as the default design strategy ENGINEERING COMMUNITY...

1

“Optimization” as the default design strategy

SIMTEQ 2019 – ENGINEERING COMMUNITY CONFERENCE

Eddie Williams

Denel Dynamics

[email protected]

2019-7-10

2ABSTRACT

Implementing optimization methodologies changes the design Engineers mind-set from asking

the question:

"Is the design good enough?“

to asking the better question;

"What design is just good enough ?".

3CONTENTS

• Introduction

• Denel’s Dynamic Mechanical Analysis Department

• Optimization: A fundamental change in thinking

• Examples of applying optimization techniques

• Current and future optimization work

• Conclusion and Questions

4

Analysis and testing departments functions

1

Static Structural analysis

Linear static - general

2 Threaded Joint analysis

3 Non - Linear analysis, general

4 Composite material, general

5 Hyper elasticity

6 Roller Bearing analysis

7Multi physics

Electro-magnetism

8 Smart materials

9

Structural Dynamics

Structural Dynamics, General

10 Frequency response analysis

11 Shock response analysis

12 Modal matching

13 Frequency response matching

14 Flutter & Aero elasticity

15

Fatigue

Fatigue, General

16 Fatigue, Welds

17 Fatigue, Dynamic Structures

18Structural Optimization

Topology optimization

19 Sizing, Topometry optimization

20

Thermal analysis

Thermal, General

21 Thermal, Aerodynamic heating

22 Thermal, Equipment cooling

23

Multibody analysis

Adams - General

24 Co - sim, control system

25 Adams flex bodies

26 Multibody Dynamics

Mechanical Analysis Department @ Denel Dynamics

Our Mandate and purpose:

1. Provide specialised support to Programs and Projects.

2. Develop analysis methodologies.

3. Establish and maintain analysis capabilities.

About the department:

5Optimization – An introduction

• Optimization can be used to find a solution when requirements are in conflict e.g. low

weight vs. high stiffness.

• Optimization can be used to not find a solution i.e. to find out (quickly) that no feasible

design exist given current parameters.

• Optimization algorithms can be used to find (non-optimization) design and engineering

solutions.

• Using optimization is interesting and rewarding.

6

http://datagenetics.com/blog/august12014

OPTIMIZATION: A simple example

7



8



9Types of Optimization (according to Nastran)

Ref: MSC Nastran 2018, Design Sensitivity and Optimization User’s Guide

• Sizing optimization refers to a design task where the analysis quantities can vary such as plate thickness, Young’s modulus and spring stiffnesses.

• For shape optimization, the design variables affect the locations of the grids that make up the finite element model and seeks the best shape.

• Topology optimization A determination is made whether each designable finite element should be there or not.

• Topometry optimization provides a simple way of generating a design task that permits each designated element to be separately designed.

• Topography optimization the finite elements grids can move normal to the shell surface as to improve the response of sheet metal parts.

10Types of Optimization (Nastran example)


Shape optimization Topology optimization Topography optimization

11The Basic Optimization Problem Statement


12Numerically Searching for an Optimum


For a single independent variable the first-forward difference is given by

The resultant gradient vector of partial derivatives of the function can be written as

where each partial derivative is a single component of the gradient vector.

13Multidisciplinary Optimization


14

1000 N

1 m

Objective: Minimize WeightConstrain: Stress < 900 Mpa

Tip displacement: 50 mm

Initial Weight: 0.703 kg

A simple finite element optimization example

15A simple finite element optimization example

(Initial mass was about 700 gram)

10

0 m

m

75 mm

0

50

100

150

200

250

300

350

400

I Channel Box

Series1 322 303 348

Mas

s (g

ram

)

Mass comparison

16Flextensional “Moonie” Actuator

Ref: Cedrat Technologies. www.cedrat.com

Ref: E. Williams, P. Loveday, and N. Theron, “Design of a Large-Force Piezoelectric Inchworm Motor with a Force Duplicator,” in Robmech conference 2013, no. 1.

Piezoelectric stacks

17

Slide constraint

Slideconstraint

Input displacement

Output

Elements omitted from analysis

TOPVAR 1 PSHELL PSHELL .1

1

TDMIN .6

$ Global Target Constraints : MASS FRACTION

DCONSTR 1 10001 0.200000

DRESP1 10001 FRM FRMASS

DRESP1 111 DISPY DISP

2 50000

DRESP2 222 DispErr 333

DRESP1 111

DEQATN 333 F1(A) = (A+4.0*27.e-3)**2

Flextensional “Moonie” Actuator

Minimize

Design domain(quarter model)

Topology optimization

18Topology optimization: From NASTRAN to 3D printer

19Design intent study

6.82 m 2.3 m

2.3 m

Employing optimization techniques in the design of the primary structure of a Ground Station

Logistical imposed weight limitM < 7000 kg

20Design intent study – Load cases

LC 1

LC 2

LC 3

21Design intent study – Results LC1

Element density distribution plots

22


Design intent study – Results LC2

23


Design intent study – Results LC3

24

Element density distribution plots.All three load cases.

Design intent study – Results- All LC’s

25Back to the ground station – Initial design

26

G1

G2

G4G2

G1

G3

CB3p

CB1 CB1

G7

G5

G5

CB3G8

G8

CB12

CB12

CB11

CB11

CB7 CB7

CB2CB2

G6 G6

G4

G3

CB13CB10

CB10CB10

G7

CB6

CB6

CB5

CB33

CB8

CB5

CB9

LAM1

LAM2

LAM3

LAM4LAM5

PAT

Defining the design variables – Property groups

A total of 96 design variables and 19 Load cases !

H

W

t1

t2

H

W

t1

t

H

W2

W1

t2

t1

t

27Design constraints

The following constraints are enforced in the optimization:

• Maximum stress <700MPa x 0.8 = 560 MPa.

• The door corners may not displaced more than +/- 5 mm from the frame corners.

• Corner displacement < 200 mm.

• Only sheet thickness of 2mm, 3mm or 4mm

• The web thickness dimensions (t) of the I-profiles must be twice the thickness of theflange thickness (t1). All other profile thicknesses must be the same.

• Fixed inside width and height for the fork lift pockets.

• The height of the beams to fit inside panels (< 46mm.)

< +/- 5mm relative displacement

< 200 mm absolute displacement

28Nastran Input deck cards

$ PROPERTY G1

$11111112222222233333333444444445555555566666666777777778888888899999999

DESVAR 11 LG1W .1 .05 .3 .5

DESVAR 12 LG1H .2 .05 .3 .5

DESVAR 13 LG1t1 .003 5.-4 .01

DESVAR 14 LG1t2 .003 5.-4 .01 55

DLINK 1 13 0. 1. 14 1.

$ Standard Steel Sheet thicknesses

DDVAL 55 2.0-3 3.0-3 4.0-3

$ PROPERTY G1

DVPREL1 11 PBEAML 1 DIM1(A)

11 1.

$ CONSTRAINT LC1 A3a

DCONADD 2200 2244 3301 3302 3303 3304 3305 3306

DCONSTR 2244 2245 -5.6+8 5.6+8

DRESP1 2245 STR1p STRESS PBEAM 8 1

2 3 4 5 6 7 14 15

16 17 18 19 20 22 23 24

25 27 13 31 33

Stress constraint

Discreet sheet thickness valuesLink flange andweb thickness

Define and constraint design variables

Link design variables with properties

29Optimization Result

30

Internal ID. Label Value (mm)

1 LG1W 50.0

2 LG1H 91.7

3 LG1T2 2.0

4 LG2W 230.3

5 LG2H 87.2

6 LG2T2 2.0

7 LG3W 188.7

8 LG3H 300.0

9 LG3T2 4.0

10 LG4W 127.1

11 LG4H 50.0

12 LG4T2 4.0

13 LG5W 50.0

14 LG5H 121.6

15 LG5T2 3.0

16 LG6W 50.0

17 LG6H 50.0

18 LG6T2 2.0

19 LG7W 63.8

20 LG7H 140.8

21 LG7T2 2.0

22 LG8W 172.1

23 LG8H 53.8

24 LG8T2 4.0

25 LAM13 4.3

26 LAM23 4.5

27 LAM33 0.7

28 LAM43 0.1

29 LAM53 0.8

30 UCB1W 51.4

31 UCB1H 146.3

32 UCB1T1 2.0


33 UCB2W 46.0

34 UCB2H 81.0

35 UCB2T1 2.0

36 UCB3W 86.1

37 UCB3H 86.2

38 UCB3T1 2.0

39 UCB3PW 50.0

40 UCB3PH 236.5

41 UCB3TP1 2.0

42 UCB5W 50.0

43 UCB5H 117.0

44 UCB5T1 3.0

45 UCB6W 50.0

46 UCB6H 50.0

47 UCB6T1 2.0

48 UCB7W 17.5

49 UCB7H 50.0

50 UCB7T1 3.0

51 UCB8W 46.0

52 UCB8H 100.0

53 UCB8T1 4.0

54 UCB9W 50.0

55 UCB9H 105.2

56 UCB9T1 3.0

57 ICB10H 37.8

58 ICB10W1 46.0

59 ICB10W2 38.8

60 ICB10T2 2.0

61 ICB11H 59.6

62 ICB11W1 95.1

63 ICB11W2 47.0

64 ICB11T2 2.0


65 ICB13H 70.6

66 ICB13W1 65.8

67 ICB13W2 57.0

68 ICB13T2 2.0

69 UCB33W 86.9

70 UCB33H 71.0

71 UCB33T1 2.0

72 PAT1F 4.0

73 LG1T1 2.0

74 LG2T1 2.0

75 LG3T1 4.0

76 LG4T1 4.0

77 LG5T1 3.0

78 LG6T1 2.0

79 LG7T1 2.0

80 LG8T1 4.0

81 UCB1T 2.0

82 UCB2T 2.0

83 UCB3T 2.0

84 UCB3PT 2.0

85 UCB5T 3.0

86 UCB6T 2.0

87 UCB7T 3.0

88 UCB8T 4.0

89 UCB9T 3.0

90 ICB10T 4.0

91 ICB10T1 2.0

92 ICB11T 4.0

93 ICB11T1 2.0

94 ICB13T 4.0

95 ICB13T1 2.0

96 UCB33T 2.0

Optimization Result - all variables

31Optimization Result – Stress verification

Rigidity verification

32Objection function history

6600

6700

6800

6900

7000

7100

7200

7300

7400

0 5 10 15 20 25

Mas

s (k

g)

Design iterations

Objection function value

Starting mass: 7275 kg of which only 2103 kg (29%) was represented in design variablesEnd Mass : 6916 kg Mass represented in design variables reduced from 2103 kg to 1775 kg (or 359 kg less)

33Design Sensitivity

0

5000

10000

15000

20000

25000

30000

35000

ICB

10T

2

LAM

43

LG8T

2

LAM

13

LAM

23

PA

T1F

UC

B7

T1

LAM

53

UC

B2

T1

UC

B1

T1

UC

B3

T1

UC

B3

TP1

UC

B3

3T1

LAM

33

UC

B6

T1

LG2T

2

ICB

11T

2

UC

B9

T1

LG5T

2

LG6T

2

LG3T

2

LG4T

2

LG7T

2

ICB

13T

2

UC

B8

T1

UC

B5

T1

UC

B7

W

UC

B2

W

LG2W

LG2H

ICB

10H

UC

B8

W

UC

B9

W

UC

B7

H

UC

B2

H

LG8W

LG8H

UC

B1

W

UC

B3

W

UC

B3

PW

UC

B3

3W

UC

B6

W

ICB

10W

1

ICB

10W

2

UC

B8

H

UC

B9

H

ICB

11H

UC

B1

H

UC

B3

H

UC

B3

PH

UC

B3

3H

LG5W

LG6W

UC

B6

H

LG5H

LG6H

LG3W

LG4W

LG7W

LG3H

LG4H

LG7H

ICB

13H

UC

B5

W

ICB

11W

1

ICB

11W

2

ICB

13W

2

ICB

13W

1

ICB

13W

2

ICB

13W

1

UC

B5

H

UC

B5

H

De

sign

se

nsi

tivi

ty c

oef

fici

en

t

Design Variable

Response sensitivity coefficient

DSAPRT(FORMATTED)=ALL

34Modal matching – Long range weapon

http://www.deneldynamics.co.za/

http://www.deneldynamics.co.za/

35

“Modulus of elasticity's” as the design variables“Moment of inertia” as the design variables

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

$TOMVAR, ID, PRYPE, PID, PNAME, XINIT, XLB, XUB, DELXV(OPTIONAL)

TOMVAR 1 PBEAM 1 E 7.0e9 0.1

Modal matching – Long range weapon

$ Design Sensitivity and Optimization Analysis

SOL 200

CEND

ECHO = PUNCH(NEWBULK)

DESOBJ(MIN) = 5000

ANALYSIS = MODES

SUBCASE 1

SUBTITLE=Modal

METHOD = 1

VECTOR(PLOT,SORT1,REAL)=ALL

SPCFORCES(PLOT,SORT1,REAL)=ALL

BEGIN BULK

PARAM POST 1

PARAM PRTMAXIM YES

INCLUDE 'bulkopto.bdf'

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

$TOMVAR, ID, PRYPE, PID, PNAME, XINIT, XLB, XUB, DELXV(OPTIONAL)

TOMVAR 1 PBEAM 1 5 2.0-5 0.1

DRESP2 5000 MALL 4000

DTABLE T1 T2

DRESP1 20 21

DRESP1 20 FREG1 FREQ 1

DRESP1 21 FREQ2 FREQ 3

DTABLE T1 45. T2 98.

DEQATN 4000 FSTAR(T1,T2,M1,M2)=(M1-T1)**2 + 0.5*(M2-T2)**2

DOPTPRM DESMAX 100

ENDDATA

Topometry analysis

36Modal matching – Long range weapon

0.00E+00

2.00E+09

4.00E+09

6.00E+09

8.00E+09

1.00E+10

1.20E+10

0 5 10 15 20 25 30 35 40

Mo

du

lus

of

Elas

tici

ty

Element Number

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

0 5 10 15 20 25 30 35 40

Mo

men

t o

f In

erti

a

Element NumberR E A L E I G E N V A L U E S

MODE EXTRACTION EIGENVALUE RADIANS CYCLES

NO. ORDER

1 1 6.619977E+04 2.572932E+02 4.094948E+01

2 2 7.090022E+04 2.662709E+02 4.237834E+01

3 3 3.791509E+05 6.157523E+02 9.800002E+01

4 4 4.758401E+05 6.898117E+02 1.097869E+02

5 5 1.509208E+06 1.228498E+03 1.955216E+02

6 6 1.688244E+06 1.299324E+03 2.067939E+02

7 7 2.148346E+06 1.465724E+03 2.332772E+02

8 8 3.978410E+06 1.994595E+03 3.174497E+02

9 9 4.172543E+06 2.042680E+03 3.251027E+02

10 10 7.832465E+06 2.798654E+03 4.454196E+02

“Moment of inertia” as the design variables “Modulus of elasticity's” as the design variables

37Design of a Sensor Mount

Sensor

Mount

• Dominant modes MUST be between 30 Hz to 140 Hz – “low pass filter”

• No modes may be between 180Hz to 320 Hz


DESOBJ(MAX) = 1000

DESGLB = 3000

ANALYSIS = MODES

SUBCASE 1

SUBTITLE=Default

***

DESSUB=3100

TOPVAR 1 PSOLID PSOLID .9 1

SYM Y 3

DCONSTR 3000 10001 0.4

DRESP1 10001 FRM FRMASS

DCONADD 3100 3200 3300 3400 3500 3600 3700

DCONSTR 3200 3201 30.0 140.0

DRESP1 3201 FMC1 FREQ 1

DCONSTR 3300 3301 30.0 140.0






DTABLE F1L 180. F1H 320.

DEQATN 4000 FSTAR(FL,FH,F)=(F-(FL+FH)/2.)**2

DRESP2 5200 F1STAR 4000

DTABLE F1L F1H

DRESP1 3401


DTABLE F1L F1H

DRESP1 3501


DTABLE F1L F1H

DRESP1 3601


DTABLE F1L F1H

DRESP1 3701

$ ((FL+FH)/2.)**2 = ((320-180)/2)**2 = 4900

DCONSTR 3400 5200 4900.

DCONSTR 3500 5300 4900.

DCONSTR 3600 5400 4900.

DCONSTR 3700 5500 4900.

DRESP1 1000 FREQ FREQ 1

𝑅 = 𝑓 −𝑓𝑙𝑏 + 𝑓𝑢𝑏

2

2

>𝑓𝑙𝑏 + 𝑓𝑢𝑏

2

2

Avoiding a frequency range


1st mode @ 109 Hz – Axial translation 2nd and 3rd mode @ 137 Hz – Lateral translation


4th mode @ 329 Hz - torsional 5th and 6th mode @ 358 Hz – Lateral rotation


Mode nr Mode description Mode frequency Requirement Result

1st Axial translation 109 Hz Must be between 30 Hz and 140 Hz Pass

2nd and 3rd Lateral translation 137 Hz Must be between 30 Hz and 140 Hz Pass

4th Torsional 329 Hz Must NOT be between 180Hz and 320 Hz Pass

5th and 6th Lateral rotation 358 Hz Must NOT be between 180Hz and 320 Hz Pass

7th Localized to each damper 664 Hz Must NOT be between 180Hz and 320 Hz Pass

Table 1: Effective modal mass

X % Y % Z %

1 0.0% 92.2% 0.0%

2 47.6% 0.0% 45.0%

3 45.0% 0.0% 47.6%

4 0.0% 0.0% 0.0%

5 0.0% 0.0% 0.0%

6 0.0% 0.0% 0.0%

7 1.4% 0.0% 0.4%

8 0.4% 0.0% 1.4%

9 0.0% 4.9% 0.0%

10 0.0% 0.0% 0.0%

94.5% 97.1% 94.5%

Effective modal massMEFFMASS(ALL)=YES

42Frequency response matching

Mount Location(CELAS1)

Mount Location(CELAS1)

Rubber Anti vibration Mount

Mass @ CoG(CONM2)

43

m ∙ ሷ𝑥 + 𝑐 ∙ ሶ𝑥 + 𝑘 ∙ 𝑥 = 𝐴 ∙ sin 𝜔 ∙ 𝑡 − 𝛼

𝜁 =𝑐

𝑐𝑐

𝑐𝑐 = 2 ∙ 𝑘 ∙ 𝑚

𝑇𝑑 =1 + 2 ∙ 𝜁 ∙ 𝑟 2

1 − 𝑟2 2 + 2 ∙ 𝜁 ∙ 𝑟 2

12

Frequency response matching

44

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

DRESP2 900 R0 450

DTABLE A1 A2 A3 A4 A5

DRESP1 210 220 230 240 250

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

DTABLE A1 1.807 A2 3.637 A3 5.666 A4 3.027

A5 0.6483

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

DEQATN 450

R(A1,A2,A3,A4,A5,b1,b2,b3,b4,b5) = (((b1 - A1) / A1)**2)

+ (((b2 - A2) / A2)**2) + (((b3 - A3) / A3)**2) + (((b4

- A4) / A4)**2) + (((b5 - A5) / A5)**2)

$ ...OPTIMIZATION CONTROL

DOPTPRM DESMAX 100

ENDDATA 23fea5fb

Frequency response matching

$ Design Sensitivity and Optimization Analysis

SOL 200

TIME 600

CEND

TITLE = MSC.Nastran job

ECHO = NONE

MAXLINES = 999999999

DESOBJ(MIN) = 900

ANALYSIS = MFREQ

LOADSET = 1

SUBCASE 1

SUBTITLE=FreqUnitX

METHOD = 1

FREQUENCY = 1

SPC = 2

DLOAD = 2

DISPLACEMENT(PLOT,SORT1,REAL)=ALL

ACCELERATION(PLOT,SORT1,PHASE)=ALL

BEGIN BULK

MDLPRM HDF5 0

PARAM PRTMAXIM YES

INCLUDE 'bulksection.bdf'

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

DESVAR 1 Sx_S 459300. 1.0e3 1.0e8 .5

DESVAR 2 Sx_D .1 1.0e-6 1.0 .5

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

DVPREL1 2 PELAS 1 4

2 1.

DVPREL1 1 PELAS 1 3

1 1.

$.......2.......3.......4.......5.......6.......7.......8.......9.......0

$DRESP1 ID LABEL RTYPE PTYPE REGION ATTA ATTB ATTi

DRESP1 210 b1 FRACCL 1 106. 1





Design objective: minimize R0

𝑅0 =𝑏1−𝐴1

𝐴1

2+

𝑏2−𝐴2

𝐴2

2+

𝑏3−𝐴3

𝐴3

2…….

Where bx is the current value at frequencyandAx is the desired value

45Frequency response matching

DESIGN VARIABLE HISTORY

----------------------------------------------------------------------------------------------------------------------------------

INTERNAL | EXTERNAL | |

DV. ID. | DV. ID. | LABEL | INITIAL : 1 : 2 : 3 : 4 : 5 :

----------------------------------------------------------------------------------------------------------------------------------

1 | 1 | SX_S | 4.5930E+05 : 3.9082E+05 : 3.7809E+05 : 3.6834E+05 : 3.6752E+05 : 3.6840E+05 :

2 | 2 | SX_D | 1.0000E-01 : 1.0983E-01 : 1.6475E-01 : 1.6782E-01 : 1.6729E-01 : 1.6626E-01 :

----------------------------------------------------------------------------------------------------------------------------------


DV. ID. | DV. ID. | LABEL | 6 : 7 : 8 : 9 : 10 : 11 :

----------------------------------------------------------------------------------------------------------------------------------

1 | 1 | SX_S | 3.6756E+05 : 3.6844E+05 : 3.6759E+05 : 3.6846E+05 : 3.6761E+05 : 3.6848E+05 :

2 | 2 | SX_D | 1.6735E-01 : 1.6623E-01 : 1.6733E-01 : 1.6620E-01 : 1.6731E-01 : 1.6619E-01 :

----------------------------------------------------------------------------------------------------------------------------------


DV. ID. | DV. ID. | LABEL | 12 : 13 : 14 : 15 : 16 : 17 :

----------------------------------------------------------------------------------------------------------------------------------

1 | 1 | SX_S | 3.6763E+05 : 3.6849E+05 : 3.6849E+05 :

2 | 2 | SX_D | 1.6730E-01 : 1.6618E-01 : 1.6618E-01 :

46Conclusion

• Optimization and design sensitivity studies is powerful design tools.

• Optimization techniques improve the designers insight of the design and the design intent.

• Optimization techniques make it practically possible to solve curtain difficult engineering

problems.

• Optimization can (and should) be implemented effectively as part of the design process.

• Optimization techniques entails a fundamental change in thinking about the design process.

47Current and future work:

150.0030.00 Hz

10.00

1.00e-6

Log

g/N

1.00

0.00

Am

plit

ude

46.78

F FRF umb:1:+Y/umb:7:+Z

F FRF umb:1:+Z/umb:7:+Z



































• Use optimization (SOL 200) to do Frequency Response Matching for a complicated system using

Modal Assurance Criterion (and/or other statistical variables) as the objection function.

Ref: MSC.ProCor 2006

48Question

“Optimization” as the default design strategy

SIMTEQ 2019 – ENGINEERING COMMUNITY CONFERENCE

Eddie Williams

Denel Dynamics

[email protected]

2019-7-10

as the default design strategy ENGINEERING COMMUNITY...

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