Structural optimization using probabilistic constraints

Abstract

In practice, there are often uncertainties associated with material as well as geometric properties, external forces, boundary conditions and operational environment in designing engineering structures. The most common and traditional approach to account for uncertainties is to introduce a factor of safety in the design model. However, such a simplistic solution fails to quantify reliability of the optimum design since a large factor of safety may not imply higher reliability. To directly account for the probabilistic nature of quantities such as material properties, loads, etc., one has to identify and define the respective quantities as random variables in the analysis model. Probability of failure (or reliability) of a structure subject to a performance constraint in the form of a limit state function can then be calculated and formulated as a constraint in the design optimization model. Probabilistic constraint formulation for explicit limit state functions is presented in this paper. Due to this formulation, probabilistic constraints can now be considered routinely in a structural optimization software with additional computational costs. Results for a representative set of structural and mechanical design problems are presented to validate the probabilistic constraint formulation. With the introduction of reliability based constraints, the optimized structure tends to be insensitive to fabrication defects and improper definition of the loading environment.