Shooting-optimization technique for large deflection analysis of structural members

Abstract

Large deflection and post-buckling responses of structural members may be obtained either by using the finite element method or by solving the exact nonlinear governing differential equation. This paper deals with the latter approach. An easy-to-use technique for solving the nonlinear two-point boundary value problem is proposed. The technique combines the idea of the shooting method and optimization algorithms. Using the shooting method, the two-point boundary value problem is converted into a set of initial value problems which are then integrated forward using the Runge-Kutta algorithm. For a solution, the terminal boundary conditions are satisfied by adjusting the unknown initial values and parameters of the differential equations. The adjustments are carried out through the minimization of the errors in the terminal boundary conditions using an optimization algorithm. The technique is demonstrated on a large class of problems involving large deflection and post buckling of a beam, a column, a ring, an arch and a frame.