Numerical Methods in Bending and Buckling of Plates

A comparison is drawn between numerical and analytical approaches to problems of plate bending and buckling. Certain analytical methods are reviewed and deficiencies are noted leading to a logical development of iterative numerical techniques for achieving essentially identical results. One such technique is presented for investigating the post-buckling behavior of circular plates possessing arbitrary boundary conditions under uniform edge loads. Although a relatively simple problem, it emphasizes the development of the computer program and the conditioning of certain classes of nonlinear differential equations to fit such a program. It is seen that such a procedure resolves a fundamental shortcoming of series solutions to simultaneous, nonlinear differential equations by avoiding arguments concerning the significant number of terms required to satisfy prescribed initial and final boundary conditions with sufficient accuracy. Instead, it replaces a two point boundary value problem with an initial value problem and a Runge-Kutta numerical integration process which may be carried out step-by-step to attain prescribed kinematic and geometric terminal conditions.