Optimization and anti-optimization solution of combined parameterized and improved interval analyses for structures with uncertainties

• Linear discretized structures with uncertain-but-bounded properties are analyzed.
• Parameterized (PIA) and Improved (IIA-EUI) Interval Analyses are compared.
• A new method combining PIA and IIA-EUI is presented.
• The new method by optimization and anti-optimization solution reduces the dependency.
• Numerical tests show efficiency of the new method to treat structural uncertainties.

A novel method to deal with structures with uncertain-but-bounded parameters is presented. In order to reduce or eliminate the overestimations due to the so-called dependency phenomenon arising in the classical interval analysis, the authors have recently introduced the parameterized interval analysis and the improved interval analysis via Extra Unitary Interval. The key idea is to develop a new method which, combining the previously two proposed procedures, overcomes their limits and by optimization and anti-optimization problem solutions allows to efficiently solve the set of governing algebraic interval equations in statics.