In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and exist...In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for yon Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.展开更多
In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainl...In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finitedimensional global attractor.展开更多
A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress f...A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation ate imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be mode by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existe in the literature.展开更多
An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a dis...An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presented to show that the numerical method works well and the model agrees well with physical observations, especially successfully simulated for the first time the telephone cord buckles with two humps along the ridge of each section of a buckle.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(2014R1A1A3A04049561)
文摘In this paper, we consider a von Karman equation with infinite memory. For yon Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for yon Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of ScienceICT and Future Planning(Grant No.2014R1A1A3A04049561)
文摘In this paper a von Karman equation with memory,utt + α?2u- γ?utt- integral from n=-∞ to t μ(t- s)?2u(s)ds = [u, F(u)] + h is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finitedimensional global attractor.
文摘A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation ate imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be mode by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existe in the literature.
基金supported by the Major State Basic Research Projects (Grant No. 2005CB321701)National Natural Science Foundation of China (Grant No. 10871011)Research Foundation of Doctoral Program of the Ministry of Education of China (Grant No. 20060001007)
文摘An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presented to show that the numerical method works well and the model agrees well with physical observations, especially successfully simulated for the first time the telephone cord buckles with two humps along the ridge of each section of a buckle.
