Manual Meta

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Appendix H

Meta4abq

Meta4abq is a toolbox for successive surrogate based optimization of finiteelement models parameterized using Abaqus/CAE. An optimization is de-fined by a project file which is opened and executed from the toolbox. A DoE(doe4meta.txt ) is prepared and loaded by the Python script defining the fi-nite element model. The Python script is executed in Abaqus/CAE and thefinite element results are then exported to result4meta.txt . A surrogate modelis adopted to the results and the optimization is performed. After conver-gence, a new region of interest is identified by panning and zooming, anda new successive optimization loop is initiated. The successive optimizationprocedure is also illustrated in Figure H.1.

PROJECT

meta4abq

DOE

DOE

Abaqus PYTHON

doe4meta.txt

result4meta.txt

iter=iter+1

project.txt

model.py

Figure H.1: Flow chart of the optimization process.

Project file

The project file (project.txt ) must be saved in the map /PROJECTS. Thefile contains a number if keywords which together define the optimization

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Nonlinear FEA and Design Optimization Appendix H

project. The keywords are explained by the tables below.

*PARAMETER

VAR1 VAR2

VAR1 Number of variables

VAR2 1 - linear regression model2 - quadratic regression model3 - OPRM41,42,43 - Kriging

*ITERATION

VAR1

VAR1 Number of iterations

*XLIMITS

VAR1 VAR2

VAR1 VAR2

VAR1 lower bound on RoI

VAR2 upper bound on RoI

*CONSTRAINT

VAR1 VAR2 . . . VARN


VAR1,VAR2,. . . A in Ax = b

VARN b

*ZOOM


VAR1 zoom factorVAR2, . . . lower limit on RoI

*RBDO

VAR1 VAR2 . . . VARN+1

VAR1 factor of safety

VAR2 1 - normal2 - lognormal

VAR3, . . . standard deviationscoefficients of variation

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*OPTIMIZATION

VAR1 VAR2 VAR3 VAR4

VAR1 1 - linear programming2 - quadratic programming3 - genetic algorithm4 - particle swarm algorithm5 - SLP6 - RBDO

VAR2 number of objectives

VAR3 number of constraints

VAR4 penalty factor

*DOES

VAR1 VAR2

VAR1 1 - linear Koshal2 - full factorial3 - face centered cubic4 - heuristic5 - quadratic Koshal + 2 center points6 - spherical7 - Box-Behnken8 - S-optimal

VAR2 number of design points

*MODEL

VAR1

VAR1 python script

*DATABASE

VAR1

VAR1 database.txt

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Examples

A number of examples are distributed as pro ject files(Meta4abqXX/PROJECT ) and Python scrips (Meta4abqXX/PYTHON ). Alist of all examples is presented in Table H.1.

Table H.1: Project files and Python scripts.

Project Python Description

project bench 1.txt bench 1.py f = sin(x1)cos(x2)project bench 2.txt bench 2.py f = (x1 − 5)2(1 + x2)2

g = x41− x2 ≤ 0

project bench 3.txt bench 3.py Rosenbrock’s bananaproject frequency.txt frequency.py Maximize frequencyproject fillet 3.txt fillet 3var.py Fillet design

project mfile.txt script file.m

( 4x− 2)4 + ( 4

y− 2)4

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