Sensitivity Analysis and Optimization Using Energy Finite Element and Boundary Element Methods

Abstract

DOI: 10.2514/1.20811 This paper presents a continuum-based design sensitivity analysis and optimization of high-frequency radiation problemsusingtheenergy finiteelementmethodandenergyboundaryelementmethod.Thenoiseradiatedfromthe vibrating structure at a high-frequency range is obtained through a sequential procedure. The structural energy finite element method calculates structural energy distribution, which is then used as the boundary condition for the energy boundary element method to calculate the energy density at a far-field observation point. For design sensitivity analysis, the direct differentiation method calculates the sensitivity of the exterior noise through the sensitivity of the structural energy density obtained from the energy finite element method. The adjoint variable method calculates the adjoint load from an acoustic energy boundary element method reanalysis, and the adjoint response is obtained from a structural energy finite element method reanalysis. The sensitivity information is obtained by carrying out numerical integration only on the structural finite element part. The proposed design sensitivity analysisapproach hasbeen applied in the design ofautomotive and navalstructures to search for thebest material layout to achieve the lowest noise level at high frequency.