Accuracy Analysis Of Numerical Manifold Method Based On Independent Covers

Numerical Manifold Method(NMM)uses two independent meshes,has the ability of solving the problems with continuous deformation or discontinuous deformation and solves the problem of pre-processing.But there are some problems in Numerical Manifold Method currently using finite element meshes as mathematical meshes,such as the low calculation accuracy at some key parts,the linear dependence of simultaneous equations when using higher order functions,the inconvenience of mesh refinement.In view of these problems caused by the forms of completely overlapping covers,NMM based on independent covers is presented by Yangtze River Scientific Research Institute.The new method adopts an analysis mode mainly concerning independent covers and has the advantage of the refinement of local meshes and the rapid convergence of specific areas over traditional NMM,providing new ideas of solving the problems above.But the method requires further research in convergence,accuracy analysis and self-adaptivity.Considering the importance of computing accuracy in the application of the new method,accuracy analysis of NMM based on independent covers is carried out.These works have been done:(1)Several examples verify the existing three error estimators,showing that these estimators are basically reasonable,that the internal error in an independent cover can not be effectively controlled,and that research needs for reasonable arrangement of covers in singular areas around crack tips are presented due to the unsatisfaction of the error estimators in these specific areas.(2)The internal error in an independent cover can not be effectively controlled.So the submodel method for error analysis of independent covers is presented.By means of increasing the cover function order in an individual independent cover,a new error estimator is obtained by calculating the differences of the results between high-order and low-order cover functions.This method is also prepared for point-by-point error control in the future.The procedure of the submodel method is introduced in detail.Then examples such as a gravity dam show that the method can effectively control the internal error of independent covers.(3)Cover arrangement around the crack tip is explored by numerical tests since the error estimators in singular areas around crack tip are not easily satisfied,finding the boundary between the analytic cover and numerical covers around the crack tip.Starting from the analytic solution of stress,the general applicability of the cover arrangement is shown in the model I crack and the model II crack.An example verifies this reasonable cover arrangement could speed convergence and make the accuracy index in the covers around the crack tip satisfied.