In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of ser...In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.展开更多
In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by...In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].展开更多
Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible eleme...Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
文摘In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
文摘In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].
文摘Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
