Safety life analysis under the required failure possibility constraint for structure involving fuzzy uncertainty

For ensuring safety service of structure under fuzzy uncertainty, some efficient methods are proposed for analyzing safety life under the constraint that the actual time-dependent failure possibility (TDFP) less than the target failure possibility. The direct dichotomy method is firstly established to solve the safety life. Since the direct dichotomy method needs to iterate the TDFP at all searching points of the safety life and results in large computational cost, the equivalent constraint method (ECM) is established to solve the safety life. In ECM, the equivalence between the constraint of the actual TDFP and the equivalent constraint of the lower boundary of the minimum of the response function is strictly proved by the reduction to absurdity. By equivalently replacing the constraint of the actual TDFP with that of the lower boundary of the minimum of the output response, the computational cost for estimating the safety life is greatly reduced. Two solutions of the safety life based on the ECM are established. One is ECM based dichotomy method. The other is ECM based Newton method, where a simplified derivative solution is deduced to reduce the computational cost. After the implementations of solving the safety life are given in detail, several examples are used to verify the rationality of the established safety life analysis model and the efficiency of the methods for solving safety life.