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ارائه تابع تخمین حداقل مربعات متحرک نگاشتی برای روش عددی بدون شبکه حداقل مربعات گسسته | ||
| نشریه مهندسی عمران امیرکبیر | ||
| مقاله 16، دوره 51، شماره 4، مهر و آبان 1398، صفحه 805-816 اصل مقاله (1.05 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/ceej.2018.13861.5505 | ||
| نویسندگان | ||
| مرتضی کلاهدوزان* 1؛ احسان امانی2؛ صائب فرجی3 | ||
| 1دانشکده عمران | ||
| 2استادیار، مهندسی مکانیک، دانشگاه صنعتی امیرکبیر (پلی تکنیک)، تهران | ||
| 3مهندسی عمران، دانشگاه صنعتی امیرکبیر (پلی تکنیک)، تهران | ||
| چکیده | ||
| روش بدون شبکه حداقل مربعات گسسته کارایی مناسب خود را برای حل معادلات دیفرانسیلی مشتقات جزیی حاکم بر مسائل مهندسی نشان داده‌است. این روش بر پایه کمینه کردن تابعک حداقل مربعاتی استوار است. تابعک حداقل مربعاتی به صورت مجموع وزن‌داری از باقیمانده‌ی معادله دیفرانسیلی و شرایط مرزی حاکم تعریف شده‌است. معمولا از تابع تخمین حداقل مربعات متحرک (MLS)، برای ساختن توابع شکل در روش بدون شبکه حداقل مربعات گسسته استفاده می‌شود. هرچند با استفاده از این نوع تابع تخمین سازگاری مورد نیاز توابع تخمین ارضا می‌شود، اما روش در صورت تجمع و نزدیکی بیش از اندازه گره‌ها کارآیی مناسب خود را از دست می‌دهد. در این مطالعه مشکل مطرح شده، با استفاده از تابع تخمین نوینی که حداقل مربعات متحرک نگاشتی (MMLS) نامیده شده است، برطرف شده‌است. در این روش خوشه‌های گرهی مجتمع به یک آرایش گرهی استاندارد نگاشت می‌یابند؛ سپس تابع تخمین و مشتقات آن با در نظر گرفتن ملاحظاتی محاسبه می‌شوند. کارایی روش تخمین پیشنهادی MMLS برای برطرف کردن مشکل تابع تخمین MLS با تخمین توابع ریاضیاتی مورد ارزیابی قرار گرفته‌است. نتایج بدست آمده قابلیت روش پیشنهادی MMLS را جهت رفع مشکل نشان داده‌اند. تابع تخمین پیشنهادی در روش بدون حداقل مربعات گسسته مختلط استفاده شده و برای حل معادلات غیر خطی برگرز به کار گرفته شده‌است. نتایج بدست آمده کارایی و دقت بالای روش پیشنهادی را نشان می‌دهند. | ||
| کلیدواژه‌ها | ||
| حداقل مربعات متحرک نگاشتی؛ حداقل مربعات متحرک؛ معادلات دیفرانسیلی مشتقات جزیی؛ روش عددی بدون شبکه؛ روش بدون شبکه حداقل مربعات گسسته | ||
| موضوعات | ||
| سازه های هیدرولیکی | ||
| عنوان مقاله [English] | ||
| Mapped Moving Least Squares Approximation Used in Mixed Discrete Least Squares Meshfree Method | ||
| نویسندگان [English] | ||
| Morteza Kolahdoozan1؛ Ehsan Amani2؛ Saeb Faraji3 | ||
| 2Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| 3Department of Civil and Environmental Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| چکیده [English] | ||
| The Mixed Least Squares Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) related to the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving Least Squares (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function are satisfied by the MLS, the method loses its appropriate efficiency when the nodal points cluster become too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving Least Squares (MMLS). In this approach, the cluster of closed nodal was pointed maps to standard nodal distribution. Then the approximation function and its derivatives were computed incorporating some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS was evaluated by approximating the mathematical function. The obtained results showed the ability of suggested MMLS method to solve the drawback. The suggested approximation function was applied in MDLSM method, and used for solving the Burgers equations. Obtained results approved the efficiency of suggested method. | ||
| کلیدواژه‌ها [English] | ||
| Mapped Moving Least Squares (MMLS), Moving Least Squares Meshfree (MLS), Partial Differential Equations (PDEs), Meshfree method, Discrete Least Squares Meshfree method (DLSM) | ||
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| مراجع | ||
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[1] R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non- spherical stars, Monthly notices of the royal astronomical society, 181(3) (1977) 375-389. [2] E. Daly, S. Grimaldi, H.H. Bui, Explicit incompressible SPH algorithm for free-surface flow modelling: A comparison with weakly compressible schemes, Advances in water resources, 97 (2016) 156-167. [3] M. Fleming, Y. Chu, B. Moran, T. Belytschko, Enriched element‐free Galerkin methods for crack tip fields, International journal for numerical methods in engineering, 40(8) (1997) 1483-1504. [4] T. Belytschko, Y.Y. Lu, L. Gu, Element‐free Galerkin methods, International journal for numerical methods in engineering, 37(2) (1994) 229-256. [5] S.N. Atluri, T. Zhu, A new meshless local Petrov- Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, 22(2) (1998) 117-127. [6] C.A. Duarte, J.T. Oden, An hp adaptive method using clouds, Computer Methods in Applied Mechanics and Engineering, 139(1-4) (1996) 237-262. [7] E. Onate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco, A stabilized finite point method for analysis of fluid mechanics problems, Computer Methods in Applied Mechanics and Engineering, 139(1-4) (1996) 315-346. [8] W.K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods, International journal for numerical methods in fluids, 20(8‐9) (1995) 1081-1106. [9] K. Kiani, A nonlocal meshless solution for flexural vibrations of double-walled carbon nanotubes, Applied Mathematics and Computation, 234 (2014) 557-578. [10] K. Kiani, A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect, International Journal of Mechanical Sciences, 52(10) (2010) 1343-1356. [11] T. Zhu, J.-D. Zhang, S. Atluri, A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach, Computational Mechanics, 21(3) (1998) 223-235. [12] G.-R. Liu, Meshfree methods: moving beyond the finite element method, CRC press, 2009. [13] S. Koshizuka, Y. Oka, Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nuclear science and engineering, 123(3) (1996) 421- 434. [14] B. Ataie-Ashtiani, L. Farhadi, A stable moving- particle semi-implicit method for free surface flows, Fluid dynamics research, 38(4) (2006) 241. [15] H. Arzani, M. Afshar, Solving Poisson’s equations by the discrete least square meshless method, WIT Transactions on Modelling and Simulation, 42 (2006) 23-31. [16] M. Afshar, M. Naisipour, J. Amani, Node moving adaptive refinement strategy for planar elasticity problems using discrete least squares meshless method, Finite Elements in Analysis and Design, 47(12) (2011) 1315-1325. [17] G. Shobeyri, M. Afshar, Simulating free surface problems using discrete least squares meshless method, Computers & Fluids, 39(3) (2010) 461-470. [18] A.R. Firoozjaee, M.H. Afshar, Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations, Engineering analysis with boundary elements, 33(1) (2009) 83-92. [19] M. Naisipour, M.H. Afshar, B. Hassani, A.R. Firoozjaee, Collocation discrete least square (CDLS) method for elasticity problems, International Journal of Civil Engineering. v7, (2009) 9-18. [20] M. Afshar, M. Lashckarbolok, G. Shobeyri, Collocated discrete least squares meshless (CDLSM) method for the solution of transient and steady‐ state hyperbolic problems, International journal for numerical methods in fluids, 60(10) (2009) 1055-1078. [21] S. Faraji, M. Afshar, Node enrichment-moving error estimate and adaptive refinement in Mixed Discrete Least Squares Meshless method for solution of elasticity problems, Modares Mechanical Engineering, 14(3) (2014) 194-202. (In persian). [22] S.N. Kazeroni, M. Afshar, An adaptive node regeneration technique for the efficient solution of elasticity problems using MDLSM method, Engineering analysis with boundary elements, 50 (2015) 198-211. [23] S. Faraji, M.H. Afshar, J. Amani, Mixed discrete least square meshless method for solution of quadratic partial differential equations, Scientia Iranica, 21(3) (2014) 492-504. [24] S. Faraji, M. Kolahdoozan, M.H. Afshar, Collocated Mixed Discrete Least Squares Meshless (CMDLSM) method for solving quadratic partial differential equations, Scientia Iranica, 25(4) (2018) 2000-2011. [25] S. Faraji, M. Kolahdoozan, M.H. Afshar, Mixed discrete least squares meshless method for solving the linear and non-linear propagation problems, Scientia Iranica, 25(2) (2018) 565-578. [26] S.F. Gargari, M. Kolahdoozan, M. Afshar, Mixed Discrete Least Squares Meshfree method for solving the incompressible Navier–Stokes equations, Engineering analysis with boundary elements, 88 (2018) 64-79. [27] S.F. Gargari, M. Kolahdoozan, M. Afshar, S. Dabiri, An Eulerian-Lagrangian Mixed Discrete Least Squares Meshfree method for incompressible multiphase flow problems, Applied Mathematical Modelling, (2019). [28] G.-R. Liu, Y.-T. Gu, An introduction to meshfree methods and their programming, Springer Science & Business Media, 2005. [29] N. Sukumar, Construction of polygonal interpolants: a maximum entropy approach, International Journal for Numerical Methods in Engineering, 61(12) (2004) 2159-2181. [30] M. Arroyo, M. Ortiz, Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, International journal for numerical methods in engineering, 65(13) (2006) 2167-2202. [31] N. Sukumar, Z. Huang, J.H. Prévost, Z. Suo, Partition of unity enrichment for bimaterial interface cracks, International journal for numerical methods in engineering, 59(8) (2004) 1075-1102. [32] L. Gu, Moving kriging interpolation and elementfree Galerkin method, International journal for numerical methods in engineering, 56(1) (2003) 1-11. [33] P. Lancaster, K. Salkauskas, Surfaces generated by moving least squares methods, Mathematics of computation, 37(155) (1981) 141-158. [34] S. Atluri, J. Cho, H.-G. Kim, Analysis of thin beams, using the meshless local Petrov–Galerkin method, with generalized moving least squares interpolations, Computational Mechanics, 24(5) (1999) 334-347. [35] K. Kiani, A. Nikkhoo, B. Mehri, Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method, Acta Mechanica Sinica, 26(5) (2010) 721-733. [36] A. Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer Science & Business Media, 2010. [37] P. Oliver, Nonlinear Partial Differential Equations, chapter 22, (http://www.math.umn.edu/~olver/am_/ npd.pdf). [38] P. Moin, Fundamentals of engineering numerical analysis, Cambridge University Press, 2010. [39] E.R. Benton, G.W. Platzman, A table of solutions of the one-dimensional Burgers equation, Quarterly of Applied Mathematics, 30(2) (1972) 195-212. | ||
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