Numerical manifold method based on isogeometric analysis
In this study,numerical manifold method(NMM)coupled with non-uniform rational B-splines(NURBS)and T-splines in the context of isogeometric analysis is proposed to allow for the treatments of complex geometries and local refinement.Computational formula for a 9-node NMM based on quadratic Bsplines is derived.In order to exactly represent some common free-form shapes such as circles,arcs,and ellipsoids,quadratic non-uniform rational B-splines(NURBS)are introduced into NMM.The coordinate transformation based on the basis function of NURBS is established to enable exact integration for the manifold elements containing those shapes.For the case of crack propagation problems where singular fields around crack tips exist,local refinement technique by the application of T-spline discretizations is incorporated into NMM,which facilitates a truly local refinement without extending the entire row of control points.A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed.Results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies.The coordinate transformation based on the NURBS basis function improves the accuracy of NMM by exact integration.The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.
Youliang ZHANG Dengxue LIU Fei TAN
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics,Chinese Academy of Sciences, Wuhan, China
国际会议
The 12th International Conference on Analysis of Discontinuous Deformation(第12届非连续变形分析国际大会)
武汉
英文
28-28
2015-10-16（万方平台首次上网日期，不代表论文的发表时间）