This paper deals with a special class of holonomic (path-independent) structural analysis problems involving nonlinear or piecewise linear softening. In particular, the formulation takes the form of a complementarity problem, an important class of mathematical problems characterized by the orthogonality of two sign-constrained vectors. A feature and difficulty associated with softening, which violates Drucker's stability postulate, is multiplicity of solutions. The main aims of this paper are to give a precise mathematical description of a wide class of softening models. This is achieved via a theoretically and computationally advantageous complementarity format. Second, key ideas underlying a recently developed complementarity solver, PATH, which has the potential of capturing any multiplicity of solutions or to show that none exists, are outlined. Two examples concerning discretized truss structures-a prototype of other more advanced finite element based structural models-are given for illustrative purposes.
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