Design Sensitivity Analysis and Optimization of High Frequency Radiation Problems Using Energy Finite Element Method and Energy Boundary Element Method

This paper presents a continuum design sensitivity analysis (DSA) and optimization of high frequency radiation problems using the Energy Finite Element Method (EFEM) and Energy Boundary Element Method (EBEM). The noise radiated from the vibrating structure at a high frequency range is obtained through a sequential procedure. The structural EFEM calculates structural energy distribution, which is then used as the boundary condition for EBEM to calculate the energy density at a far-field observation point. For DSA, the direct differentiation method calculates the sensitivity of the exterior noise through the sensitivity of the structural energy density obtained from EFEM. The adjoint variable method calculates the adjoint load from an acoustic EBEM re-analysis, and the adjoint response is obtained from a structural EFEM re-analysis. The sensitivity information is obtained by carrying out numerical integration only on the structural FE part. The proposed DSA approach has been applied in the design of automotive and naval structures to search for the best material layout to achieve lowest noise level at high frequency.