Quadratically convergent direct calculation of critical points for 3d structures undergoing finite rotations

In this work we present the implementation details of a quadratically conve rging, Newton-method-based algorithm for direct computation of instability points for 3d structures undergoing finite rotations. The structural model chosen for illustration is the 3d geometrically exact beam. The proposed al gorithm makes use of an extended system, where equilibrium equations are su pplemented with the loss-of-stability condition which roughly doubles the t otal number of equations. Nonetheless, the latter requires only an insignif icant increase in computational cost due to judicious use of the bordering algorithm For computing the solution. The main thrust of our work is direct ed towards a careful development of linearized forms of the governing equat ions employed by Newton's method. The corresponding results are presented b oth in material and spatial versions. A set of numerical examples is used t o illustrate a very satisfying performance of the proposed algorithm. (C) 2 000 Elsevier Science S.A. All rights reserved.