Template of a Structural Optimization Problem

Recitation 1

Template of a Structural Optimization Problem

ME260 Indian Inst i tute of Sc ience

Str uc tur a l O pt imiz a t io n : S iz e , Sha pe , a nd To po lo g y

G . K. Ana ntha s ur e s h

P r o f e s s o r , M e c h a n i c a l E n g i n e e r i n g , I n d i a n I n s t i t u t e o f S c i e n c e , B e n g a l u r u

s u r e s h @ i i s c . a c . i n

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mailto:[email protected]

Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc

Structural optimization problem statement

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MinimizeObjective(optimization variables, state variables)

Subject to

Constraints on state variablesConstraints on resourcesConstraints on performance

Limits on variables

Optimization variables

Data

Displacements, temperature, electric field, etc.

Governing differential equations

Weight, cost, size, etc.

Stiffness, strength, frequency, etc.

Related to the geometrical features

Material properties, loads, etc.

This is a typical structural optimization problem statement. Make it a habit to write in this format, including the data.


Can you think of another conflict in SO?

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Sure, there is conflict in structural optimization.◦ If you want to make a stiff structure for given loading, you need more material; more material

increases the weight and cost.

◦ So, there is conflict if you want to design the stiffest structure with least amount of material.

What if we want to make a lightest structure with high natural frequency? ◦ Light structures have low inertia and low stiffness too, at least in general. This will mean that

their frequencies will be low.

◦ So, there is conflict.

Suppose that you want to make a flexible structure that is very strong.◦ Flexible structures deform and it may seem that they are weak when strains are large in them.

◦ So, there is conflict too.

Imagine a structure that is subject to multiple loading conditions.◦ Making a structure stiff under one loading may cause it less stiff in another loading.

◦ So, there will be conflict.

Imagine more situations of designing structures. There will be enough conflict!


Conflict in SO

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What else can be optimized for?

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Optimizing a structure for

◦ Stiffness

◦ Strength

◦ Flexibility, desired motion

◦ Natural frequency, mode shapes, dynamic response

◦ Stability, preventing buckling

◦ Weight reduction

◦ Cost reduction

◦ Manufacturability

◦ Reliability

◦ Controllability

◦ Safety

◦ Aesthetics


What else can be optimized for?

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Do you understand these in SO context?

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HierarchyModularityComplementarity


Hierarchy

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Modularity

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Most buildings and other civil structures are modular. Eiffel exploited modularity to a great extent.

There is more to modularity… examine these ancient sculptures from a temple in Lepakshi, Andhra Pradesh.


Modularity (contd.)

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Sundaram, M., Limaye, P., and Ananathasuresh, G. K., “Design of Conjugate and Conjoined

Shapes and Tilings using Topology Optimization,” Structural and Multidisciplinary Optimization,

Vol. 45(1), pp. 65-81, 2012.

Usual topology-optimized design

Modular topology-optimized design

What’s special about this?


Complementarity

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No complementarity Simple complementarity Non-trivial complementarity

Think of 3D printing. Can we reduce or even avoid support material?


Complementarity (contd.)

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Sundaram, M., Limaye, P., and Ananathasuresh, G. K., “Design of Conjugate and

Conjoined Shapes and Tilings using Topology Optimization,” Structural and

Multidisciplinary Optimization, Vol. 45(1), pp. 65-81, 2012.M. C. Escher’s designs

Escher-like compliant mechanism topologies

A “centrifugal clutch” and “circumferentially-actuated radial motion compliant mechanism” sharing a circular space.

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Template of a Structural Optimization Problem