The Nonlinear Analyses Of Thin Circular Plates With Arbitrarily Variable Thickness Under A Concentrated Load

In this paper, it is researched that the non-linear bending problem about circular plates with arbitrarily variable thickness.The essay gives the basic equations of the large deflection of thin circular plates with arbitrarily variable accurate thickness and variable loads. The non-linear differential equations are acquired by using power functions as trial functions and through the collocation method when the results of basic equations are sought. The Newton-iterative method is adopted in order to acquire the keys of the differential equations because the equations are non-linear differential equations. The Newton- iterative method is concise, and the convergence velocity of the method is very quick.When we analyses the non-linear bending problem of thin circular plates with arbitrarily variable thickness, loads imposed may be concentrated load at its center, uniformly distributed load, uniformly distributed radial moments and forces along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value was in great excess of normal one. In this paper, not only four boundary conditions, such as rigidly clamped edge, clamped but free to slip edge, simply hinged edge and simply supported edge, but also the elastic support is considered. The most research work in the paper is made up of the non-linear analyses of thin circular plates with arbitrarily variable thickness and a concentrated load at its center. Under action of a concentrated load at its center, linear solutions of thin circular plates with linearly or quadratic variable thickness are compared with those obtained by the parameter method. In addition, ANSYS which is one of the large-scale finite element softwares provides the results for many examples given in the paper. By comparison, it is indicated that the method of this paper is reliable.All of above contents have been programmed with Mathematica and tested on the computer. The program is simple in use and has good currency.