A Penalty Optimization Algorithm for Eigenmode Optimization Problem Using Sensitivity Analysis

2014 ◽  
Vol 15 (3) ◽  
pp. 776-796 ◽  
Author(s):  
Zhengfang Zhang ◽  
Weifeng Chen ◽  
Xiaoliang Cheng
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Algorithm ◽  
Penalty Method ◽  
Optimization Problem ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
First Variation ◽  
Quadratic Penalty Method ◽  
The First Variation ◽  
Time Term

AbstractThis paper investigates the eigenmode optimization problem governed by the scalar Helmholtz equation in continuum system in which the computed eigenmode approaches the prescribed eigenmode in the whole domain. The first variation for the eigenmode optimization problem is evaluated by the quadratic penalty method, the adjoint variable method, and the formula based on sensitivity analysis. A penalty optimization algorithm is proposed, in which the density evolution is accomplished by introducing an artificial time term and solving an additional ordinary differential equation. The validity of the presented algorithm is confirmed by numerical results of the first and second eigenmode optimizations in 1Dand 2Dproblems.

Sensitivity analysis of sandwich beams and plates accounting for variable support conditions

2013 ◽  
Vol 61 (1) ◽  
pp. 201-210 ◽  
Author(s):  
R. Studziński ◽  
Z. Pozorski ◽  
A. Garstecki
Keyword(s):  
Sensitivity Analysis ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Practical Applications ◽  
The Core ◽  
State Of Stress ◽  
Thin Steel ◽  
Influence Of Temperature On ◽  
Support Conditions ◽  
Variable Support

Abstract The paper addresses the problems of the sensitivity analysis and optimal design of multi-span sandwich panels with a soft core and flat thin steel facings. The response functional is formulated in a general form allowing wide practical applications. Sensitivity gradients of this functional with respect to dimensional, material and support parameters are derived using adjoint variable method. These operators account for the jump of the slope of a Timoshenko beam or a Reissner plate at the position of concentrated active load or reaction, thus extending the sensitivity operators known in literature. The jump of slope is the effect of shear deformation of the core. Special attention is focussed on sensitivity and optimisation allowing for variable support position and stiffness, because local phenomena observed in supporting area of sandwich plates often initiate failure mechanisms. Introducing optimally located elastic supports allows to reduce the unfavourable influence of temperature on the state of stress. Several examples illustrate the application of derived sensitivity operators and demonstrate their exactness

Sensitivity analysis for elastic problems by the adjoint variable method based on the LBM

2018 ◽  
Vol 2018.13 (0) ◽  
pp. 119
Author(s):  
Takashi YODONO ◽  
Takayuki YAMADA ◽  
Kazuhiro IZUI ◽  
Shinji NISHIWAKI
Keyword(s):  
Sensitivity Analysis ◽  
Variable Method ◽  
Adjoint Variable Method ◽  
Adjoint Variable
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