Xueyong Qu

Deterministic and Reliability-Based Optimization of Composite Laminates for Cryogenic Environments

Designs of composite laminates are investigated for hydrogen tanks in cryogenic environments. Large residual strains, which can develop due to thermal mismatch between matrix and fibers, result in matrix cracking at cryogenic temperatures and increase hydrogen leakage through the tank wall. To reduce thermal mismatch, ply angles need to be close to each other, but this leads to a substantial weight increase under biaxial loading. First deterministic optimization is used to investigate possible weight reduction measures. Reducing axial loads on walls by auxiliary stiffening mechanisms led to significant weight reduction. Reliability-based optimizations were performed to identify the uncertainties in composite material properties with the largest influences on the optimum design. Then measures for reducing uncertainty in important parameters are examined. The results indicate that the most effective measure for reducing thickness is quality control.

Inverse reliability measures and reliability-based design optimisation

Several inverse reliability measures (e.g. Probabilistic Performance Measure (PPM) and Probabilistic Sufficiency Factor (PSF)) that are essentially equivalent have been introduced in recent years as measures of safety. The different names for essentially the same measure reflect the fact that different researchers focused on different advantages of inverse measures. These advantages include improved computational efficiency of Reliability-Based Design Optimisation (RBDO), accuracy in Response Surface Approximations (RSAs) and easy estimates of resources needed for achieving target safety levels. This paper surveys these inverse measures and describes their advantages compared with the direct measures of safety such as probability of failure and reliability index. Methods to compute the inverse measures are also described. RBDO with inverse measure is demonstrated with a beam design example.

Safety Factor and Inverse Reliability Measures

Probability performance measure and probability sufficiency factor are two inverse reliability measures that have gained importance as alternate measures of safety. Inverse measures have several advantages, including improving accuracy in response surface approximations, computational efficiency, and allowing easy estimates of resources needed for achieving the target safety levels. This paper establishes the relationship between the two inverse measures, and describes their advantages compared to the direct measures of probability and reliability index. Methods to compute the inverse measures are also described. Reliability based design optimization with inverse measure is demonstrated with a beam design example.

Design Under Uncertainty Using Monte Carlo Simulation and Probabilistic Sufficiency Factor

Monte Carlo simulation is commonly employed to evaluate system probability of failure for problems with multiple failure modes in design under uncertainty. The probability calculated from Monte Carlo simulation has random errors due to limited sample size, which create numerical noise in the dependence of the probability on design variables. This in turn may lead the design to spurious optimum. A probabilistic sufficiency factor (PSF) approach is proposed that combines safety factor and probability of failure. The PSF represents a factor of safety relative to a target probability of failure, and it can be calculated from the results of Monte Carlo simulation (MCS) with little extra computation. The paper presents the use of PSF with a design response surface (DRS), which fits it as function of design variables, filtering out the noise in the results of MCS. It is shown that the DRS for the PSF is more accurate than DRS for probability of failure or for safety index. The PSF also provides more information than probability of failure or safety index for the optimization procedure in regions of low probability of failure. Therefore, the convergence of reliability-based optimization is accelerated. The PSF gives a measure of safety that can be used more readily than probability of failure or safety index by designers to estimate the required weight increase to reach a target safety level. To reduce the computational cost of reliability-based design optimization, a variable -fidelity technique and deterministic optimization were combined with probabilistic sufficiency factor approach. Example problems were studied here to demonstrate the methodology.

Reliability-Based Global Optimization of Stiffened Panels Using Probabilistic Sufficiency Factor

This paper explores reliability-based global optimization of isogrid stiffened panels subjected to system reliability constraints. Uncertainties in material properties and geometric manufacturing uncertainties are represented by random variables. Polynomial response surface approximations are fit to the most critical safety margins in the panel. Panel system probability of failure is calculated by Monte Carlo simulation using response surface approximations. A probabilistic sufficiency factor approach is employed to convert reliability-based optimization to sequential deterministic optimization in order to reduce the computational cost of global reliability-based optimization. The reliability-based design of a composite isogrid stiffened panel is presented in the paper. The multiple near optima obtained by the global optimization offer designers the option of considering features not included in the optimization formulation.

Reliability-based design optimization of stiffened panels

We explore reliability-based designs of isogrid stiffened panels. Uncertainties in material properties and geometric manufacturing uncertainties are represented by random variables. Due to the multiple failure modes in the stiffened panels, polynomial response surface approximation are fit to the most critical safety margins in the panel. Probability of failure is calculated by Monte Carlo simulation using the polynomial response surfaces. A probabilistic sufficiency factor approach is employed to facilitate the design optimization