Adjoint Variable Method Combined with Complex Variable for Structural Design Sensitivity

A noise-vibration-harshness (NVH) design optimization of a complex vehicle structure is presented using finite element and boundary element analyses. The steady-state dynamic behavior of the vehicle is calculated from the frequency response finite element analysis, while the sound pressure level within the acoustic cavity is calculated from the boundary element analysis. A reverse solution process is employed for the design sensitivity calculation using the adjoint variable method. The adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process over the structural part where the design variable is defined. A design optimization problem is formulated and solved, where the structural weight is reduced while the noise level in the passenger compartment is lowered.

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2D Acoustic Design Sensitivity Analysis Based on Adjoint Variable Method Using Different Types of Boundary Elements

Acoustics Australia ◽

10.1007/s40857-016-0065-4 ◽

2016 ◽

Vol 44 (2) ◽

pp. 343-357 ◽

Cited By ~ 6

Author(s):

Leilei Chen ◽

Linchao Liu ◽

Wenchang Zhao ◽

Haibo Chen

Keyword(s):

Sensitivity Analysis ◽

Boundary Elements ◽

Design Sensitivity ◽

Variable Method ◽

Design Sensitivity Analysis ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Acoustic Design ◽

Different Types

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Second-Order Design Sensitivity Analysis of Mechanical System Dynamics by a Mixed Direct Differentiation Adjoint Variable Method

Volume 2: 24th Design Automation Conference ◽

10.1115/detc98/dac-5575 ◽

1998 ◽

Author(s):

Javier Urruzola ◽

José Manuel Jiménez

Keyword(s):

Sensitivity Analysis ◽

Design Sensitivity ◽

Second Order ◽

Variable Method ◽

Adjoint Variable Method ◽

Adjoint Variable ◽

Direct Differentiation ◽

Design Variables ◽

Adjoint Variables ◽

Derivatives Of

Abstract This paper presents a new approach to second order sensitivity analysis of multibody dynamics. Adjoint variables together with direct differentiation are used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. It is shown that the proposed method can be compared advantageously to the fully adjoint variable method proposed by Haug in terms of simplicity and numerical cost. In order to validate the algorithm, a simple oscillator example proposed by Haug is solved analytically and by the mixed method, with identical results.

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Parametric Design Sensitivity Analysis of High Frequency Structural-Acoustic Problems Using Energy Finite Element Method

Volume 2: 29th Design Automation Conference, Parts A and B ◽

10.1115/detc2003/dac-48753 ◽

2003 ◽

Cited By ~ 5

Author(s):

Kyung K. Choi ◽

Jun Dong ◽

Nickolas Vlahopoulos ◽

Aimin Wang ◽

Weiguo Zhang

Keyword(s):

Finite Element Method ◽

Sensitivity Analysis ◽

Finite Element ◽

High Frequency ◽

Parametric Design ◽

Design Sensitivity ◽

Variable Method ◽

Design Sensitivity Analysis ◽

Adjoint Variable Method ◽

Adjoint Variable

A design sensitivity analysis of high frequency structural-acoustic problem is formulated and presented. The Energy Finite Element Method (EFEM) is used to predict the structural-acoustic responses in high frequency range, where the coupling between the structural and acoustic domain are modeled by using radiation efficiency. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural-acoustic coupling matrix. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and the numerical sensitivity results show excellent agreement comparing with the finite difference results.

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