The Nonlinear Stability Of Shallow Spherical Shells Under Center Concentrated Loads

The analysis of shallow shell bearing force becomes a very important question with the abroad applications of shells.This paper is concerned with the nonlinear stability problem of shallow spherical shells with identical thickess under the action of central concentrated loads.The essay use power functions as trial functions and take advantage of collocation method to get the results of equilibrium equations ,and critical loads are computed at successive increment of concentrated loads, and so the internal force and deflections。The Newton-iterative method is adopted to acquire the keys to the equilibrium equations because the equations are non-linear differential equations. This method is simple and convergent speed is fast. At the same time ,this paper model shallow shells with ANSYS finite-element with different boundary conditions and different shell rise to analyze film internal force, which is anastomosed to the programme value with FORTRAN well and also testify the programme with FORTRAN is convenient , has high precision and good currency in use.Four boundary conditions and different shell rises are considered to get critical loads in this paper,which are fixed clamp ,motive clamp,pinned bearing,simpleness bearing. good convergency results can be gained although the shell rise is large using the programme .All of above have been programmed with FORTRAN and some have analysed with ANSYS finite-element and tested on the computer. The examples testify that the collocation method has the advantages of less calculation quantities and accurate results.