This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d...This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).展开更多
A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. A...A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.展开更多
In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundam...In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.展开更多
The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the materia...The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.展开更多
3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stres...3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.展开更多
基金Project (Nos. 10472102 and 10432030) supported by the NationalNatural Science Foundation of China
文摘This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).
文摘A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.
文摘In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.
文摘The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.
文摘3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.
