Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems. (English) Zbl 1147.74047

Liew, K. M.; Cheng, Yumin; Kitipornchai, S.

Int. J. Numer. Methods Eng. 65, No. 8, 1310-1332 (2006).

Summary: We discuss the moving least-square approximation (MLS) method. In some cases, the MLS may form an ill-conditioned system of equations, so that the solution cannot be correctly obtained. Hence, in this paper we propose an improved moving least-square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and accuracy than the MLS, and will not lead to ill-conditioned systems of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element-free method (BEFM), is presented for two-dimensional elasticity. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution for nodal variables, and boundary conditions can be applied easily; hence, it has higher computational accuracy. For demonstration purpose, we give selected numerical examples.

MSC:

74S15	Boundary element methods applied to problems in solid mechanics
74B05	Classical linear elasticity

Keywords:

improved moving least-square approximation; weighted orthogonal function

References:

[1]	Beer, International Journal forNumerical Methods in Engineering 28 pp 1233– (1989)
[2]	Beer, International Journal forNumerical Methods in Engineering 36 pp 3579– (1993)
[3]	Tabatabai-Stocker, Communications in Numerical Methods in Engineering 14 pp 355– (1998) · Zbl 0906.73075
[4]	Liew, International Journal for Numerical Methods in Engineering 56 pp 2331– (2003)
[5]	Liew, International Journal for Numerical Methods in Engineering 57 pp 599– (2003)
[6]	Liew, International Journal for Numerical Methods in Engineering 60 pp 1861– (2004)
[7]	Liew, International Journal for Numerical Methods in Engineering 63 pp 1014– (2005)
[8]	Belytschko, Computer Methods in Applied Mechanics and Engineering 139 pp 3– (1996)
[9]	Lancaster, Mathematics of Computation 37 pp 141– (1981)
[10]	Liew, International Journal for Numerical Methods in Engineering 56 pp 2331– (2003)
[11]	Liew, International Journal for Numerical Methods in Engineering 57 pp 599– (2003)
[12]	Gu, Computer Methods in Applied Mechanics and Engineering 190 pp 4405– (2001)
[13]	Mukherjee, International Journal for Numerical Methods in Engineering 40 pp 797– (1997)
[14]	Chati, International Journal for Numerical Methods in Engineering 46 pp 1163– (1999)
[15]	Chati, International Journal for Numerical Methods in Engineering 47 pp 1523– (2000)
[16]	Zhu, Computational Mechanics 21 pp 223– (1998)
[17]	. Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970.
[18]	Elementary Fracture Mechanics (3rd edn). Martinus Nijhoff: The Hague, 1982.