Acoustic Shape Optimization Based on Isogeometric Wideband Fast Multipole Boundary Element Method with Adjoint Variable Method

A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable method under isogeometric analysis (IGA) conditions. A set of efficient parameters of the wideband fast multipole method has been identified for IGA boundary element method. Shape optimization is performed by applying the method of moving asymptotes. IGA WFMBEM is validated through an acoustic scattering example. The proposed optimization approach is tested on a sound barrier and two multiple structures to demonstrate its potential for engineering problems.

Parameter Identification on Flexible Multibody Models Using the Adjoint Variable Method and Flexible Natural Coordinate Formulation

This work proposes a methodology for in situ parameter identification using system-level measurements of (flexible) multibody systems, opposed to dedicated component-level identification. The sensitivity information employed for the optimization is obtained using the adjoint variable method (AVM). This method has the advantage of obtaining sensitivity information at a computational cost independent of the amount of model parameters. The underlying flexible multibody formulation employed is a novel approach called the flexible natural coordinates formulation (FNCF). This formulation combines the advantageous properties of the floating frame of reference formulation (FFRF) and the generalized component mode synthesis (GCMS) methods and results in a constant mass and stiffness matrix with quadratic constraint equations. This work shows how the specific structure of equations obtained through FNCF drastically reduces the complexity of the AVM as the simulation derivatives can be readily obtained and are of limited order. The proposed approach has been implemented in an in-house object-oriented matlab multibody code. The methodology is illustrated by identifying 13 model parameters of a MacPherson suspension model, in situ and using system-level measurements.