摘要
在有限元数值计算平台上,建立了一套基于后验误差评估和Delaunay三角剖分的网格自适应方案,针对饱和砂土静力受压和地震液化的特性进行模拟。验证了超收敛单元片回归(SPR)误差评估中原用于四边形单元的双线性回归函数在用于三角形单元网格时的适用性和可靠性;在饱和砂土动、静力算例中,网格自适应计算获得的变形、应变、超孔压比等的变化规律与常规有限元结果趋势一致。随着网格的再生成,参考点的位移和全域的平均相对误差逼近精确值。对于初始网格,讨论了合理的自适应程度并应用于地震液化的自适应数值模拟中,也对Delaunay三角剖分实施了一些改进。最终证明该自适应方案在提高计算效率的同时,亦可以保证计算所需的精准度。
Based on the finite element method with a posterior error estimation and the Delaunay triangulation, an adaptive mesh scheme is set up to simulate the saturated sand behaviors when being compressed statically and when being liquefied during earthquakes. The bilinear recovered function, usually being used for quadrilateral elements in superconvergent patch recovery （SPR） error estimation, is confirmed to be available and reliable for triangular element mesh. In both the static and dynamic examples of saturated sand, the changing laws of deformation, strain, excess pore water pressure ratio, etc. due to the adaptive mesh calculation are maintained in the same trend as the normal finite element calculation. The displacement of the reference point is approaching to the exact value as the mesh is regenerated, so is the average relative error of the whole area. The suitable adaptation degree for an initial mesh is discussed and applied to the adaptive numerical simulation of the seismic liquefaction. Also, some improvement for the initial mesh is implemented in the Delaunay triangulation. This adaptive mesh scheme is proved to improve calculating efficiency, and to ensure the desired accuracy as well.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2014年第7期2079-2087,2117,共10页
Rock and Soil Mechanics
基金
国家高技术研究发展计划863资助项目(No.2012AA112510)
