Mest 16888 ES077 Multidisciplinary System Design Optimization(MSDO) Structural Optimization Design Space Optimization Lecture 18 Apr7,2004 Yong Kim C Massachusetts Institute of Technology-Dr ll Yong Kim
1 © Massachusetts Institute of Technology – Dr. Il Yong Kim Multidisciplinary System Design Optimization (MSDO) Structural Optimization & Design Space Optimization Lecture 18 April 7, 2004 Il Yong Kim
16888 ESD.J7 I. Structural Optimization Integrated Structural optimization I. Design Space Optimization o Massachusetts Institute of Technology-Dr Il Yong Kim
2 © Massachusetts Institute of Technology – Dr. Il Yong Kim I. Structural Optimization II. Integrated Structural Optimization III. Design Space Optimization
Mlesd Structural optimization 16888 E77 Definition An automated synthesis of a mechanical component based on structural properties. A method that automatically generates a mechanical component design that exhibits optimal structural performance o Massachusetts Institute of Technology-Dr Il Yong Kim
3 © Massachusetts Institute of Technology – Dr. Il Yong Kim Structural Optimization * Definition - An automated synthesis of a mechanical component based on structural properties. - A method that automatically generates a mechanical component design that exhibits optimal structural performance
Mles 16888 od Structural Optimization ESD.J7 minimize f(x) subject to g(x)≤0 X X∈S Typically, FEM is used BC's are given Loads are given How to represent the structure? or Which ty pe of design variables to use? min compliance (1)Size Optimization s.t. m smc (2 Shape Optimization 3)Topology Optimization o Massachusetts Institute of Technology-Dr Il Yong Kim
4 © Massachusetts Institute of Technology – Dr. Il Yong Kim Structural Optimization minimize ( ) subject to ( ) 0 () 0 f g h S d x x x x BC’s are given Loads are given How to represent the structure? or Which type of design variables to use? Typically, FEM is used. (1) Size Optimization (2) Shape Optimization (3) Topology Optimization min compliance s.t. m dmC ?
Mlesd Size optimization example 16888 E77 Beams (2-Dim minimize f(x) subject g(x)≤0 h(x)=0 X∈ Design variables(x) fx): compliance x: thickness of each beam g(x): mass h(x): state equation Number of design variables(ndv) ndv= 5 o Massachusetts Institute of Technology-Dr Il Yong Kim
5 © Massachusetts Institute of Technology – Dr. Il Yong Kim Size Optimization Example f(x) : compliance g(x) : mass h(x) : state equation • Design variables (x) x : thickness of each beam • Number of design variables (ndv) ndv = 5 Beams (2-Dim) minimize ( ) subject to ( ) 0 () 0 f g h S d x x x x
Mlesd Shape Optimization Example 16888 E77 B-spline(2-Dim) minimize f(x) subject g(x)≤0 h(x)=0 X∈ Design variables(x) fx): compliance x: control points of the B-spline g(x): mass (position of control points h(x): state equation Number of design variables (ndv ndy 8 o Massachusetts Institute of Technology-Dr Il Yong Kim
6 © Massachusetts Institute of Technology – Dr. Il Yong Kim Shape Optimization Example • Design variables (x) x : control points of the B-spline (position of control points) • Number of design variables (ndv) ndv = 8 B-spline (2-Dim) minimize ( ) subject to ( ) 0 () 0 f g h S d x x x x f(x) : compliance g(x) : mass h(x) : state equation
Mlesd Topology Optimization Example Eo. Cells(2-Dim) minimize f(x) subject g(x)≤0 h(x)=0 X∈ Domain shape is determined at the beginning Design variables(x) fx): compliance x: density of each cel■ g(x): mass (0≤p≤1) h(x): state equation Number of design variables(ndv) ndv= 27 o Massachusetts Institute of Technology-Dr Il Yong Kim
7 © Massachusetts Institute of Technology – Dr. Il Yong Kim Topology Optimization Example • Design variables (x) x : density of each cell (0 d U d 1) • Number of design variables (ndv) ndv = 27 Cells (2-Dim) Domain shape is determined at the beginning minimize ( ) subject to ( ) 0 () 0 f g h S d x x x x f(x) : compliance g(x) : mass h(x) : state equation
Mest 16888 Structural Optimization ES077 Size optimization Shape optimization Topology optimization Shape -Topology is given Topology are given Optimize boundary shape Optimize cross sections Optimize topology o Massachusetts Institute of Technology-Dr Il Yong Kim
8 © Massachusetts Institute of Technology – Dr. Il Yong Kim Structural Optimization Size optimization Shape optimization Topology optimization - Topology is given - Optimize boundary shape - Shape Topology - Optimize cross sections are given - Optimize topology
Mest 16888 Size Optimization ES077 Simplest method Changes dimension of the component and cross sections Applied to the design of truss structures Schmit(1960) General approach to structural optimization Coupling FEA&NL math Programming A Changed Length of the members Thickness of the members Unchanged Layout of the structure Ndv:10~100 o Massachusetts Institute of Technology-Dr Il Yong Kim
9 © Massachusetts Institute of Technology – Dr. Il Yong Kim Size Optimization Schmit (1960) - General approach to structural optimization - Coupling FEA & NL math. Programming - Simplest method - Changes dimension of the component and cross sections - Applied to the design of truss structures - Length of the members - Thickness of the members - Layout of the structure * Unchanged * Changed Ndv: 10~100
Mest 16888 Shape Optimization ESD.J7 Design variables control the shape Size optimization is a special case of shape optimization Various approaches to represent the shape Zolesio(1981), Haug and Choi et al. (1986)-Univ of lowa A general method of shape sensitivity analysis using the material derivative method adjoint variable method Radius of a circl Ellipsoid Bezier curve Etc Nodal positions Basis function when the fem is use0)∑a(xy) (control points Ndv:10~100 o Massachusetts Institute of Technology-Dr Il Yong Kim
10 © Massachusetts Institute of Technology – Dr. Il Yong Kim Shape Optimization Zolesio (1981), Haug and Choi et al. (1986) – Univ. of Iowa - A general method of shape sensitivity analysis using the material derivative method & adjoint variable method - Design variables control the shape - Size optimization is a special case of shape optimization - Various approaches to represent the shape Nodal positions (when the FEM is used) Basis functions B-spline (control points) Radius of a circle Ellipsoid Bezier curve Etc… Ndv: 10~100 1 (, ,) n i i i D I xyz ¦
