考虑间断速度场的光滑有限元极限分析上限法

Upper bound limit analysis using smoothed finite element method considering discontinuous velocity field

基于应变光滑技术的有限元极限分析方法,为岩土工程稳定性分析提供了一种有效和高精度的数值分析途径。通过改进基于节点光滑域的方法,使其可以考虑间断的运动许可速度场,提出一种新型节点光滑有限元极限分析上限法。在土与结构接触面处引入间断速度场,以间断面处节点速度差表征间断速度场的大小,进而基于间断节点重新构造节点光滑域。在Mohr-Coulomb屈服准则和关联流动法则的基础上,分别计算间断面和光滑域内的内能耗散,并将屈服准则和流动法则的约束条件转化为一系列的二阶锥约束方程,最终将考虑间断速度场的节点光滑有限元上限法转化为标准的二阶锥规划模型。此模型可以采用高效的原对偶内点算法进行求解。通过岩土工程中经典问题的数值分析,验证了新方法的可靠性,并通过数值分析发现,结构与土体接触的强度性质对结构的失稳模式和极限承载力具有明显的影响。

The finite element limit analysis based on strain smoothing provides an effective and highly accurate numerical approach for stability analysis in geotechnical engineering.A novel upper bound limit analysis using node-based smoothed finite element(NSFEM)is proposed to account for the discontinuous kinematic velocity field.By introducing a discontinuous velocity at the soil-structure interface,characterized by nodal velocity jumps between interface nodes,the strain-smoothed domains are reconstructed based on these interface nodes.The plastic dissipation rates of interfaces and strain-smoothed domains are separately calculated according to the Mohr-Coulomb yield criterion and associated flow rule.These criteria and rules are represented as a series of standard second-order cones.Consequently,the NSFEM-based upper bound limit analysis is formulated as a second-order cone programming(SOCP)problem,solvable effectively using the primal-dual interior point algorithm.The proposed method’s reliability was initially confirmed through benchmark problem analysis in geotechnical engineering,revealing that the interface strength between soil and structure significantly influences the failure mechanism and ultimate bearing capacity of structures.