Extension of the Linear Matching Method to frame structures made from a material that exhibits softening

This paper considers the problem of evaluating the maximum load that an elastic–plastic frame structure can withstand when material or element softening is present. Here we propose an extension of the Linear Matching Method to take into account material softening. The technique has two major steps: reduction of the total potential energy to obtain the solution of a linear problem and scaling of the resulting mechanism of deformation to maximize the load. Two procedures are evaluated for the second of these steps; a direct approach which simply examines how the solution evolves along a radial path in degree of freedom space, and an incremental method which takes into account how the solution might evolve along paths away from this radial line. It is demonstrated that the incremental approach is more robust and provides stable solutions for high and low levels of softening, but numerical instabilities in the procedure can occur for intermediate degrees of softening.