Use of arc-length method for capturing mode jumping in postbuckling aerostructures

<p>The arc-length method has become a widely established solution technique for studying nonlinear structural behavior. By augmenting the set of nonlinear equilibrium equations with a constraint equation, which is a function of both the displacements and load increment, it is capable of traversing limit points. Numerous investigations have shown that highly nonlinear behavior such as sharp "snap-backs" can still lead to numerical difficulties. Two practical examples are presented to assess the effectiveness of this solution technique in capturing secondary instabilities in postbuckling structures, which present themselves as abrupt mode jumps. Although the first example poses no special difficulties, in the second case the nonlinear procedure fails to converge. An improvement to the method's formulation is suggested, which accounts for the residual forces that are usually neglected, when proceeding to the next increment once convergence is reached on the current increment. The choice of a correct load increment at the first iteration, within a predictor-corrector scheme, is central to the method's effectiveness. Current strategies for a choice of this load increment are discussed and are shown to be no longer consistent with the modified formulation; therefore, a new approach is proposed.</p>