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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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.
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
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!
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
Conflict in SO
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Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
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
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
What else can be optimized for?
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Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
Do you understand these in SO context?
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HierarchyModularityComplementarity
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
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.
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
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?
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
Complementarity
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No complementarity Simple complementarity Non-trivial complementarity
Think of 3D printing. Can we reduce or even avoid support material?
Structural Optimization: Size, Shape, and TopologyME260 / G. K. Ananthasuresh, IISc
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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