Holonomic softening: Models and analysis

This paper deals with a special class of holonomic (path-independent) struc tural 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 orthogona lity of two sign-constrained vectors. A feature and difficulty associated w ith softening, which violates Drucker's stability postulate, is multiplicit y of solutions. The main aims of this paper are to give a precise mathemati cal description of a wide class of softening models This is achieved via a theoretically and computationally advantageous complementarity format. Seco nd, key ideas underlying a recently developed complementarity solver, PATH, which has the potential of capturing any multiplicity of solutions or to s how that none exists, are outlined. Two examples concerning discretized tru ss structures-a prototype of other more advanced finite element based struc tural models-are given for illustrative purposes.