Interval finite element analysis and reliability-based optimization of coupled structural-acoustic system with uncertain parameters

• Uncertainties in both physical parameters and boundary conditions are considered.
• Modified Taylor series is proposed to predict the ranges of matrices and vectors.
• Higher order terms of the Neumann expansion are retained in MIPPM.
• Uncertain optimization model is presented based on interval satisfaction degree.

A modified interval parameter perturbation finite element method (MIPPM) and a reliability-based optimization model are proposed for the coupled structural-acoustic field prediction and structural design with uncertainties in both the physical parameters and boundary conditions. Interval variables are used to quantitatively describe all the uncertain parameters with limited information. The interval matrix and vector are expanded by the modified Taylor series. Compared with the traditional perturbation method, the proposed MIPPM can yield more accurate ranges of the uncertain structural-acoustic field, in which the higher order terms of Neumann series are employed to approximate the interval matrix inverse. The reliability idea is introduced to establish an interval optimization model relying on the satisfaction degree of interval. The uncertain constraints can be transformed into deterministic ones if given the confidence level. The proposed MIPPM is used to predict the intervals of the constraints, and whereby eliminate the optimization nesting. Numerical results about a 3D car are given to demonstrate the feasibility and efficiency of the proposed model and algorithm.