Reliability-based shape optimization of a pressure tank under random and stochastic environments

Reliability-based design of a pressure tank under timeindependent random and time-dependent stochastic uncertainties is considered. This pressure tank is an essential element in a reverse osmosis (RO) filtration system for storing filtered water and providing a useable flow rate from the faucet outlet. In this study, we consider the randomness in the welding strength between the upper and lower tanks, and the stochastic pressure applied to the inner surfaces of the tank as the main sources of uncertainty. A pressure tank with 90% reliability against fracture failure is desired. To enable the re-design of the pressure tank, the geometry is parametrized and then used as design variables in a shape optimization scheme. Kriging models are created to approximate the expensive finite element analyses in accessing the performances of each design. The uncertainty model of the welding strength between the upper and lower tanks is found to be well represented by a Gaussian distribution. The stochastic behavior of the pressure loading is modeled by a Markov-chain process. All models are integrated in a reliability-based design optimization problem formulation that has both time-independent and time-dependent reliability constraints. The first passage time and crossover rate are considered in the time-dependent reliability constraint and results of different constraint formulations are compared. The final optimal design satisfies all reliability constraints and reduces the material usage by as many as 46% comparing to the original design. Copyright © 2008 by ASME.