有限元上限分析网格自适应方法及其工程应用

Adaptive mesh refinement of upper bound finite element method and its applications in geotechnical engineering

网格离散误差是有限元上限分析计算误差的主要来源。为了对计算网格进行优化,从而有效地降低数值离散误差,基于前沿推进网格划分技术并以单元内能量耗散率的相对大小为控制指标,提出了一种有限元上限分析的网格自适应策略。首先,引入前沿推进网格划分技术,实现在网格生成过程中对单元尺寸和形状的灵活控制;其次,将当前计算网格中各单元能量耗散率的相对大小转化为新计算网格中单元尺寸的分布信息,并以此指示新计算网格的生成,成功地实现了有限元上限分析计算网格的自适应优化;最后,通过算例分析验证了所提出方法的有效性。

The grid discretization error is the main source of calculation error of finite element upper bound limit analysis. To optimize the calculation mesh and reduce the numerical discretization error, an adaptive mesh refinement strategy is proposed based on the advancing front grid generation technique and taking the relative value of elemental energy dissipation as control index. Firstly, the advancing front grid generation technique is introduced to gain a more flexible control of sizes and shapes of elements during the mesh generation process. Secondly, the relative value of elemental energy dissipation in the current mesh is transformed into the distribution information of element sizes in the new mesh, and then this information is used to indicate the new mesh generation, which successfully realizes the optimization of calculation mesh of finite element upper bound limit analysis. Finally, the effectiveness of the proposed method is verified by example analysis.