SOLUTION METHOD FOR NONLINEAR PROBLEMS WITH MULTIPLE CRITICAL-POINTS

An improved method is presented for solving nonlinear problems with multiple limit points and snap-back points. It is formulated in N + 1 dimensional space that includes one load parameter and N displacements as the unknowns. To solve these unknowns, a constraint equation is needed in addition to the N equations of equilibrium. Whether the constraint equation is proper can be justified from the bounded nature of the load parameter. The method presented herein may be referred to as the "generalized displacement control method." With the introduction of a general stiffness parameter, the method has been demonstrated to be numerically stable at the critical points, effective in adjusting the step sizes, and self-adaptive in changing the loading directions. Two examples with curves of the looping type have been solved by the present method for illustration.