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Presented By Guided By
Gore A. S. Prof. Rodge M.K.
2010MME007
M. Tech. CAD/CAM
CAD Based Optimization
Department of Production
Engineering, SGGSIE&T, Nanded
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.
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
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.
Commonly used Optimization Techniques
1. Mathematical Programming Techniques : To find the
minimum of a function of several variables under a
prescribed set of constraints, e.g. sequential quadratic
programming (SQP)
2. Stochastic Process Techniques : To analyze problems
described by a set of random variables with known
probability distribution , e.g. queuing theory
3. Statistical Techniques : To build empirical models from
experimental data through analysis, e.g. Design of
Experiments
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.
Role of Optimization
Softwares used:
ANSYS
IDEAS
CATIA
Unigraphics NX
TOSCA
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.
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.
Element Type
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
Example:- Bracket
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]
Iterations
Set 1:-
o V max- 344.58MPa
o Vol- 16199 mm3
Set 2:-
o V max -283.73 MPa
o Vol-12956 mm3
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
Set 5:-
o V max-350.77 MPa
o Vol-8829.1 mm3
Results Design Variables R1,R2,R3,R4,W
Volume
Von Mises Stresses
Application of Bracket
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
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 OF TEXAS 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.
Thank You