二阶奇异微分方程组边值问题两个正解的存在性

利用锥拉伸和锥压缩不动点定理,给出了一类二阶微分方程组奇异边值问题两个正解的存在性.     

Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior

A constitutive model of unsaturated soils with coupling capillary hystere- sis and skeleton deformation is developed and implemented in a fully coupled transient hydro-mechanical finite-element model （computer code U-DYSAC2）. The obtained re- sults are compared with experimental results, showing that the proposed constitutive model can simulate the main mechanical and hydraulic behavior of unsaturated soils in a unified framework. The non-lineaxity of the soil-water characteristic relation is treated in a similar way of elastoplasticity. Two constitutive relations axe integrated by an implicit return-mapping scheme similar to that developed for saturated soils. A consistent tan- gential modulus is derived to preserve the asymptotic rate of the quadratic convergence of Newton＇s iteration. Combined with the integration of the constitutive model, a complete finite-element formulation of coupling hydro-mechanical problems for unsaturated soils is presented. A number of practical problems with different given initial and boundary conditions are analyzed to illustrate the performance and capabilities of the finite-element model.     

毛细滞回内变量模型的高效数值积分方法

毛细滞回内变量模型是基于热动力学基本原理推导出来的土水特征本构模型,能够有效地描述干湿循环情况下非饱和土中的毛细滞回现象.研究了该模型的形式特点和数值积分方法,就经典的Euler法、4阶Runge-Kutta法和4阶Adams-Bashforth法的积分效果进行了对比.计算结果表明,Euler法精度很低,累计误差较大;4阶Adams-Bashforth法精度最高,且运算效率高于同阶的Runge-Kutta法,适合对该模型进行求解和参数标定.将基于Adams-Bashforth法的子程序集成到有限元程序中,两相渗流模拟结果的精度有了较大提高.