Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the curren...Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.展开更多
The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matchi...The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.展开更多
In this paper,for the 3D quadratic nonlinear Klein-Gordon equation on the product space R^(2)×T,we focus on the lower bound of the lifespan of the smooth solution with slowly decaying initial data.When the size o...In this paper,for the 3D quadratic nonlinear Klein-Gordon equation on the product space R^(2)×T,we focus on the lower bound of the lifespan of the smooth solution with slowly decaying initial data.When the size of initial data is bounded by ε_(0)>0,it is shown that a smooth solution exists up to the time C_(0)/20 with0 being sufficiently small and e^(c0)/ε_(0)^(2)>0 being some suitable constant.Note that the solution of the corresponding 3D linear homogeneous Klein-Gordon equation on R^(2)×T only admits the optimal time-decay rate(1+t)−1,from which we generally derive the lifespan of the nonlinear Klein-Gordon equation up to e^(c0/ε0)rather than the more precise e^(c0/ε^(2)0) here.展开更多
We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares func...We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 50709014)China National Funds for Distinguished Young Scientists (Grant No. 50925931)State Key Laboratory of Hydroscience and Engineering of China (Grant No. 2008-TC-2)
文摘Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.
基金This work was subsidized by the special funds for major state basic research projects under 2005CB321700 and a grant from the National Science Foundation （NSF） of China （No. 10471144）.
文摘The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.
基金supported by National Natural Science Foundation of China(Grant No.11871030)supported by National Natural Science Foundation of China(Grant No.11731007)。
文摘In this paper,for the 3D quadratic nonlinear Klein-Gordon equation on the product space R^(2)×T,we focus on the lower bound of the lifespan of the smooth solution with slowly decaying initial data.When the size of initial data is bounded by ε_(0)>0,it is shown that a smooth solution exists up to the time C_(0)/20 with0 being sufficiently small and e^(c0)/ε_(0)^(2)>0 being some suitable constant.Note that the solution of the corresponding 3D linear homogeneous Klein-Gordon equation on R^(2)×T only admits the optimal time-decay rate(1+t)−1,from which we generally derive the lifespan of the nonlinear Klein-Gordon equation up to e^(c0/ε0)rather than the more precise e^(c0/ε^(2)0) here.
文摘We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
