Local Heaviside weighted MLPG meshless method approach to extended Flamant problem using radial basis functions

• Autorzy: Ossowski R.
• Konferencja: Proceedings of the 14th French-Polish Colloguium "Soli and Rock Mechanics. soil Mechanics - Geomaterials" Grenoble, August 29-31, 2007
• Języki publikacji: EN

Abstrakty

EN

The meshless local Petrov-Galerkin (MLPG) method with Heaviside step function as the weighting function is applied to solve the extended Flamant problem. There are two different classes of trial functions considered in the paper: classical radial basis functions (RBF) as extended multiquadrics and compactly supported radial basis functions (CSRBF) as Wu and Wendland functions. The method presented is a truly meshless method based on a set of nodes only. This approach allows direct imposing of essential boundary conditions; moreover, no domain integration is needed and no stiffness matrix assembly is required. The solution of the extended Flamant problem is presented. The performance of RBFs and CSRBFs proposed is compared and the effect of the sizes of local subdomain and interpolation domain is studied. The results obtained show the accuracy and numerical performance of the method.

Słowa kluczowe

EN

meshless local Petrov-Galerkin (MLPG); numerical performance; boundary conditions

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2008
• Tom: Vol. 30, nr 1-2
• Strony: 173--180
• Opis fizyczny: bibliogr. 14 poz.,

Twórcy

autor

Ossowski R.

• Gdańsk University of Technology, Department of Geotechnics and Applied Geology, Narutowicza 11/12, 80-952 Gdańsk, Poland.

Bibliografia

• [1] ATLURI S.N., ZHU T., A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput. Mech., 1998, Vol. 22.
• [2] ATLURI S.N., SHEN S., The meshless local Petrov–Galerkin (MLPG) method: a simple & less-costly alternative to the FE and BE methods, Comput. Model. Eng. Sci., 2002, Vol. 3, No.1.
• [3] BABUŠKA I., MELENK J., The partition of unity method, Int. J. Numer. Meth. Eng., 1997, Vol. 40.
• [4] BELYTSCHKO T., LU Y.Y., GU L., Element-free Galerkin methods, Int. J. Numer. Meth. Eng., 1994, Vol. 37.
• [5] DUARTE C.A., ODEN J.T., An h-p adaptive method using clouds, Comput. Meth. Appl. Mech. Eng., 1996, Vol. 139.
• [6] GINGOLD R.A., MONAGHAN J.J., Smooth particle hydrodynamics: theory and application to nonspherical stars, Mon. Not. Roy. Astron. Soc., 1977, Vol. 181.
• [7] HARDY R.L., Multiquadratic equations of topography and other irregular surfaces, J. Geophys. Res., 1971, Vol. 76.
• [8] LIU G.R., GU Y.T., A local point interpolation method for stress analysis of two-dimensional solids, Struct. Eng. Mech., 2001, Vol. 11.
• [9] LIU W.K., JUN S., ZHANG Y.F., Reproducing kernel particle methods, Int. J. Numer. Meth. Fluids, 1995, Vol. 20.
• [10] NAYROLES B., TOUZOT G., VILLON P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., 1992, Vol. 10.
• [11] WENDLAND H., Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Adv. Comput. Math., 1995, Vol. 4.
• [12] WU Z., Compactly supported positive definite radial basis functions, Adv. Comput. Math., 1995, Vol. 4.
• [13] XIAO J.R., MCCARTHY M.A., A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions, Computational Mechanics, 2003, Vol. 31.
• [14] XIAO J.R., Local Heavside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions, Comput. Methods Appl. Mech. Engrg., 2004, Vol. 193.