地基沉降大变形有限元分析的几何刚度效应

Effects of geometrical stiffness on foundation settlement by finite-strain finite element analysis

研究了基于完全拉格朗日(Total Lagrangian)描述的大变形有限元法分析地基沉降问题的几何刚度效应。在有限元列式的推导过程中严格考虑了土力学表述习惯的影响。通过算例分析,主要研究了几何刚度效应对荷载-沉降曲线的影响,并对比分析了不同率型大变形分析中的几何刚度效应问题。结果表明,几何刚度效应的存在减小了地基大变形有限元系统的刚度;忽略几何刚度效应将导致沉降计算结果偏小,在地基变形较大的情况下误差更明显,Truesdell率型大变形分析的最终沉降结果与小变形法的结果一致。几何刚度效应在地基大变形有限元分析中具有一定程度的影响,处理不当可能出现结构刚度增大的现象。大变形分析结果的性质偏于刚硬。

Based on the total Lagrangian description, the finite-strain finite element method （FEM） for foundation settlement is formulated and investigated from the viewpoint of the effect of geometrical stiffness （EGS）. The soil mechanics sign convention was considered in the derivation of the FEM formulation. An illustrative example is used to study the EGS on the curve of load vs. settlement, and to analyze comparatively the EGS on the finite-strain FEM based on constitutive relations using different stress rates. The results indicate that：（1） the occurrence of EGS decreases the stiffness of the finite-strain FEM system for foundation settlement problems; （2） the ignorance of EGS will underestimate the values of simulated results, esp. for the case of large deformation; （3） the ultimate settlement predicted by finite-strain FEM based on the constitutive relation with Truesdell stress rate would be the same with that by conventional small-strain method, etc. The EGS of finite-strain FEM for foundation settlement plays an important role in accurate simulation, and should be treated appropriately. Any improper treatment of EGS would change the property of finite-strain analysis results with higher stiffness.