无单元法形函数及非凸区权函数影响域的研究

Research on shape function of meshless method and influence domain of weighted function adjacent to nonconvex fields

构造了新的无单元形函数.通过Taylor展开理论,实现无单元形函数的高阶连续性;用Shepard插值,实现移动最小二乘技术中的"从局部到整体的移动性"及有限元方法中的"过点插值性".将这两种基本理论有机结合,借助于高斯积分技术,构造了易于本质边界条件处理且避免大量求逆运算的新型函数.在非凸边界区域影响域的处理,克服了目前几种处理方法的缺点,建立了简便有效的新准则———弧弦准则.

A new meshless shape function is constructed. The high-order continuity of the meshless shape function is realized by means of the Taylor expansion theory, and the 'moving characteristics from part to whole' in the moving least square method (MLSM) and the 'interpolating characteristics at nodes' in the finite element method are also realized by use of the Shepard interpolation. By combination of the above theories and adoption of the Gauss integral technique, a new shape function is established, with which the essential boundary conditions are easily to be treated, and a large amount of inverse matrix calculation is avoided. The new shape function overcomes some disadvantages of other methods currently used in the treatment of the influence domain of the weighted function adjacent to the nonconvex boundary, and a new, simple and effective criterion-the arc-string criterion is developed.