1、 第 1 頁(yè)中文 中文 2300 字Analytical solution nonrectangular plate with in-plane Variable stiffnessTian-chong YU， Guo-jun NIE， Zheng ZHONG， Fu-

2、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 basi

3、c 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 f

4、ollowing 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 equati

5、on 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 prese

6、nt 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

7、design of rectangular plates with in-plane variable stiffness. Keywords: in-plane variable stiffness ,power form，Levy-type solution，rectangular plateChinese Library Classification 03432010 Mathematics Subject Classific

8、ation 74B05第 3 頁(yè)It is assumed that the flexural rigidity of the plate varies only along the Y-direction according to the following power form:Where Y and P are two material parameters describing the in homogeneity of D,

9、Do is the flexural rigidity at，Y=0, and Db is the flexural rigidity at Y=b. In this ‘case, Eq. (1) can be reduced to3 SolutionThe rectangular plate is assumed to be simply supported along two opposite edges parallel to

10、 the Y-direction. To solve the governing equation with the prescribed boundary conditions, a generalized Levy-type approach is employed aswhere Ym(y) is an unknown function to be determined.Substituting Eq. (4) into Eq.