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

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1. 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. 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. 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. 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. 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. 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. 7. Role of Optimization
8. 8. Softwares used:  ANSYS  IDEAS  CATIA  Unigraphics NX  TOSCA
9. 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. 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. 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. 12. Example:- Bracket
13. 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. 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. 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. 16.  Set 5:- o V max-350.77 MPa o Vol-8829.1 mm3
17. 17. Results  DesignVariables R1,R2,R3,R4,W
18. 18.  Volume
19. 19.  Von Mises Stresses
20. 20. Application of Bracket
21. 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. 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. 23. Thank You