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Introduction to Evolutionary

(ESO)Professor Mike Xie

Head of Civil Engineering Discipline

RMIT University

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Introduction

The Evolutionary Structural Optimization(ESO) method is based on the concept of

material from a structure to achieve an

optimal design.

The ESO method is simple to understand and

element analysis software packages (e.g.Nastran, Abaqus, Strand6/7, Ansys).

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An example

Gravity

under gravity loadinge n e e emen mes

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Evolution of the object

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movie

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General a licabilit of the method

applied to a wide range of engineeringo timization roblems includin

- minimizing stress, displacement;

-

- maximizing frequency, buckling load;

-- minimizing contact stresses, etc.

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ESO for tension-only or-

-

Examples of possible applications

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yy

yz

xz

yx

x

z

xy

zy

z

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Design CriteriaDesign Criteria

e

von Mises stress VM

Tension 1

Tension 2

11

Compression 133

ompress on 332211

ESO will remove elements with the lowest e

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-

Elements with the highest compressive

first.

Then the less tensile elements will be

deleted as well.

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-

Elements with the highest tensile stresses

.

Then the less compressive elements will

be deleted.

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An example of tension-only

G

Movie of the evolution history of the above structure using Tension Criterion 2

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A 3D tensile exam leT

Movie of evolution history of the above structure using Tension Criterion 2

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Example of compression-only

Sa rada Familia Church FaSa rada Familia Church Fa adeade

Barcelona, SpainBarcelona, SpainMovie

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3D print-out

Wax prototype of the Passion Faade colonnade

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(a)Elastic-perfectly-plastic material model

near ma er a mo e

(c) Power-law material model

(a) (b) (c)

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-

Power-law material model = 0.2

Strain energy criterion

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=

Linear design Nonlinear design

Movie Movie

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Force vs. deformation relationships

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Bi-directional ESO

A 3D beam with a solid deck at the to

Initial design for the above structure

Movie

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A stool?

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A brid e-t e structure

A 3D beam with a solid deck at the to and a a in the middle

Initial design for the above structure

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An o timal brid e-t e structure

Movie

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S ace under round

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Initial design

Movie

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Final design

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Load transfer structure

movie

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Cellular matrix roof

,

movie

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Cellular matrix roofase : curve , our corners suppor e