The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the...The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.展开更多
In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement f...In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.展开更多
By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution...By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution of two-dimensional model system of linearly viscoelastic ＂membrane＂ shell.展开更多
文摘The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.
基金The authors would like to thank China National Natural Science Foundation （91630201, U1530116, 11726102, 11771179）, and the Program for Cheung Kong Scholars of Ministry of Education of China, Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, 3ilin University, Changchun, 130012, P.R. China.
文摘In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.
基金National Natural Science Foundation of China(No.10271030)Foundation of Qufu Normal University for Ph.D
文摘By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution of two-dimensional model system of linearly viscoelastic ＂membrane＂ shell.
