Pseudo-linearization procedure of nonlinear ordinary differential equations for large deflection problem of circular plates

摘要

The large deflection problem of the circular plate is considered in this paper. Generally, there are some nonlinear terms in the ordinary differential equation resulted. For example, one term takes the form (dw/dr)~2, where w(r) is the deflection function and r is the radial coordinate. Different from the previously suggested procedures, an alternative procedure is suggested in this paper. In the procedure, one factor dw/dr in the nonlinear term (dw/dr)~2 is replaced by a temporarily given function g(r). This means that the term (dw/dr)~2 is replaced by g(r)(dw/dr) where the function g(r) is obtained from the previous round iteration. A linear ordinary differential equation is obtained by using this substitution and we can make the relevant iteration. Therefore, the method is called a pseudo-linearization procedure in this paper. It is proved that the convergence range for the nondimensional loading is significantly elevated by using this approach.