Interaction Problems on Soil and Structures using BE/FE Hibrid Techniques

采用有限元和边界元的耦合方法，对土与结构的相互作用问题进行了数值分析。采用该方案计算了各种问题，如层上基础问题、裂隙体边坡问题、稳态热传导问题和非稳态热传导问题。结果表明：(1)该方法可有效地应用于复杂边界，即用有限元对较为复杂的边界进行离散，用边界元对较为简单的边界进行离散。这样，不仅减少了输入数据，而且减少了计算机资源。(2)如果一个材料体由不同材料常数的子域组成，则引入连接子域的连接单元。这样就可以处理子域之间的滑动现象。当多个子域完全连通且无滑移时，我们可以近似地取关节单元的弹性常数为<K_s> =100G, <K_n> =100E。(3)等效有限元方案更容易用计算机代码编写。但是，该方案需要对系数矩阵g进行逆变换。然后，为了减小g的大小，需要将BE区域划分为几个子域。在划分过程中，还可以引入上述的联合元素。(4)对于非线性应力传递分析，假定破坏区域采用有限元离散化，假定破坏区域采用边界元离散化。这是解决无穷问题最现实的离散化方案之一。本研究利用SUP法和BE法开发了另一种混合技术。结果表明，所提出的耦合方法对于分析各种无限问题是非常有效的。

The coupling procedure,using finite and boundary elements,is proposed numerically to analize interaction problems on soil and structures. Various problems, such as footings on layers, slope problems with fractured masses, steady state heat conduction problems and unsteady state heat ones are calculated by this proposed scheme. Results are summarised as follows:(1)This procedure is efficiently applicable to complicated boundaries, namely, rather complicated boundaries are discretized by finite elements and simpler ones are done by boundary elements. Then, not only input data but also computer resources are reduced.(2) If a material body consists of subdomains whose material constants are different, joint elements are introduced connecting the subdomains. Then slipping phenomena between subdomains can be treated. If several subdomains are entirely connected without slip, we may choose spring constants of the joint elements approximately as <K_s> =100G and <K_n> =100E.(3) The equivalent FE scheme is much easier to program in a computer code. However, this scheme needs to invert coefficient matrix G. Then, the BE region should be divided into several subdomains in order to reduce the size of G. In this divided procedure, the joint elements mentioned above can also be introduced.(4) For the non-linear stress transfer analysis, the region where failure is supposed is discretized by finite elements, and others by boundary elements. This is one of the most realistic discretization schemes for the infinite problem. In this research the other hibrid technique is developed using SUP method and BE method. It is concluded that the proposed coupling procedure is very efficient to analyze various infinite problems.