A study of incremental‐iterative strategies for non‐linear analyses

Abstract

SUMMARYThe paper describes a study of incremental-iterative solution techniques for geometrically non-linear analyses. The solution methods documented are based on a modified Newton-Raphson approach, meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations. A consistent mathematical notation is employed in the description of the iterative and load incrementation strategies, enabling the simple inclusion of several solution options in a computer program. The iterative strategies investigated are iteration at constant load, iteration at constant displacement, iteration at constant 'arc-length', iteration at constant external work, iteration at minimum unbalanced displacement norm, iteration at minimum unbalanced force norm and iteration at constant 'weighted response'. The load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step, strategies based on the 'current stiffness parameter' and a strategy based on a parabolic approximation to the load4eflection response. Criteria for detecting when the applied external load increment should reverse sign are described.A challenging example of a circular arch exhibiting snap-through (load limit point) behaviour and snapback (displacement limit point) behaviour is solved using several different iterative and load incrementation strategies. The performance of the solution schemes is evaluated and conclusions are drawn.

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