Several types of uncertainties are encountered in the design of machines and structures. The geometric parameters or dimensions are specified in terms of nominal values and tolerances, the experimentally determined material properties exhibit scatter over a range, and many types of loads are inherently variable (loads due to wind, floods, and earthquakes). It is difficult to develop probability distributions to all such uncertain parameters. Even if probability distributions are developed, their confidence levels need to be established using a t- or chi-squared distribution. However, it is easier and more accurate to model the uncertain quantities/parameters as intervals. Thus, for example, in the interval parameter-based optimization, only the known or expected ranges of the design parameters are used with no need to establish the confidence levels of their intervals. This work presents an interval parameter-based optimum design of structural components. Although the field of interval analysis deals with computation of interval numbers, it suffers from the so-called dependency problem, whereby the computations get more and more inaccurate, resulting in wider intervals of the computed response quantities as compared to the true intervals if multiple arithmetic operations are performed using the same interval number or if complicated expressions are evaluated using interval numbers. Hence, a more accurate method, known as the universal grey number theory, is used in this work for the analysis and computations involved in the optimization procedure. Two numerical optimization problems, which are the design of a stepped bar subjected to an axial load and the design of a welded beam subjected to a transverse load, are presented to illustrate the procedure.
Uncertainty-Based Structural Optimization Using Universal Grey Number Theory
AIAA Journal ; 57 , 11 ; 5002-5013
2019-11-01
Article (Journal)
Electronic Resource
English
Airline Network Optimization using Grey Theory
AIAA | 2007
|Airline Network Optimization using Grey Theory
British Library Conference Proceedings | 2007
|Ship structural component contribution evaluation based on grey target theory
DOAJ | 2017
|Design Optimization Under Uncertainty Using Evidence Theory
SAE Technical Papers | 2006
|