EXTREMUM METHODS OF STRUCTURAL ANALYSIS FOR SYSTEM RELIABILITY ASSESSMENT

Discrete extremum methods of systems analysis are demonstrated as a tool for structural system reliability assessment. Specifically, linear and multiobjective linear programming based procedures are developed for structural analysis of ductile frames under proportional and multiparameter loading, respectively. Kinematic and static approaches for rigid plastic analysis form a primal-dual pair in each of these models and have a polyhedral format. Duality relations link extreme points and hyperplanes of these polyhedra and lead naturally to dual methods for computing system reliability, depending upon the treatment of uncertainty.; Random events-based procedures require enumeration of the failure modes, and these are identified as the extreme points of the convex polytope for the kinematic model. An algorithmic procedure is used for the generation of the multiple failure modes of frames under proportional loading in ascending order of their collapse loads. The method can be used to generate a prespecified number of modes or all modes up to a specified level of significance. Modal collapse loads, failure mode expressions, bending moment distributions, modal correlations and bounds on the number of failure modes are easily available.; Random variable methods proceed from the limit surface demarcating the safe and unsafe regions. A static multiobjective programming model is formulated for frames under multiparameter loading, in which the weak noninferior sets represent the limit surfaces in load and basic variable spaces. Powerful computational procedures are utilized for generating the global n dimensional polyhedral limit hypersurfaces. The maximal facets of the polyhedra represent unique failure modes. Bending moment distributions, load combinations leading to a given mode, and modal correlations can be obtained.; A new approach for the estimation of structural system reliability based on the random variable approach is presented. The proposed method replaces the safe region of the structure with an analytically tractable region of equivalent volume, where this volume may be of different order and dimension. The system reliability can be computed from the properties of the substituted region. A hyperspherical equivalent region is used for polytopic limit surfaces, and the system reliability is directly available from probability tables.