An Adaptive Subinterval Finite Element Method Based on Dynamic Sensitivity Analysis for Structures with Uncertain-but-Bounded Parameters

Abstract

To overcome computational inefficiency of the traditional subinterval finite element method, a novel adaptive subinterval finite element method based on dynamic sensitivity analysis is proposed to evaluate static response bounds of structures with uncertain-but-bounded parameters. Firstly, the original interval is divided into subintervals, and expansion routes for each displacement component are constructed based on dynamic sensitivity analysis. Then, the structural response bounds are analysed using a modified interval finite element method within each subinterval on the expansion route. Finally, the bounds of all displacement components are obtained via the interval union operation. To determine the appropriate number of subintervals, an adaptive convergence mechanism is proposed. The proposed method has accuracy and efficiency advantages over traditional subinterval finite element methods. The accuracy and effectiveness of this method are verified via numerical calculations of a nine-bar truss and an impeller.

Keywords

• subinterval finite elements
• uncertainty analysis
• dynamic sensitivity
• Neumann series
• static response