中厚板生产车间工艺设计外文翻译.doc

第 PAGE 20页 Analytical solution nonrectangular plate with in-plane Variable stiffness Tian-chong YU， Guo-jun NIE， Zheng ZHONG， Fu-yun CHU (School of Aerospace Engineering and Applied Mechanics, Tongji University,Shanghai 200092, P.R. China) Abstract: The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form，and Poisson’s ratio is constant．A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation，and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads．The validity of the present solution is shown by comparing the present results with those of the classical solution．The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples．The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness. Keywords: in-plane variable stiffness ,power form，Levy-type solution，rectangular plate Chinese Library Classification 0343 2010 Mathematics Subject Classification 74B05 1 Introduction The term” variable stiffness” implies that the stiffness parameters vary spatially throughout. The structure[1]．Functionally graded materials (FGMs) are inhomogeneous composites，in which. the mechanical properties vary smoothly with the position to meet the predetermined functional. performance．The structures composed of the FGMs are of variable stiffness． There are extensive literatures on the bending，vibration，and fracture of the FGM structures[2-9]．The deformation of a functionally graded beam was studied by the d