无单元法在高速公路沉降计算中的应用研究

Study on application of meshless method to settlement calculation of expressway

无单元法是一种新型数值计算方法,它只需要节点相关信息就能建立离散模型。笔者首先介绍了不等阶多项式基的径向点插值法基本理论,接着将其应用到分级施工下的软基高速公路断面沉降计算中,推导出此类问题的系统矩阵方程,并与有限元法解进行了分析对比。结果表明:该法不但计算精度高,而且在求解路堤分级施工的这类移动边界问题的沉降时,比有限元法更方便,故在工程实践中将具有广阔的应用前景。

Meshless method is a new type numerical calculation method, which can use only a set of nodes to formulate the discrete model. After the basic theory of radial point interpolation method with unequal polynomial basis (URPIM) is introduced, and then URPIM is applied to calculate the settlement and deformation of expressway subjected to multi-stage loadings on soft ground. Furthermore, the system stiffen equation of this problem is developed and the results are also compared with those of finite element method. It is found that the URPIM is more accurate and more convenient to handle the moving boundary problem as embankment constructed by stages. This method will has wide application foreground in engineering.