非连续性结构的样条QR法

Spline QR methods for discontinue construction

混凝土结构中本身存在的或在使用过程中出现的诸如节理、裂纹和孔隙等缺陷往往对整个结构的失稳或破坏起着控制作用。在有限元的基础上提出一个能模拟诸如裂纹、节理等非连续性结构的新技术——非连续样条QR法,该方法采用样条QR法并结合非有限元法的优点,可以很方便计算非连续性结构,无需要重新划分网格。该方法与有限元相比,具有较大的优势,避免了流动法则理论带来的困难及缺陷,在算法上数值计算量不大,迭代收敛速度快,不仅计算快,而且精度高。

Whole structure is often controlled by some discontinuous structure during it＇s destroy and losing stabilization, such as cracks and joints.Spline QR method, as a new technique for modeling discontinuities such as cracks and joints in the finite element framework,is presented. This method takes advantage of excellence of QR and finite element methods.A standard displacement-based approximation is enriched near a discontinuity by incorporating both discontinuous fields and the near tip asymptotic fields function. This technique allows the entire discontinuity to be represented independently of the mesh, and so remeshing is not necessary to model the evolvement of discontinuity.Comparing with finite element, this method is more economical and forthright for computing, and difficulties in flow rule is avoided.Then, iteration convergence and computing is more rapid, what＇s more, computing precision is higher.The computed result show that QR method is a better method.