{'fraction_non_alphanumeric': 0.02247191011235955, 'fraction_numerical': 0.0, 'mean_word_length': 5.941558441558442, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
HOLONOMIC SOFTENING: MODELS AND ANALYSIS*

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.