By analyzing the relationship between Reissner’s and Kirchhoff’s plate theories, a new solution for Reissner’s plate bending is presented in this paper, where the perturbation method is applied to deduce Reissner’...By analyzing the relationship between Reissner’s and Kirchhoff’s plate theories, a new solution for Reissner’s plate bending is presented in this paper, where the perturbation method is applied to deduce Reissner’s plate problem into a series of Kirchhoff’s one which is easy to solve. An example is given to show that the method presented is simple and of high accuracy.展开更多
In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner’s theory.First,the paper gives the basic solution of the bending of thick rectangular p...In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner’s theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate withthree clamped edges and one free edge under umiformly distributed load is found byRTM, finally, we analyze numerical results of the sohution.展开更多
The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The el...The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.展开更多
In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thi...In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.展开更多
文摘By analyzing the relationship between Reissner’s and Kirchhoff’s plate theories, a new solution for Reissner’s plate bending is presented in this paper, where the perturbation method is applied to deduce Reissner’s plate problem into a series of Kirchhoff’s one which is easy to solve. An example is given to show that the method presented is simple and of high accuracy.
文摘In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner’s theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate withthree clamped edges and one free edge under umiformly distributed load is found byRTM, finally, we analyze numerical results of the sohution.
基金supported by the National Natural Science Foundation of China(Nos.90305023 and 11172332)
文摘The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.
文摘In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.
