Shape sensitivity analysis of sequential structural–acoustic problems using FEM and BEM
Abstract A shape design sensitivity formulation for structural–acoustic problems using sequential finite element and boundary element methods is presented. Frequency-response analysis is used to obtain the dynamic behavior of the structure, while boundary element analysis is used to solve for the pressure response of the acoustic domain. It is shown that the adjoint method, which takes the reverse direction to response analysis, provides a very efficient way of sensitivity calculation. In addition, it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem. The only difference is the numerical integration that evaluates the sensitivity coefficient. The combination of the semi-analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation. The accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method.
A constrained optimization based method for acoustic finite element model updating of cavities using pressure response
Abstract A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy.
Structural shape sensitivity analysis : relationship between material derivative and control volume approaches
The material derivative and control volume approaches for structural shape design sensitivity analysis are presented, analyzed, and compared. Starting with a continuum formulation and a general response functional needing sensitivity analysis, the two approaches are derived. It is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other. Thus, the two approaches are theoretically equivalent. Discretizations of the continuum expressions are presented, and it is shown that the two approaches can lead to different implementations for numerical calculations. A unified interpretation is developed in which the explicit design variations (partial derivatives with respect to the design variables) of the internal and external forces are the major calculations needed to implement the design sensitivity analysis. The discretized forms of the continuum sensitivity expressions are also compared with the ones obtained by starting with the discretized model ab initio. This comparison shows that these two approaches lead to similar expressions for numerical calculations. Therefore, the exact same procedures can be used for computer implementations for both of the approaches. The presented analyses give insights for implementation of the design sensitivity analysis theory with the finite element analysis programs.