Nonlinear Stability Of Shallow Spherical Shells With Arbitrarily Variable Thickness Under A Concentrated Load

This paper is concerned with the nonlinear stability problem of shallow spherical shells with arbitrarily variable thickness under the action of a concentrated load.The essay first gives the basic presupposition and the basic equations, then we can get the basic equations of the large deflection of shallow spherical shells with arbitrarily variable thickness under the action of a concentrated load.Base on the basic presupposition and the basic equations of the large deflection of shallow spherical shells with arbitrarily variable thickness under the action of a concentrated load,the essay gives the non-linear differential equations.By using power functions and logarithm functions as trial functions, ,we can get the coefficient of the functions and critical loads are computed at successive increment of concentrated loads through the collocation method,and so the internal force and deflections.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 is concise and the convergence velocity of the method is very quick.When we anslyses the non-linear bending problem of shallow spherical shells with arbitrarily variable thickness, loads imposed may be concentrated loads at its center, uniformly distributed load, uniformly distributed radial moments and forces along the edge respectively or their combinations (There we just talk about the concentrated load at the central).Convergent solutions can still be obtained by this method under the load with great excessof normal value.The essay considers four boundary conditions and different shell rises(fixed clamp,motive clamp,pinned bearing,simpleness bearing) and gets very good convergency results.In addition, ANSYS which is one of the large-scale finite element software 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.