The Nonlinear Axisymmetrical Analyses Of Circular Plates With Arbitrarily Variable Thickness

The essay mostly analyses the nonlinear bending problem of circular plates witharbitrarily variable thickness, and apply it to the practice of engineering, andanalyses the optimization design of circular plats.Cubic B-splines taken as trial function, the large deflection of circular plateswith arbitrarily variable thickness was calculated by the method of point collocation.Because of the discontinuous smoothness of the cubic B-spline function, the functionis very flexible for the problem of the function approach. The Newton-iterativemethod is used to solve the nonlinear differential equation of circular plates. Themethod is concise, and the convergence velocity of the method is very quick. Notonly four boundary conditions, such as rigidly clamped edge, clamped but free toslip edge, simply hinged edge and simply supported edge, but also the elastic supportis considered.When we analyses the nonlinear bending problem of circular plats witharbitrarily variable thickness, loads imposed may be polynomial distributed loads,uniformly distributed radial forces of moments along the edge respectively of theircombinations. Convergent solutions can still be obtained by this method under theload whose value was in great excess of normal one. Under action of uniformlydistributed loads, linear solutions of circular plates with linearly or quadraticvariable thickness are compared with those obtained by the parameter method.Buckling of a circular plate with identical thickness beyond critical thrust iscompared with those obtained by the power series method.During the analysis of the optimization design of circular plates, only oneboundary is considered. It is the rigidly clamped edge. On the basis of theabove-mentioned theory, in view of the saving of the material, and the techniques orthe difficulties of the construction, we think that the design of the linear thickness ofcircular plates is the optimization design. The example of brass is used to analyze thecoefficient of the function of thickness. From the problem, we apply the theory to thepractice.All of above contents have been programmed with FORTRAN and tested on thecomputer. The program is simple in use and has good currency.