Users:Structural Optimization/Response Functions/Eigenvalue

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Contents

General Description

Short Info

In contrast to the Kreisselmeier-Steinhauser approach this response function only considers one single eigenvalue and the corresponding eigenmode of the eigen dynmaic problem. As therefore the internal weighting becomes needless, this function can be described shortly.

This response function also assumes that the eigenvalue has to be maximized.

Input Parameters

Block headline
Parameter Values, Default(*) Description
OPT-RESPONSE_FCT int : EIGENVALUE_DYN Function ID and response function type.
Common compulsory parameters
ETA real Finite difference disturbance for sensitivity analysis
GRAD DIRECT, ADJOINT Method of gradient computation
SA GLOBAL_FD, SEMI_ANALYTIC, EXACT_SEMI_ANALYTIC, ANALYTIC Method of derivative computations inside sensitivity analysis
FDA FOREWARD, CENTRAL, BACKWARD Method of finite difference approximation (if neccessary for the chosen sensitivity analysis method)
DESVAR OPT-VAR vector of integers Design variables that are considered in the sensitivity analysis of this response function
Common optional parameters
WEIGHT real, 1.0* The weighting factor for this response function in multi-objective optimization
ANALYSIS PC-ANALYSIS int ID of the underlying analysis
Specific parameters
NUM_EIGENVALUE int Number of eigenvalue to be considered. NUM_VALUE has to be smaller or equal the NUM_ROOT flag inside the eigenvalue analysis.
Common Compulsory Parameters for Constraints
Parameter Values, Default(*) Description
REL_LIMIT real Relative limit for constraint, depending on the actual value.
ABS_LIMIT real Absolute limit for constraint. Only one limit can be defined for a constraint.
CONSTRAINT_TYPE INEQUALITY_LT, INEQUALITY_GT, EQUALITY Type of constraint
Common Optional Parameters for Constraints
REL_TOLERANCE real, 0* Upper relative limit until which an inactive constraint is concidered as an active one
LAMBDA_ABS_MAX real, 1/cepsilon* Upper limit for lagrangian multiplier

Example of a Complete Input Block

OPT-RESPONSE_FCT 1 : EIGENVALUE_DYN
 WEIGHT=1.0 ANALYSIS=PC-ANALYSIS 1 ETA=1e-06
 GRAD=ADJOINT SA=SEMI_ANALYTIC FDA=FOREWARD
 DESVAR=OPT-VAR 1
! -- response function dependant parameters
 NUM_EIGENVALUE = 1
! -- constraint parameters
 REL_LIMIT = 1.1
 REL_TOLERANCE = 0.1
 CONSTRAINT_TYPE = INEQUALITY_LT
 LAMBDA_ABS_MAX = 20

A complete test example

Model description

The test example for single eigenvalue optimization is a squared and Navier supported plate. The first four eigenvalues are considered and for each of them an optimization is performed. In the next section we examine the different results.

The following animation illustrates the eigenmodes of the plate.

eigenmodes of a squared plate

Input File

Here the full input file can be downloaded.

Documented Results

The results show the expected behaviour. Each solution generates stiffness towards a certain eigenmode. As the modes two and three are symmetric it is not surprising that the design updates are symmetric, too.

References





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