Sheet metal spinning is an incremental forming process for producing axisymmetric thinwalled parts through continuous local deformation under the action of rollers.While studying the spinning process by finite element...Sheet metal spinning is an incremental forming process for producing axisymmetric thinwalled parts through continuous local deformation under the action of rollers.While studying the spinning process by finite element(FE)method,a critical bottleneck is the enormous simulation time.For beating off this challenge,a novel multi-mesh method is developed.The method can dynamically track the movement of rollers and adaptively refine the mesh.Thus,a locally refined quadrilateral computation mesh can be generated in the locally-deforming zone and reduce the unnecessary fine elements outside the locally-deforming zone.In the multi-mesh system,the fine elements and coarse elements are extracted from a storage mesh and a background mesh,respectively.Meanwhile,the hanging nodes in the locally refined mesh are removed by designing 4-refinement templates.Between computation mesh and storage mesh,a bi-cubic parametric surface fitting algorithm and accurate remapping methods are conducted to transmit geometric information and physical fields.The proposed method has been verified by two spinning processes.The results suggest that the method can save time by up to about 67%with satisfactory accuracy,especially for distributions of thickness and strain compared with the fully refined mesh.展开更多
A new multi-mesh contact algorithm for three-dimensional material point method is presented. The contact algorithm faithfully recovers the opposite acting forces between colliding bodies. Collision procedures between ...A new multi-mesh contact algorithm for three-dimensional material point method is presented. The contact algorithm faithfully recovers the opposite acting forces between colliding bodies. Collision procedures between regular bodies and/or rigid bodies are treated within the same framework. Multi-value of momentum and mass are defined on every node to describe the contact/sliding/separation procedure. Both normal and tangential velocities of each particle at the contact surface are calculated in respective individual mesh. A Coulomb friction is applied to describe the sliding or slipping between the contacting bodies. The efficiency of the contact algorithm is linearly related to the number of the contacting bodies because the overlapped nodes are labeled by sweeping the material particles of all bodies when the nodal momentum and mass are formed at every time step. Numerical simulation shows that our contact algorithm possesses high accuracy and low numerical energy dissipation, which is very important for solving collision problems.展开更多
In this work,we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two-and three-dimensions.The governing equations used are the phase field model,where the regularit...In this work,we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two-and three-dimensions.The governing equations used are the phase field model,where the regularity behaviors of the relevant dependent variables,namely the thermal field function and the phase field function,can be very different.To enhance the computational efficiency,we approximate these variables on different h-adaptive meshes.The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li(J.Sci.Comput.,pp.321-341,24(2005)).It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.展开更多
In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential e...In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential equation. The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. Of[line-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space （typically small）. Parareal in time algorithms based on a multi-grids finite element method and a multi-degrees finite element method are also presented. Some numerical results are reported.展开更多
We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show...We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time.We also show that due to large qualitative and quantitative differences between the two solution components,it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM.The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEMwith several other adaptive FEM algorithms.展开更多
基金co-supported by the supports of Guangdong Basic and Applied Basic Research Foundation(No.2019B1515120047)the National Natural Science Foundation of China(No.52130507)。
文摘Sheet metal spinning is an incremental forming process for producing axisymmetric thinwalled parts through continuous local deformation under the action of rollers.While studying the spinning process by finite element(FE)method,a critical bottleneck is the enormous simulation time.For beating off this challenge,a novel multi-mesh method is developed.The method can dynamically track the movement of rollers and adaptively refine the mesh.Thus,a locally refined quadrilateral computation mesh can be generated in the locally-deforming zone and reduce the unnecessary fine elements outside the locally-deforming zone.In the multi-mesh system,the fine elements and coarse elements are extracted from a storage mesh and a background mesh,respectively.Meanwhile,the hanging nodes in the locally refined mesh are removed by designing 4-refinement templates.Between computation mesh and storage mesh,a bi-cubic parametric surface fitting algorithm and accurate remapping methods are conducted to transmit geometric information and physical fields.The proposed method has been verified by two spinning processes.The results suggest that the method can save time by up to about 67%with satisfactory accuracy,especially for distributions of thickness and strain compared with the fully refined mesh.
基金The project supported by the Science Foundation of Laboratory of Computational Physics,Science Foundation of China Academy of Engineering Physics,and National Natural Science Foundation of China under Grant Nos.10702010,10775018,10472052,and 10604010
文摘A new multi-mesh contact algorithm for three-dimensional material point method is presented. The contact algorithm faithfully recovers the opposite acting forces between colliding bodies. Collision procedures between regular bodies and/or rigid bodies are treated within the same framework. Multi-value of momentum and mass are defined on every node to describe the contact/sliding/separation procedure. Both normal and tangential velocities of each particle at the contact surface are calculated in respective individual mesh. A Coulomb friction is applied to describe the sliding or slipping between the contacting bodies. The efficiency of the contact algorithm is linearly related to the number of the contacting bodies because the overlapped nodes are labeled by sweeping the material particles of all bodies when the nodal momentum and mass are formed at every time step. Numerical simulation shows that our contact algorithm possesses high accuracy and low numerical energy dissipation, which is very important for solving collision problems.
基金Part of Hu’s research was carried out while visiting Hong Kong Baptist UniversityHis research was also supported by an National Basic Research Program of China under the grant 2005CB32170+2 种基金Li’s research was partially supported by the National Basic Research Programof China under the grant 2005CB321701Foundation forNational ExcellentDoc-toral Dissertation Award of China and the Joint Applied Mathematics Research Institute between Peking University and Hong Kong Baptist UniversityTang’s research was sup-ported by CERG Grants of Hong Kong Research Grant Council and FRG grants of Hong Kong Baptist University.
文摘In this work,we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two-and three-dimensions.The governing equations used are the phase field model,where the regularity behaviors of the relevant dependent variables,namely the thermal field function and the phase field function,can be very different.To enhance the computational efficiency,we approximate these variables on different h-adaptive meshes.The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li(J.Sci.Comput.,pp.321-341,24(2005)).It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.
文摘In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential equation. The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. Of[line-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space （typically small）. Parareal in time algorithms based on a multi-grids finite element method and a multi-degrees finite element method are also presented. Some numerical results are reported.
基金supported by the Grant Agency of the Academy of Sciences of the Czech Republic under Grant No.IAA100760702and by the U.S.Department of Energy Research Subcontract No.00089911+1 种基金The third author acknowledges the financial support of the U.S.Office of Naval Research under Award N000140910218The fourth author acknowledges the financial support of the Estonian Ministry of Education,grant#SF0180008s08.
文摘We are concerned with a model of ionic polymer-metal composite(IPMC)materials that consists of a coupled system of the Poisson and Nernst-Planck equations,discretized by means of the finite element method(FEM).We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time.We also show that due to large qualitative and quantitative differences between the two solution components,it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM.The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEMwith several other adaptive FEM algorithms.
