Cad based shape optimization

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