This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） metho...This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.展开更多
The coupling iteration (CI) of the finite element method(FEM) is used to simulate the magnetic and mechanical characteristics for a GMM actuator. The convergent ability under different prestress and different load typ...The coupling iteration (CI) of the finite element method(FEM) is used to simulate the magnetic and mechanical characteristics for a GMM actuator. The convergent ability under different prestress and different load types is investigated. Then the calculated deformations are compared with the experimental values. The results convince that the CI of FEM is suitable for the simulation of energy coupling and transformation mechanism of the GMM. At last, the output deformation properties are studied under different input currents, showing that there is a good compromise between good linearity and large strain under the prestress 6 MPa.展开更多
There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement compo...There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.展开更多
Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Tw...Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11671106)the Fundamental Research Funds for the Central Universities(No.2016MS33)
文摘This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.
基金This project is supported by National Natural Science Foundation of China (No.50077019).
文摘The coupling iteration (CI) of the finite element method(FEM) is used to simulate the magnetic and mechanical characteristics for a GMM actuator. The convergent ability under different prestress and different load types is investigated. Then the calculated deformations are compared with the experimental values. The results convince that the CI of FEM is suitable for the simulation of energy coupling and transformation mechanism of the GMM. At last, the output deformation properties are studied under different input currents, showing that there is a good compromise between good linearity and large strain under the prestress 6 MPa.
文摘There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.
基金National Natural Science Foundation of China (Grant Nos. 11271298 and 11362021)
文摘Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.
