Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method.In the polar coordinate system,three group invar...Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method.In the polar coordinate system,three group invariant solutions are constructed by the invariants of the Lie group,which are admitted by the governing equations for the two-dimensional elastodynamics problem.The graphical figures of the group invariant solutions are presented,and the physical meanings of the group invariant solutions are expounded in some cases.展开更多
The tilted waves in steel strip during rolling and leveling of sheet metal can be classified into two different types of buckling, oblique and herringbone buckling, respectively. Numerical considerations of oblique an...The tilted waves in steel strip during rolling and leveling of sheet metal can be classified into two different types of buckling, oblique and herringbone buckling, respectively. Numerical considerations of oblique and herringbone buckling phenomena are dealt with by the spline finite element method （FEM）. It is pointed out that the shear stress due to residual strains caused by the rolling process or applied non-uniform loading is the main reason of oblique and herringbone buckle. According to the analysis of stress distribution in plane, the appropriate initial strain patterns are adopted and the corresponding buckling modes are calculated by the spline FEM. The developed numerical model provides an estimation of buckling critical load and wave configuration.展开更多
The ribbing problem has serious influence on the steel product quality, which produces additional shape waves on the surface of uncoiled steel strip on the process of curl. Nonlinear spline finite element method （n-s...The ribbing problem has serious influence on the steel product quality, which produces additional shape waves on the surface of uncoiled steel strip on the process of curl. Nonlinear spline finite element method （n-spline FEM） is adopted to establish the relationship between the ribbing height and deflection of additional shape wave, for example, post buckling deformation. The proposed spline FEM is more effective and convenient than traditional finite element method in the buckling analysis. Using the spline FEM, the shape wave caused by the ribbing is calculated, and then the ribbing values can be obtained which are difficult to measure in practice. At the same time, the judgment rule is also given for estimating the strip quality according to the ribbing value.展开更多
基金Supported by the key project of the 8th Five Year Plan of Scientific Committee of Guizhou Province(1993 No.2037)the key project of the"9th Five Year Plan”of Scientific Committee of Guizhou Province.(1996 No.1028)
文摘Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method.In the polar coordinate system,three group invariant solutions are constructed by the invariants of the Lie group,which are admitted by the governing equations for the two-dimensional elastodynamics problem.The graphical figures of the group invariant solutions are presented,and the physical meanings of the group invariant solutions are expounded in some cases.
基金Item Sponsored by National Natural Science Foundation of China(5107531,50675021)
文摘The tilted waves in steel strip during rolling and leveling of sheet metal can be classified into two different types of buckling, oblique and herringbone buckling, respectively. Numerical considerations of oblique and herringbone buckling phenomena are dealt with by the spline finite element method （FEM）. It is pointed out that the shear stress due to residual strains caused by the rolling process or applied non-uniform loading is the main reason of oblique and herringbone buckle. According to the analysis of stress distribution in plane, the appropriate initial strain patterns are adopted and the corresponding buckling modes are calculated by the spline FEM. The developed numerical model provides an estimation of buckling critical load and wave configuration.
基金Sponsored by National Natural Science Foundation of China(51075031,50675021)
文摘The ribbing problem has serious influence on the steel product quality, which produces additional shape waves on the surface of uncoiled steel strip on the process of curl. Nonlinear spline finite element method （n-spline FEM） is adopted to establish the relationship between the ribbing height and deflection of additional shape wave, for example, post buckling deformation. The proposed spline FEM is more effective and convenient than traditional finite element method in the buckling analysis. Using the spline FEM, the shape wave caused by the ribbing is calculated, and then the ribbing values can be obtained which are difficult to measure in practice. At the same time, the judgment rule is also given for estimating the strip quality according to the ribbing value.
