1. Welcome ME 482/582 OPTIMAL DESIGN Rudy J. Eggert, Professor Emeritus
Mechanical & Biomedical Engineering

2. Today’s lecture Optimization Design Analysis versus design
Phases of design
Parametric design
Mathematics review

3. OPTIMAL DESIGN Definition:
The development and use of analytical and computer methods to provide an optimal design of a product or process with minimal computational effort.
That’s right…
The thing we design will be optimal AND the
methods we use will be optimal. .

4. Product Realization Process
Realized
Product
Product Development
Product Develpoment
Disposal
Production Design
Service
Engineering Design
Distribution
Industrial Design
Manufacturing
(Production)
Sales / Marketing
Customer
Need

5. Design Set of decision making processes and activities to determine:
Design
Set of decision making processes and activities to determine:
the form of an object,
given the customer’s desired function.
Design
control
hold
move
protect
store 
decision making processes
shape
configuration
size
materials
manufacturing processes
Function
Form

6. Analysis is not Design
Which of the following is design and which is analysis?
A. Given that the customer wishes to fasten together two steel plates, select appropriate sizes for the bolt, nut and washer.
B. Given the cross-section geometry of a new airplane wing we determine the lift it produces by conducting wind tunnel experiments.
Problem Type
Solution
Design
Form
(size, shape, matls,cnfg, mfg )
Analysis
Predicted behavior
(performance)

7. System Evolution (Arora)
Figure 1.1 System evolution model.

8. Design Phases Formulation Concept Preliminary Design Configuration
Embodiment Design
Parametric
Detail

9. From Customer Needs thru Concept Design?
Formulation
Customer Needs
Customer requirements
Importance weights
Eng. characteristics
House of Quality
Eng. Design Spec’s
Concept Design
Abstract embodiment
Physical principles
Material
Geometry

10. Configuration Design Architecture Abstract embodiment
Special Purpose Parts:
Features
Arrangements
Relative dimensions
Attribute list (variables)
Standard Parts:
Type
Abstract embodiment
Physical principles
Material
Geometry
Architecture

11. Design Phases Cont’d Special Purpose Parts: Features Arrangements
Relative dimensions
Variable list
Standard Parts:
Type
Design variable values
e.g. Sizes, dimensions
Materials
Mfg. processes
Performance predictions
Overall satisfaction
Prototype test results
Parametric
Design
Detail
Design
Product specifications
Production drawings
Performance Tests
Bills of materials
Mfg. specifications

12. Design Optimal Design
Figure 1.2 Comparison of (a) conventional design method and (b) optimum design method.

13. Systematic Parametric Design
Engineering Design, Eggert, 2010

14. Tools used in Optimal Design
Algebra
Calculus
Vector and matrix aritmetic
Excel (computation & graphing)
Graphing (hand)
Computer Programming (any language)
Engineering principles

15. Systematic Parametric Design

16. Mathematical Notation
Recall from Calculus, a function of many variables:
We shall use vectors for multiple variables:
All vectors are
columns
The transpose is used to show a row

17. Handwritten vectors
The book shows vectors as lower case bolded, for example:
For handwritten homework and tests… we will use lower case hand-printed with an underscore, for example:

18. Points P, x(1) and x(2) Superscripts (1),(2)
Figure 1.3 Vector representation of a point P that is in 3-dimensional space.

19. Vector or point?
Is a “vector” a “point” in n-dimensional space denoted as R(n) ?

20. Set of Points, S S = {x|(x1 – 4)2 + (x2 – 4)2  9}.
Figure 1.4 Image of a geometrical representation for the set S = {x|(x1 – 4)2 + (x2 – 4)2  9}.

21. Dot Product From Engineering Statics: In optimal Design:
How do we know if two vectors are orthogonal (normal) ?
In optimal Design:

22. Vector or Scalar?
Is a dot product of two vectors a vector or scalar quantity?

23. Norm of a vector
The length or magnitude of a vector is called the NORM.

24. Product of vector and matrix
Is the product a scalar or vector?

25. Triple Product
Rusty? …. Review appendix A, pgs

26. Function continuity
Figure 1.5 Continuous and discontinuous functions: (a) and (b) continuous functions; (c) not a function;
(d) discontinuous function.

27. First Partial Derivatives of a function
Gradient vector
We’ll se a lot of these in chapter 4.

28. Second Partial Deriivatives of a function…
Hessian Matrix
What does the x* mean?

29. Summary Design Optimal design Design Phases
Systematic Parametric Design
Vector, matrix review