固结问题的非线性局部点插值法解研究

Study on calculation of consolidation problem using nonlinear local point interpolation method

局部点插值法是一种新型的无单元法,该法构造出的位移和孔隙水压力的形函数具有d函数特性,所以,本质边界条件很易处理。首先,介绍了基本理论,给出求解比奥固结问题的主要公式。其次,对复层软基堆载引起的固结和沉降问题作了计算,其中节点采用均匀分布方式,且为了考虑土体的非线性特性计算程序中耦合了邓肯-张模型。最后,把计算值与有限元法、一维固结理论计算结果进行了对比。结果表明该法精度高,令人满意。

Local point interpolation method is a new type meshless method. Because its shape functions for displacements and pore water pressures possess delta function property, the essential boundary conditions can be imposed easily. After the basic theory is introduced and the main equations for solving Biots consolidation problem are developed, the consolidation and settlement of one multi-layer soft ground subjected to heaped loadings are calculated with it. Furthermore, the famous Duncan-Chang model is adopted in consideration of nonlinear properties of soil, and the uniform point distribution mode is selected. At last, comparisons with the results of one-dimensional consolidation method and FEM show that this method is more accurate and satisfying.