Structural System Reliability Using Linear Programming and Simulation

Abstract

The assessment of structural system reliability for reasonably complex structures is addressed. The general case of random loads and resistances with arbitrary probability distributions is examined for failure caused by simple plastic mechanisms. A combined simulation/linear programming approach gains its efficiency from the fact that every simulation derives an associated failure condition and its probability. The advantage of the method, therefore, is for highly reliable systems for which traditional Monte Carlo simulation techniques are notoriously inefficient. Load and resistance proportionalities are determined by each simulation, and the associated failure mode is identified by linear programming as a vertex on the system polytope. Significant modes are found naturally by the procedure and, in general, the number of such modes will be much less than the number of simulations. A single numerical integration without variable transformation determines the modal reliabilities, which are then combined into a system reliability.