B-Spline Function Method for the Problem of the Large Deflection of Circular Plate Subjected to Axisymmetrical Distributed Load
|Keywords||nonlinear analysis circular ring plate trial function B-spline function newton-iterative method|
The essay analyses the nonlinear problem of large deflection of circular ring plate.The cubic B-spline function is used as the trial function in the essay. Because of its discontinuous smoothness, the function is very flexible for the problem of the function approach. The Newton-iterative method is used to solve the nonlinear differential equation of circular plate. The convergence velocity of the method is very quick. Four outer boundary conditions, such as A1 (outer edge can not be movable along radial and vertical direction and rotational),A2(outer edge can be movable along radial direction but can not be movable along vertical direction and rotational),A3(outer edge can not be movable along radial and vertical direction but can be rotational),A4(outer edge can be movable along radial direction and rotational but can not be movable along vertical direction) and four inner boundary conditions, such as B1 (inner edge can not be movable along radial direction and rotational but can be movable vertical direction l),B2(inner edge can be movable along radial and vertical direction but can not be rotational),B3(inner edge can not be movable along radial direction but can be movable along vertical direction and rotational),B4(inner edge can be movable along radial and vertical direction and rotational ) are considered. At the same time, four loads such as uniformly distributed load, uniformly distributed load along inner edge uniformly distributed moment along inner edge. uniformly distributed moment along outer edge, are considered.About the condition of the uniformly distributed load, some examples are calculated and the results are very good. By comparing to other methods, the validity of the method is also demonstrated. With regard to circular ring plate subjected to axisymmetrical distributed load,in this paper, In all examples convergent results are obtained but results are compared with that obtained by the method of perturbation and so on. As a result the advantages of the method of cubic spline are large convergent range, high precision and little amount of computing time. Because inner and outer edge include four kinds of boundary conditions, accordingly sixteen combined boundary conditions were gained and complicated. At the same time. A1B1and A1B4 edge are more familiar. Thus the circular ring plate under action of uniformly distributed load which outer edge was d A1 and inner edge was B1or B4 were <WP=5>detailedly discussed. Besides, the circular ring plate under action of uniformly distributed load along edge which outer edge was A1 and inner was B1 and the circular ring plate under action of uniformly distributed moment along edge which outer edge was A1 and inner edge was B4 were cursorily discussed so as to validate these results in the paper.All of above contents have been programmed and tested on the computer. The program is simple in use and has good currency.