An effective optimization-based parameterized interval analysis approach for static structural response with multiple uncertain parameters

Abstract

The framework of parameterized interval analysis (PIA) and optimization and anti-optimization problems (OAP) was recently proposed for considerably reducing or eliminating the overestimation of the interval solution arising in the classical interval analysis. However, reducing the computational effort of this framework still remains a challenging task, especially for large-scale structures with a large number of uncertain parameters. In this regard, an effective approach formulated in the framework is proposed for evaluating the static structural response with multiple uncertain-but-bounded parameters. First, the PIA is used to describe uncertain input properties incorporated into the interval stiffness matrix and the interval load vector of finite element model. Subsequently, the parametric inverse of the stiffness matrix is handled using a Neumann series expansion. To efficiently solve the objective function of OAP, a robust optimization solver known as lightning attachment procedure optimization algorithm is applied in the field of IFEM for the first time. Finally, the numerical investigations on three kinds of structures concerning truss, frame and plate structures with multiple uncertain parameters are presented to demonstrate the accuracy and effectiveness of the proposed approach.