The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts high...The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.展开更多
Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric ana...Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.展开更多
In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the for...In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.展开更多
基金supported by the National Key R&D Program of China (Grant No.2018YFC0407002)the National Natural Science Foundation of China(Grant Nos.11502033 and 51879014)
文摘The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.
文摘Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.
文摘In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.
