Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bendin...Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.展开更多
By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi...By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.展开更多
To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the met...To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.展开更多
Firstly, the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with va...Firstly, the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with variable thickness in polar coordinates system. This cross equation in polar coordinates system is united with radical and tangential equations in polar coordinates system, and then three equilibrium equations were obtained. Physical equations and nonlinear deformation equations of strain at central plane are substituted into superior three equilibrium equations, and then three unsymmetrical nonlinear equations with three deformation displacements were obtained. Solution with expression of Fourier series is substituted into fundamental equations; correspondingly fundamental equations with expression of Fourier series were obtained. The problem was solved by modified iteration method under the boundary conditions of clamped edges. As an example, the problem of circular thin plate with variable thickness subjected to loads with cosin form was studied. Characteristic curves of the load varying with the deflection were plotted. The curves vary with the variation of the parameter of variable thickness. Its solution is accordant with physical conception.展开更多
文摘Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.
文摘By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.
文摘To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.
文摘Firstly, the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with variable thickness in polar coordinates system. This cross equation in polar coordinates system is united with radical and tangential equations in polar coordinates system, and then three equilibrium equations were obtained. Physical equations and nonlinear deformation equations of strain at central plane are substituted into superior three equilibrium equations, and then three unsymmetrical nonlinear equations with three deformation displacements were obtained. Solution with expression of Fourier series is substituted into fundamental equations; correspondingly fundamental equations with expression of Fourier series were obtained. The problem was solved by modified iteration method under the boundary conditions of clamped edges. As an example, the problem of circular thin plate with variable thickness subjected to loads with cosin form was studied. Characteristic curves of the load varying with the deflection were plotted. The curves vary with the variation of the parameter of variable thickness. Its solution is accordant with physical conception.
