SUMMARYIn this study, we first 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 precision than the MLS, and will not lead to an ill-conditioned system 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), for two-dimensional elasticity is presented. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied easily; hence, it has higher computational precision. For demonstration purpose, selected numerical examples are given.

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No statistically significant differences were noted between the groups concerning the Fowler angle and parallel pitch lines. The posterior calcaneal step spur and Achilles tendon calcification were statistically significant between these two groups. The Fowler angle and parallel pitch lines were of little predictive value for the Haglund syndrome.

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Wang Ju-Feng(王聚丰) a)b) , Sun Feng-Xin(孙凤欣) a)c) , and Cheng Yu-Min(程玉民) a) †

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