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
The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displace...The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.展开更多
The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and ele...The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.展开更多
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.
文摘The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.
文摘The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.
