h-Adaptivity Analysis Based on Multiple Scale Reproducing Kernel Particle Method
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摘要: 基于多尺度再生核质点法（RKPM）的多分辨分析特性，给出了适于求解二维问题的h型自适应分析方法，讨论了不同高梯度指标对检测高梯度区的影响，同时还提出了基于邻节点搜索（SNN）及局部Delaunay三角分解（LDT）技术的适于任意节点分布的无网格自适应分析节点加密技术．通过对二维线弹性平面应力及平板弯曲问题的h型自适应分析，说明了不合适的高梯度指标将对自适应分析的收敛造成不良影响，且LDT节点加密技术较SNN技术的效率更高．数值算例的结果说明自适应分析的有效性、稳定性及良好的收敛特性．Abstract: An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two nodes refinement strategies were constructed using searching-neighbor-nodes (SNN) and local-Delaunay-triangulation (LDT) techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h-adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h -adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.
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