Introduction to Optimization, techniques of optimization, tools used for optimization, simple example.

1. Presented By Guided By
GoreA. S. Prof. Rodge M.K.
2010MME007
M.Tech. CAD/CAM
CAD Based Optimization
Department of Production
Engineering, SGGSIE&T, Nanded

2. Introduction
 Optimization may be defined as the process of
maximizing or minimizing a desired objective function
while satisfying the prevailing constraints.
 It is Operation Research based technique.

3. Statement of a Optimization Problem:
 An optimization problem can be stated as follows:
Minimizes f(X)
subject to the constraints
gj (X)≤0, j=1,2,…….,m and lj (X)=0 , j=1,2,……...,p
 To find X={𝑥1 𝑥2 𝑥3... 𝑥n}T
where,
X is an n-dimensional vector i.e. the design vector
f(X) is termed the objective function
gj (X) and lj(X) are known as inequality and equality constraints
n number of variables
m and /or p number of constraints

4. Objectives:
 In the conventional design procedures there will be
more than one acceptable design, the purpose of
optimization is to choose the best one of the many
acceptable designs available.
 Example minimization of weight in aircraft and
aerospace structural design problems.
 Minimization of cost In civil engineering structural
designs
 Maximization of mechanical efficiency in mechanical
engineering systems design.

5. Commonly used OptimizationTechniques
1. Mathematical ProgrammingTechniques : To find the
minimum of a function of several variables under a
prescribed set of constraints, e.g. sequential quadratic
programming (SQP)
2. Stochastic ProcessTechniques : To analyze problems
described by a set of random variables with known
probability distribution , e.g. queuing theory
3. StatisticalTechniques : To build empirical models from
experimental data through analysis, e.g. Design of
Experiments

6. Optimization based on Finite Elements
 Used for dynamic response, heat transfer, fluid flow,
deformation and stresses in a structure subjected to loads
and boundary conditions.
Classification :
a. Parameter or size optimization : The objective function is
typically weight of the structure and the constraints
reflecting limits on stress and displacement.
b. Shape optimization : deals with determining the outline of
a body, shape and/or size of a hole, etc. The main concept
is mesh parameterization
c. Topology optimization : distribution of material, creation
of holes, ribs or stiffeners, creation/deletion of elements,
etc.

7. Role of Optimization

8. Softwares used:
 ANSYS
 IDEAS
 CATIA
 Unigraphics NX
 TOSCA

9. Optimization Methods in ANSYS
 Subproblem Approximation:-
o It is an advanced zero-order method.
o Requires only the values of the dependent variables, and
not their derivatives.
o It converts problem to an unconstrained optimization
problem because minimization techniques for the latter
are more efficient.
o The conversion is done by adding penalties to the
objective function.

10. Optimization Methods in ANSYS
 First Order:-
o It is based on design sensitivities, for high accuracy.
o It converts the problem to an unconstrained one by
adding penalty functions to the objective function.
o finite element representation is minimized and not an
approximation.
o Both methods series of analysis-evaluation-modification
cycles.

11. ElementType
 PLANE82:-
o Higher order version of the 2-D, four-node element
o For mixed (quadrilateral-triangular) automatic meshes
Assumptions
o The area of the element must be positive.
o The element must lie in a global X-Y plane

12. Example:- Bracket

13.  Problem Formulation:-
o Minimize,
Volume = f(R1;R2;R3;R4;W) [10 mm3]
o Subject to,
0 ≤VM ≤ 349:33 [1 MPa]
25≤ R1 ≤ 45 [1 mm]
15 ≤ R2 ≤ 45 [1 mm]
5 ≤ R3 ≤ 45 [1 mm]
5 ≤ R4 ≤ 45 [1 mm]
5 ≤W ≤ 170 [1 mm]

14. Iterations
 Set 1:-
o V max- 344.58MPa
o Vol- 16199 mm3
 Set 2:-
o V max -283.73 MPa
o Vol-12956 mm3

15.  Set 3:-
o V max-345.78 MPa
o Vol-8907.4 mm3
 Set 4:-
o V max-349.65 MPa
o Vol-8843.8 mm3

16.  Set 5:-
o V max-350.77 MPa
o Vol-8829.1 mm3

17. Results
 DesignVariables R1,R2,R3,R4,W

18.  Volume

19.  Von Mises Stresses

20. Application of Bracket

21. Conclusion
 The First order method is good method for optimization
 The optimization helps reduce 45.4% of the structure weight
 As material reduced then obviously cost is also reduced

22. References
 CAD Based Optimization by Celso Barcelos, Director of
Development MacNeal-Schwendler Corporation2003
 Multiphysics CAD-Based Design Optimization A. Vaidya, S.
Yang and J. St. Ville
 D. Spath, W. Neithardt and C. Bangert, “Integration of Topology
and Shape Optimization in the Design Process”, International
CIRP Design Seminar, Stockholm, June 2001.
 CAD-based Evolutionary Design Optimization with CATIA V5
Oliver KÄonig, Marc Winter mantel
 Structural optimization using ANSYS classic and radial basis
function based response surface models by Vijay Krishna
THE UNIVERSITY OFTEXAS AT ARLINGTON MAY 2009
 J.P. Leiva, and B.C. Watson, “Shape Optimization in the Genesis
Program”, Optimization in Industry II, Banff, Canada, Jun 6-100,
1999.

23. Thank You