Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the t...Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.展开更多
The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are reso...The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are resolved by homotopy perturbation method which is applied in reaction diffusion model. This model is utilized to verify the effect of the density of forest cover with the following variables namely seed reproduction, seed deposition, seed establishment rates, coefficients of aging of old tree and coefficients of mortality on the space variable.展开更多
基金Project(51321065,51479191,11672360)supported by the National Natural Science Foundation of China。
文摘Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.
文摘The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are resolved by homotopy perturbation method which is applied in reaction diffusion model. This model is utilized to verify the effect of the density of forest cover with the following variables namely seed reproduction, seed deposition, seed establishment rates, coefficients of aging of old tree and coefficients of mortality on the space variable.
