Redundant robust topology optimization of truss

• Published in: Optimization and engineering Vol. 15; no. 4; pp. 945 - 972
• Main Authors: Mohr, Daniel P., Stein, Ina, Matzies, Thomas, Knapek, Christina A.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-12-2014; Springer Nature B.V
• Subjects: Approximation; Control; Damage; Engineering; Environmental Management; Financial Engineering; Mathematical models; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Redundant; Systems Theory; Topology optimization; Trusses; Uncertainty; Coding theory; Uncertainty; Robust optimization; Structural optimization; Redundancy; Ground structure; Sizing optimization; Redundant; Robustness; Fail-safe; Truss topology optimization
• ISSN: 1389-4420; 1573-2924
• DOI: 10.1007/s11081-013-9241-7

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints have to be approximated by finite expressions to generate a computable problem. Here, using the example of topology optimization of a truss, a method is proposed to deal with such uncertainties by utilizing robust optimization techniques. This leads to an approach without the necessity of any approximation.
Another common problem in the optimization of structures is the consideration of possible damages. The typical approach is to prevent these damages by a convenient structure—this concept is known as safe-life. The method developed here applies the principle of redundancy to resist damages, which is the design philosophy of fail-safe. In general this leads to a high dimensional partitioning problem. By using a linear ansatz we get a computable problem.
Finally, robust and redundant methods are combined, and simple numerical examples of typical problems illustrate the application of the methods.
Our new redundant robust topology optimization of truss, based on known concepts of different research fields, gives a structure which is not only “safe” for parameter perturbations but for failure of bars, too. This introduces the fail-safe concept to structural optimization.