The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave dire...In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave direction and the overtopping discharge on the top of the sloping dike is focused on and put into analysis and discussion; and a modified formula for mean overtopping discharges under oblique irregular waves is proposed. The study shows that the mean overtopping discharge generally goes down as the relative wave obliquity fl increases for a fixed measurement point and the mean overtopping discharge generally increases as the wave steepness H/L decreases (the cycle increases) for a fixed relative wave obliquity.展开更多
The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded tra...The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
基金supported by the National Key Research and Development Program of China(Grant Nos.2016YFC1402000 and 2016YFC1402002)the Special Funds Targeting at Industrial Scientific Researches for Public Welfare of Ministry of Water Resources(MWR)(Grant No.201401004)+3 种基金the National Natural Science Foundation of China(Grant No.51579156)the Major Project of Nanjing Hydraulic Research Institute Funds(Grant No.Y214009)the Jiangsu Province Hydraulic Science and Technology Projects(Grant No.2012001-8)the Jiangsu Province Hydraulic Science and Technology Projects(Grant No.2014048)
文摘In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave direction and the overtopping discharge on the top of the sloping dike is focused on and put into analysis and discussion; and a modified formula for mean overtopping discharges under oblique irregular waves is proposed. The study shows that the mean overtopping discharge generally goes down as the relative wave obliquity fl increases for a fixed measurement point and the mean overtopping discharge generally increases as the wave steepness H/L decreases (the cycle increases) for a fixed relative wave obliquity.
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 10432030)the Natural Science Foun-dation of Zhejiang Province (No. Y605040)Ningbo City (No.2005A610024), China
文摘The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.