Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The p...Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.展开更多
Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. Th...Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. The solution of a fully clamped rectangular plate is presented using two different series solutions. The results of a square plate are compared with the results of the classical plate theory, Reissner- Mindlin theory and the three dimensional theory of elasticity for different aspect ratios. Two types of clamped boundary conditions are investigated. The obtained results show that Bergan-Wang approach gives good agreement for both very thin and moderately thick plates.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51108412,11472244,and 11202186)the National Basic Research Program of China(973 Program)(No.2013CB035901)+1 种基金the Fundamental Research Funds for the Central Universities(No.2014QNA4017)the Zhejiang Provincial Natural Science Foundation of China(No.LR13A020001)
文摘Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.
文摘Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. The solution of a fully clamped rectangular plate is presented using two different series solutions. The results of a square plate are compared with the results of the classical plate theory, Reissner- Mindlin theory and the three dimensional theory of elasticity for different aspect ratios. Two types of clamped boundary conditions are investigated. The obtained results show that Bergan-Wang approach gives good agreement for both very thin and moderately thick plates.
