×

zbMATH — the first resource for mathematics

Moving particle finite element method. (English) Zbl 1169.74606
Summary: This paper presents the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74M20 Impact in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Liu, International Journal for Numerical Methods in Engineering 20 pp 1081– (1995) · Zbl 0881.76072
[2] Liu, International Journal for Numerical Methods in Engineering 38 pp 1655– (1995) · Zbl 0840.73078
[3] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) · Zbl 0796.73077
[4] Beissel, Computer Methods in Applied Mechanics and Engineering 139 pp 49– (1996) · Zbl 0918.73329
[5] Belytschko, Journal of Computational and Applied Mathematics 74 pp 111– (1996) · Zbl 0862.73058
[6] Gingold, Monthly Notices of the Royal Astronomical Society 181 pp 375– (1977) · Zbl 0421.76032
[7] Randles, Computer Methods in Applied Mechanics and Engineering 139 pp 375– (1996) · Zbl 0896.73075
[8] Swegle, Journal of Computational Physics 116 pp 123– (1995) · Zbl 0818.76071
[9] Melenk, Computer Methods in Applied Mechanics and Engineering 39 pp 289– (1996) · Zbl 0881.65099
[10] Babu?ka, International Journal for Numerical Methods in Engineering 40 pp 727– (1997) · Zbl 0949.65117
[11] Strouboulis, International Journal for Numerical Methods in Engineering 181 pp 43– (2000)
[12] Oden, Computer Methods in Applied Mechanics and Engineering 153 pp 117– (1998) · Zbl 0956.74062
[13] Yagawa, International Journal for Numerical Methods in Engineering 47 pp 1419– (2000) · Zbl 0955.74080
[14] Furukawa, International Journal for Numerical Methods in Engineering 47 pp 1445– (2000) · Zbl 0987.74066
[15] Chen, Computer Methods in Applied Mechanics and Engineering 139 pp 195– (1996) · Zbl 0918.73330
[16] Chen, Computational Mechanics 22 pp 289– (1998) · Zbl 0928.74115
[17] Li, International Journal for Numerical Methods in Engineering 48 pp 1285– (2000) · Zbl 1052.74618
[18] Li, International Journal for Numerical Methods in Engineering 45 pp 289– (1999)
[19] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999) · Zbl 0955.74066
[20] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001) · Zbl 0981.74062
[21] Belytschko, International Journal for Numerical methods in Engineering 45 pp 601– (1999) · Zbl 0943.74061
[22] An extended finite element method with discontinuous enrichment for applied mechanics. PhD Thesis, Theoretical and applied mechanics, Northwestern University, 1999.
[23] Bonet, International Journal for Numerical Methods in Engineering 47 pp 1189– (2000) · Zbl 0964.76071
[24] Atluri, Computer Modeling and Simulation in Engineering 3 pp 187– (1998)
[25] Atluri, Computational Mechanics 25 pp 169– (2000) · Zbl 0976.74078
[26] Chen, International Journal for Numerical Methods in Engineering 50 pp 435– (2001) · Zbl 1011.74081
[27] Huerta, International Journal for Numerical Methods in Engineering 48 pp 1615– (2000) · Zbl 0976.74067
[28] Liu, Computer Methods in Applied Mechanics and Engineering 139 pp 1– (1996)
[29] Liu, International Journal for Numerical Methods in Engineering 49 pp 721– (2000)
[30] Chen, Computational Mechanics 25 pp 99– (2000)
[31] Wagner, International Journal for Numerical Methods in Engineering 47 pp 1367– (2000) · Zbl 0965.76069
[32] Wagner, International Journal for Numerical Methods in Engineering 50 pp 507– (2001) · Zbl 1006.76073
[33] Sukumar, International Journal for Numerical Methods in Engineering 43 pp 839– (1998) · Zbl 0940.74078
[34] Sukumar, International Journal for Numerical Methods in Engineering 50 pp 1– (2001) · Zbl 1082.74554
[35] The Finite Element Method. Prentice-Hall: Engelwood Cliffs, NJ, 1987.
[36] Simo, Journal of Applied Mechanics 53 pp 51– (1986) · Zbl 0592.73019
[37] Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000. · Zbl 0959.74001
[38] Multi-scale damage model. 2001, manuscript to be submitted.
[39] Liu, International Journal for Numerical Methods in Fluids 21 pp 901– (1995) · Zbl 0885.76078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.