scholarly journals Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Peter Sergeant ◽  
Ivan Cimrák ◽  
Valdemar Melicher ◽  
Luc Dupré ◽  
Roger Van Keer
Keyword(s):  
Adjoint System ◽  
Design Sensitivity ◽  
Computational Effort ◽  
Magnetic Shielding ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Cpu Time ◽  
Gradient Optimization ◽  
Sensitivity Approach ◽  
Active Shield

For shielding applications that cannot sufficiently be shielded by only a passive shield, it is useful to combine a passive and an active shield. Indeed, the latter does the “finetuning” of the field reduction that is mainly caused by the passive shield. The design requires the optimization of the geometry of the passive shield, the position of all coils of the active shield, and the real and imaginary components of the currents (when working in the frequency domain). As there are many variables, the computational effort for the optimization becomes huge. An optimization using genetic algorithms is compared with a classical gradient optimization and with a design sensitivity approach that uses an adjoint system. Several types of active and/or passive shields with constraints are designed. For each type, the optimization was carried out by all three techniques in order to compare them concerning CPU time and accuracy.

Design Optimization for Structural-Acoustic Problems Using FEA-BEA With Adjoint Variable Method

2003 ◽  
Vol 126 (3) ◽  
pp. 527-533 ◽  
Author(s):  
Jun Dong ◽  
Kyung K. Choi ◽  
Nam H. Kim
Keyword(s):  
Finite Element ◽  
Design Optimization ◽  
Boundary Element ◽  
Design Sensitivity ◽  
Variable Method ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Structural Part

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.

Sizing Design Sensitivity Analysis and Optimization of a Hemispherical Shell With a Nonradial Penetrated Nozzle

1998 ◽  
Vol 120 (3) ◽  
pp. 238-243
Author(s):  
A. L. Rusu-Casandra ◽  
I. R. Grindeanu ◽  
K.-H. Chang
Keyword(s):  
Optimization Problems ◽  
Design Sensitivity ◽  
Adjoint Variable Method ◽  
Pressure Loading ◽  
Adjoint Variable ◽  
Continuum Approach ◽  
Sizing Optimization ◽  
Variational Equations ◽  
Hemispherical Shell ◽  
Intersection Area

This paper presents a sizing optimization of a hemispherical shell with a nonradial penetrated nozzle, under internal pressure loading. The objective of the optimization is to decrease the stress concentration in the intersection area, through the variation of the thicknesses of the shells, on condition the volume have a minimum value. This is accomplished by performing a stress analysis and by developing a sizing optimization. The variational equations of elasticity and an adjoint variable method are employed to calculate sizing design sensitivities of stresses. This continuum approach combined with a gradient method could be applied to broad classes of elastic structural sizing optimization problems.

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

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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