1. Structural Optimization Design ( Structural Analysis & Optimization )
Hai Huang
School of Astronautics, BUAA

2. Mai functions of Structures and mechanisms in a spacecraft
Preserving the outline configuration of the spacecraft;
Providing the space to install or mount other subsystems or equipments, meanwhile guaranteeing the precision of the installation;
supporting and protecting equipments, and ensuring their safety under various loading cases;
providing enough stiffness, strength as well as thermal protection, and ensuring the integrality of the spacecraft;
And supplying other functions such as unlocking, deploying, releasing, separation, pointing and locking of solar array or antenna. 2
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3. Traditional Structural Design
Question: Best design? Could be further improved?
Structural optimization
(Structural Synthesis, Structural Optimization Design, Structural Design Optimization)
—— a kind of design technology to find the best solutions for structure systems to be designed
—> Structural Analysis
—> Design Adjust
Initial Design
—> Re-Analysis
—>Re-Adjust
… —> Until Satisfying
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4. Chapter 1 Introduction to Structural Optimization
§1.1 General concepts of Structural Optimization
Optimization —— generally refers to find the best solution for projects, designs, products etc.
4 Examples
(1) Bus routes
(2) Area of rectangle
(3) Beam sectional function
(4) Engineering design
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5. (1) Bus routes
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6. (2) Area of rectangle
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7. Fig. 1.3 Thin walled Structural Design
(3) Engineering design
Fig Thin walled Structural Design
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8. §1.2 Mathematical Basis of Optimization
1.2.1 Mathematical Programming
Find
—Design Variables
—Objective Function
(NLP)
—Constraints
—Constraint functions
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9. (a) convex set (b) non-convex set,
1.2.2 Definitions in optimization
Convex Set
A set is said to be convex if, for arbitrary two points , ， in S,
for
(a) convex set (b) non-convex set
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10. (a) convex-like function (b) non convex-like function
Convex-like Functions
(a) convex-like function (b) non convex-like function
Convex –like Function
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11. Convex Set ---- feasible domain
Convex Programming
Convex Set ---- feasible domain
Convex-like Function---- objective function
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12. Structural Analysis and Optimization
Quick Review

13. Theorem 1
Suppose and are differentiable, and is the optimum solution of (NLP), at which the constraints meet the eligibility requirement, then it must exist a set of parameters called Lagrange multipliers which let Kuhn-Tucker (KT) condition be satisfied.
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14. Kuhn-Tucker conditions
If is the optimum of (NLP), and at the point meet the eligibility requirement, then
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15. The gradients of objective and constraint functions at

16. Theorem 3
If problem (NLP) is a convex programming, then any local optimum of the problem must be a global minimum; furthermore if and only if the function is strictly convex on the convex feasible domain R, the minimum of the problem (NLP) is unique.
Theorem 4
If problem (NLP) is a convex programming, and satisfies Kuhn- Tucker condition (KT), then must be the optimum of problem (NLP).
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17. Sufficient conditions to meet eligibility
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18. Traditional Structural Design
Structural optimization
(Structural Synthesis, Structural Optimization Design, Structural Design Optimization)
——Combining the theories of mathematical programming and the methods of structural analysis to seek the best feasible design according to a selected quantitative measure of effectiveness for loaded structures with computers as tools.
—> Structural Analysis
—> Design Adjust
Initial Design
—> Re-Analysis
—>Re-Adjust
… —> Until Satisfying
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19. §1.3 Model of typical structural optimization
Optimum objective —structural weight
Constraint conditions —strength, deformation, dynamic (vibration) performance, etc.
Design variables
(1) Cross-sectional Areas
(2) Shape variables
(3) Topology variables
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20. 3 Kinds of Structural Optimization
1。 Cross-sectional Areas
10 Bar truss
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21. 3 Kinds of Structural Optimization
2。 Shape variables
15 Bar truss
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22. 3 Kinds of Structural Optimization
3。 Topology variables
Original
After Optimization
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23. Model of typical structural optimization is a mathematical programming
Characteristics
1。 implicit function
2。Large number of variables
3。 Large number of constraints
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24. Characteristics of Typical Structural Optimization
(1) Constraint function usually is a complex non-linearly implicit function of design variables. Only numerical solutions are available using structural analysis such as FEM.
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25. (2) Design variable space is usually very high dimensional.
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26. Solution with Computer as A Tool
(3) Automatic design produces by using computers and develops with computer technology
Numerical
Optimization
Computer
Code
+ FEM
==》
Solution with Computer as A Tool
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27. E-3 Navigation Satellite
Compacted state
Deployed state
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28. History of structural optimization
(1) in 1960, L.A.Scmmit introduced the theories of mathematical programming into structural design
(2) Criterion methods (60s~70s)
(3) Approximation concepts ( 1976)
(4) Programming methods (after 1976)
(5) Dual method (proposed in 1980)
(6) Applications and Topology research
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29. Concerned research areas
Efficient numerical algorithm
Adaptive ability of the methods
Practical engineering problem applications
Sensitivities analysis
Shape and topology optimization.
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30. Typical topics the course will conduct
(1) Criterion methods
(2) Sensitivity analysis
Calculating for derivatives of primal constraint functions respect to design variables.
(3) Approximation concepts and programming methods
(4) Dual methods
(5) Two-level multi-point Approximation method
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31. Thank You for your attention !
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