free Galerkin method and non linear programming. Computer Methods in Applied Mechanics and Engineering. 197, 3911–3921 (2008).
dc.relation.referencesen[6] Belaasilia Y, Timesli A, Braikat B., Jamal M. A numerical mesh-free model for elasto-plastic contact problems. Engineering Analysis with Boundary Elements. 82, 68–78 (2017).
dc.relation.referencesen[7] Alfaro I., Racineux G., Poitou A., Cueto E., Chinesta F. Numerical Simulation of Friction Stir Welding by Natural Element Methods. International Journal of Material Forming. 1, 1079–1082 (2008).
dc.relation.referencesen[8] Timesli A., Braikat B., Lahmam H., Zahrouni H. An implicit algorithm based on continuous moving least square to simulate material mixing in friction stir welding process. Modelling and Simulation in Engineering. 2013, 1–14 (2013).
dc.relation.referencesen[9] Timesli A., Braikat B., Lahmam H., Zahrouni H. A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding. Engineering Analysis with Boundary Elements. 50, 372–380 (2015).
dc.relation.referencesen[10] Mesmoudi S., Timesli A., Braikat B., Lahmam H., Zahrouni H. A 2D mechanical-thermal coupled model to simulate material mixing observed in Friction Stir Welding process. Engineering with Computers. 33, 885–895 (2017).
dc.relation.referencesen[11] Rao B. N., Rahman S. An enriched meshless method for non-linear fracture mechanics. International Journal for Numerical Methods in Engineering. 59, 197–223 (2004).
dc.relation.referencesen[12] Xu Y., Saigal S. Element free Galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials. Computational Mechanics. 22, 255–265 (1998).
dc.relation.referencesen[13] Xu Y., Saigal S. An element-free galerkin analysis of steady dynamic growth of a mode i crack in elasticplastic materials. International Journal of Solids and Structures. 36, 1045–1079 (1999).
dc.relation.referencesen[14] Liu T., Liu G., Wang Q. An element-free Galerkin-finite element coupling method for elasto-plastic contact problems. Journal of Tribology. 128, 1–9 (2005).
dc.relation.referencesen[15] Rabczuk T., Areias P., Belytschko T. A meshfree thin shell method for nonlinear dynamic fracture. International Journal for Numerical Methods in Engineering. 72, 524–548 (2007).
dc.relation.referencesen[16] Alfaro I., Yvonnet J., Cueto E., Chinesta F., Doblar´e M. Meshless Methods with Application to Metal Forming. Computer Methods in Applied Mechanics and Engineering. 195, 6661–6675 (2006).
dc.relation.referencesen[17] Li S., Hao W., Liu W. K. Mesh-free simulations of shear banding in large deformation. International Journal of solids and structures. 37, 7183–7206 (2000).
dc.relation.referencesen[18] Martinez M. A., Cueto E., Alfaro I., Doblar´e M., Chinesta F. Updated lagrangian free surface flow simulations with Natural Neighbour Galerkin methods. International Journal for Numerical Methods in Engineering. 60, 2105–2129 (2004).
dc.relation.referencesen[19] Li S., Liu W. K. Reproducing kernel hierarchical partition of unity part I: formulation and theory. International Journal for Numerical Methods in Engineering. 45, 1285–1309 (1999).
dc.relation.referencesen[20] Li S., Liu W. K., Rosakis A., Belytschko T., Hao W. Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. International Journal of solids and structures. 39, 1213–1240 (2002).
dc.relation.referencesen[21] Liu W. K., Junn S., Li S., Adee J. Reproducing Kernel Particle Methods for structural dynamics. International Journal for Numerical Methods in Engineering. 38, 1655–1679 (1995).
dc.relation.referencesen[22] Liu W. K., Jun S., Zhang Y. F. Reproducing Kernel Particle Methods. International Journal for Numerical Methods Fluids. 21, 1081–1106 (1995).
dc.relation.referencesen[23] Liu W. K., Li S., Belytschko T. Moving least square reproducing kernel method (I) methodology and convergence. Computer Methods in Applied Mechanics and Engineering. 143, 113–154 (1997).
dc.relation.referencesen[24] Dolbow J., Belytschko T. Volumetric locking in the finite element free Galerkin method. International Journal for Numerical Methods in Engineering. 46, 925–942 (1999).
dc.relation.referencesen[25] De S., Bathe K. J. Displacement/pressure mixed interpolation in the method of finite spheres. International Journal for Numerical Methodsin Engineering. 51, 275–292 (2001).
dc.relation.referencesen[26] Liu W. K., Chen Y., Jun S., Chen J. S., Belytschko T. Advances in multiple scale kernel particle methods. Computational Mechanics. 18, 73–111 (1996).
dc.relation.referencesen[27] El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S. A coupled Meshless-FEM method based on strongform of Radial Point Interpolation Method (RPIM). Journal of Physics: Conference Series. 1743, 012039 (2021).
dc.relation.referencesen[28] El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S. Meshless approach based on MLS with additional constraints for large deformation analysis. Journal of Physics: Conference Series. 1743, 012015 (2021).
dc.relation.referencesen[29] Timesli A. Optimized radius of influence domain in meshless approach for modeling of large deformation problems. Iranian Journal of Science and Technology-Transactions of Mechanical Engineering. (2021).
dc.relation.referencesen[30] Cochelin B. A path-following technique via an asymptotic-numerical method. Computer and Structures. 53, 1181–1192 (1994).
dc.relation.referencesen[31] Mitchell M. An Introduction to Genetic Algorithms. Cambridge, MA, MIT Press (1996).
dc.relation.referencesen[32] Saffah Z., Timesli A., Lahmam H., Azouani A., Amdi M. New collocation path-following approach for the optimal shape parameter using Kernel method. SN Applied Sciences. 3, 249 (2021).
dc.relation.referencesen[33] Dolbow J., Belytschko T. An introduction to programming the meshless element free Galerkin method. Archives of Computational Methods in Engineering. 5, 207–241 (1998).
dc.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectвеликі деформації
dc.subjectсильна форма
dc.subjectбезсітковий метод
dc.subjectгенетичний алгоритм
dc.subjectавтоматичний вибір найближчого околу
dc.subjectlarge deformations
dc.subjectstrong form
dc.subjectmeshless method
dc.subjectgenetic algorithm
dc.subjectautomatic choice of nearest neighbors
dc.titleOptimal variable support size for mesh-free approaches using genetic algorithm
dc.title.alternativeОптимальна підтримка змінного розміру для безсіткових підходів з використанням генетичного алгоритму
dc.typeArticle

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Mathematical Modeling And Computing. – 2021. – Vol. 8, No. 4