| Plates are of an important of engineering structural members, which has been widely used in such fields as civil engineering, aerospace structures and so on. Plate can be divided into thin plate and thick plate. Since an elastic rectangular thin plate is the most common type in plate structural members, this study is mainly focus on the bending problems of rectangular thin plate. One of the main deformation characteristics of plate is bending, so it is of great significance to do a research about the plate bending deformation under various loads. Mathematical model of the plate bending problem is essentially the differential equation under certain boundary conditions. Usually the plate’s bending problem is very difficult to solve directly. Analytical solutions of the plate’s bending problem can be obtained not only when the shape of plate is regular, such as rectangle and circle, but also when the load on the plate is relatively simple, such as uniformly distributed load, concentrated load and so on. Therefore, the numerical method is commonly needed in the study of plate bending deformation.The barycentric rational interpolation method is a method of numerical calculation for solving differential equations. The barycentric rational interpolation method has so many advantages, such as simple computational formulas, fast speed of the programming running, high precision, convenient application of boundary conditions, and good node adaptability. For the situation of large sequences of points, rational interpolation has better approximations than polynomial interpolation. By employing the rational function as the interpolation basis function, it not only can improve the precision of interpolation, but also can overcome the instability problem of interpolation effectively. However, in the classical rational function interpolation, the occurrence of poles in the interval of interpolation can not be controlled. Berrut and Mittelmann suggested that it might use rational functions of higher degree in order to avoid poles. Floater and Hormann proposed a family of barycentric rational interpolants which not only have arbitrarily high approximation orders on any real interval, but also have no real poles and the interpolation function with infinite time smoothness. Barycentric rational interpolation has higher accuracy both in the situation of the special distribution of interpolation node, and also in the equidistant nodes.The center of gravity rational interpolation method for solving the problem of rectangular plate bending under different boundary conditions and different loads. Gives the four sides clamped rectangular plate (CCCC), simply supported rectangular plate (SSSS), on the side of the rectangular plate simply supported and clamped on the edge of a rectangular plate (SSCC), the role of the four sides of rectangular plates moment (FFFF), four sides on the role of simply supported rectangular plate uniformly distributed load, the load on the triangle edges simply supported rectangular plate and the role of linear distributed load of seven examples of rectangular plates on four sides simply supported the role. The first three examples rational interpolation method for the analysis of the center of gravity is not the same boundary conditions for accuracy and computational efficiency, the latter four examples analytical accuracy and computational efficiency of circumstances rational interpolation method for on-board gravity effect when different loads. Numerical examples results show that the center of gravity of rational interpolation method has good numerical stability, high accuracy and computational procedures to facilitate the preparation of the advantages... |
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