2-D问题条形传递函数方法与有限元法的分区耦合

Coupling of the strip distributed transfter function method with FEM for the analysis of 2-D elastic problems

将条形传递函数法 (SDTFM)和有限元法 (FEM)结合起来 ,给出了一种求解弹性 2 - D问题的新方法。该方法通过把二维求解区域分解成多个子区域 ,利用 SDTFM建立矩形子区域 (超级单元 )基于边界结点的刚度矩阵和结点力矢量 ,而对于其它几何形状的子区域则用有限元法建立刚度矩阵和结点力矢量 ,从而将 SDTFM推广到了任意几何形状的平面区域 ,克服了 SDTFM只能用于规则几何平面区域的不足。与单纯用有限元法求解相比较 ,本文方法具有划分单元少、求解速度快、计算精度高等优点 ,特别在求解高梯度应力时 。

A new method for the analysis of 2 D elastic problems, is presented by coupling the Strip Distributed Transfer Function Method(SDTFM) with the Finite Element Method. In the analysis with the method, the plane region concernd is first divided into a few rectangular subregions and other non\|regular geometrical ones. Based on the boundary nodes, the stiffness matrix and nodal force vector of the rectangular subregion, which is regarded as ‘super element’, are established according to the theory of SDTFM. The stiffness matrice and nodal force vectors of other non regular geometrical subregions are obtained with FEM. The assembly of the stiffness matrices and nodal force vectors is similar to FEM. By doing so, the application of SDTFM is extended to random geometrical plane region. Compared with FEM, the method has such the advantages as using fewer elements, faster convergence and highter accuracy of computation especially in dealing with high gradient stress.