•  Research work which originated in UK Universities in the 1980’s and 1990’s (7 PhD’s on related topics).

•  This work done in the 1980’s and 1990’s is the source of most commercial frequency domain tools today.

•  First published work on frequency based fatigue using FE results in 1999. •  NAFEMS book published in 2000. •  Core people involved in CAEfatigue and CAE Software Solutions were

originally involved in SBIR Acoustic Fatigue project with USAF (see below).

•  Early collaboration with NASA Langley, WPAFB and NASA JSC. •  Same people (plus others) now involved in CAEfatigue Limited (UK) and

CAE Software Solutions LLC (MI, USA).

Who are CAEfatigue Limited?

3

CAEfatigue VIBRATION Concept (High Level) A Frequency Based Random Response & Fatigue Solver

Stress response PSD

Stress range response pdf

CAEfatigue VIBRATION works by taking, as input, the Power Spectral Densities (PSD) of loading along with a system transfer function, from which the stress response PSD’s for all output positions (grid ID’s) are calculated. These stress response PSD’s are then used to calculate the stress Rainflow Cycle Count (RCC) and resultant fatigue damage or life. This is shown in the flow chart below.

www.caefatigue.com

Fringe Data Output From CFV Analysis?

Response Statistics •  m0, m1, m2, m4 •  Zero crossings •  Peaks per second •  Irregularity factor •  Mean stress •  Mean+P*rms stress •  Mean-P*rms stress •  Mean+P*rms strain •  Mean-P*rms strain •  RMS stress •  RMS strain

Fatigue Results •  Damage •  Log damage •  Life •  Log of life •  Margin of safety

Solids and shells, as well as nodes and elements, all allowed at the same time for specific layer or worst layer

4

P is a user definable variable

www.caefatigue.com

Transition From 1st to 2nd Generation Vibration Fatigue Solvers •  Automotive customers need to be able to apply multiple (eg 100 simultaneous) inputs

(Many automotive OEM’s are very keen to use these methods for large models)

5

NB PSD

Sine waves

Deterministic Components

Random PSD

Combined Loads – Frequency Domain

Stress pdf

Fatigue Damage

Loads have to be combined before calculation of the

stress pdf

Mean Load

Response Parameters (if Needed)

Time Domain

Frequency Domain

1st generation tools do not allow either

•  Aerospace customers need to be able to apply mixed random and deterministic loads (eg sine sweep + mean + random or random + narrow band + mean)

www.caefatigue.com

User Interface (in V3.0)

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

6

•  Non-linear rms strain and max strain •  displacement, velocity and acceleration,

force (R3.0) •  Composite layers (R4) •  Ansys support (R2.1) •  Abaqus support (R2.1)

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective More Accurate Solutions – avoiding both false positives and in service

failures

www.caefatigue.com

Cool Technology: Frequency Domain Stress-Strain Hysteresis Loops

Displacement, velocity, acceleration and force output in R3.0

7

www.caefatigue.com

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

8

•  Very easy template system •  Ideal for batch and solver integration •  easy pre processing of loads

User Interface (in V3.0)

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

8

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective More Accurate Solutions – avoiding both false positives and in service

failures

www.caefatigue.com

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

•  Complex principal stress •  Gershgorin Circle Theorem

(eigenvalue extraction) •  Strain-life solver •  Seam welds (R2.1) •  Temp dependant materials (R 2.1) •  Spot welds (R3.0)

User Interface (in V3.0)

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

9

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective More Accurate Solutions – avoiding both false positives and in service

failures

www.caefatigue.com

Cool Technology: Frequency Domain Strain-Life Fatigue & Other Material Definitions (like MMPDS) Supported

100.00$

1000.00$

10000.00$

100000.00$

1.E+00$ 1.E+01$ 1.E+02$ 1.E+03$ 1.E+04$ 1.E+05$ 1.E+06$ 1.E+07$ 1.E+08$ 1.E+09$

Strain'amlitud

e'

Cycles'to'failure'(2Nf)'

εelas8c'

εplas8c'

εtotal'

(2Nf)b + εf’(2Nf)c

σf’

E Δε2

=

Elastic (Basquin)

Plastic (Coffin-Manson)

0.0000#

100.0000#

200.0000#

300.0000#

400.0000#

500.0000#

600.0000#

0.0000# 0.0010# 0.0020# 0.0030# 0.0040# 0.0050# 0.0060# 0.0070# 0.0080# 0.0090# 0.0100#

Stress&

Strain&

Stress*Strain&Curve&

εa = σa σa

E K’

1/n’ + [ ]

Romberg-Osgood Relationship

Plus SWT and Morrow mean stress correction

10

www.caefatigue.com

Cool Technology: Complex von-Mises and Principal Stresses Classic von-Mises doesn't work for complex stresses because von-Mises result is function of complex phase! Instead we use complex version by Segalman (1998) Where Sx, Sy, Sz are the x, y and z PSD’s of response, Sxy, Syz, Sxz are the shear PSD’s and the Sx*Sy, Sy*Sz, and Sx*Sz terms are cross PSD’s

Plus 2 versions of Maximum Principal (exact and fast using Gershgorin) for complex stresses

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700

Equi

vale

nt S

tres

s

phase

Von-Mises

11

www.caefatigue.com

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

12

•  “Running Sum” moment technology •  Fast OP2 stress file interrogation •  1000+GB results files easily processed

User Interface (in V3.0)

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

12

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective Faster Time To Market – reducing

analysis and user processing

times.

www.caefatigue.com

Cool Technology: Clever Use of Response Moments is The Key To The CAEfatigue VIBRATION Approach

(Stress)2

Hz

Frequency, Hz

Gk(f)

fk

m0

m1m2

m4

Running moment sum

13

www.caefatigue.com

Cool Technology: Unique Running Moment Sum Allows Huge Models To Be Processed

2nd generation software has no practical limitation related to stress OP2 file sizes

run t

imes

(mins

)

Number of Grid ID’s

8.34GB OP2 file 2000 GB OP2 file limit of some 1st

generation solvers

14

www.caefatigue.com

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

15

•  Mixed random plus harmonics (MIL-STD-810G)

•  New sine sweep technology •  Unique sine-on-random •  Unique narrow-band-on-random •  Embedding of MMPDS material data

User Interface (in V3.0)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

15

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective More Accurate Solutions – avoiding both false positives and in service

failures

www.caefatigue.com

Cool Technology: Examples of Different Types of Frequency Based Loads That Can Be Handled

Plus any mixture of the above and all of the above with mean loads applied

(g) PSD + Sine Wave

!30$

!20$

!10$

0$

10$

20$

30$

0$ 500$ 1000$ 1500$ 2000$ 2500$ 3000$ 3500$ 4000$

16

www.caefatigue.com

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

17

•  Multiple correlated loads (eg 100 inputs)

•  MATLAB time to PSD scripts

User Interface (in V3.0)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

17

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective More Accurate Solutions – avoiding both false positives and in service

failures

www.caefatigue.com

Conversion of Simultaneous Time Histories to PSD Matrix (currently done with MATLAB)

time signal 1 time signal 2

time signal 3 time signal 4 time signal 5

time signal 6

time signal 7 time signal 8

time signal 9 time signal 10 time signal 11

time signal 12

PSD matrix for event 6 Time signals for event 6

event 6 loading

Complete duty cycle

Complete duty cycle

PSD Matrix Event 1 152 seconds

PSD Matrix Event 2 42 seconds

PSD Matrix Event 3 18 seconds

PSD Matrix Event 4 18 seconds

PSD Matrix Event 5 480 seconds

PSD Matrix Event 6 1682 seconds

PSD Matrix Event 7 378 seconds

PSD Matrix Event 8 18 seconds

PSD Matrix Event 9 18 seconds

PSD Matrix Event 10 68 seconds

18

www.caefatigue.com

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

19

Linked to any 3rd party optimisation code (eg Mode Frontier) which connects ascii Control file input (Nastran and/or CFV) to ascii CSV output

User Interface (in V3.0)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

19

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective Lightweighting – options for

reducing material volume/weight.

www.caefatigue.com

Cool Technology: Stochastics (Embedded in Mode Frontier)

For the first time CAEfatigue VIBRATION makes the task of computing “damage sensitivity” to input parameters a practical option

20

www.caefatigue.com

•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

21

TIME2PSD Expert System will make conversion of test data to PSD format easier, more accurate, and less prone to user errors

User Interface (in V3.0)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

21

Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

Business Objective Faster Time To Market – reducing

analysis and user processing

times.

www.caefatigue.com

New Internal CAEFatigue VIBRATION process Process for N events, each event containing X inputs (time histories)

RPC/text file 1 with X time histories

RPC/text file 2 with X time histories

RPC/text file 3 with X time histories

RPC/text file N with X time histories

TIME2PSD Expert System

PSD matrix file 1

PSD matrix file 2

PSD matrix file 3

PSD matrix file N

TIME2PSD Expert System Control File Entry

means file (optional)

rms scaling file (optional)

•  Basic statistics (min, max, mean, std, skew, kurtosis)

•  Spectral moments •  Time period used in averaging (may

not be the same as the total period) •  Number of averages

www.caefatigue.com

23

TIME2PSD Control File Entries TIME2PSD SRATE EVIDST TABIDST EVENT_N WINDOW FORMAT MEANS MAXF

“filename” TS_filenameX

"mapping" skip CHAN_N T_UNITS chan1 chan2 chan3 chan4

chan5 chan6 chan7 chan8 chan9 chan10 chan11 cont

"EV_OPTS" EV_NUM NSI RMSI TSMOOTH

SF T δ

t1 t2 t3 t4 t5 t6 cont

SRATE Number of samples in 1 second (real) – then dt = 1/srate. (required). EVIDST Start ID for events (required). TABIDST Start ID for VTABRND tables (required). EVENT_N Number of time history event files (integer > 0) (optional – default = 1). WINDOW Window function to use (optional – choices Hanning or None - default – Hanning). This is applied to the “block” of date extracted from the total time signal. FORMAT Format of time signal files (RPC or CSV) (optional – default = CSV). MEANS Used to decide if means to be calculated (yes/no) (default = no). Ignored if no mean stress correction specified. (optional – default = no). MAXF Max frequency in output (used to over ride the Nyquist frequency when outputting

PSD data) (optional - default = Nyquist). “filename” Used to specify names and location of Event time history files. TS_filenameX This should correspond to the names of the time history files with a number (X) at

the end of the files, eg filename1, filename2, . . . . filenameN, where N is the number of time history files (required).

“mapping” Used to specify format and order of channel data. skip Number of header lines to skip in an asci file. (optional – default = 0).

www.caefatigue.com

24

TIME2PSD Control File Entries TIME2PSD SRATE EVIDST TABIDST EVENT_N WINDOW FORMAT MEANS MAXF

“filename” TS_filenameX

"mapping" skip CHAN_N T_UNITS chan1 chan2 chan3 chan4

chan5 chan6 chan7 chan8 chan9 chan10 chan11 cont

"EV_OPTS" EV_NUM NSI RMSI TSMOOTH

SF T δ

t1 t2 t3 t4 t5 t6 cont

CHAN_N Number of channels in event file to use. (optional – needed if all channels are not used or if mapping is not 1 to 1 etc).

T_UNITS Time units (optional - default = seconds). chani location in asci input file for channel “i” of data (optional). “EV_OPTS” Optional Event parameters (one set for each Event). EV_NUM Number of this Event. NSI Number of non-stationary intervals for this Event (optional - default = 1). RMSI Number of rms scaling intervals for this Event (optional - default = 1). TSMOOTH Number of adjacent time points to be used for temporal smoothing of response PSD

for this Event (optional – default = 1). SF Scale factor to apply to time signals in this Event before FFT (optional - default = 1). T Length of window function in time for this Event (real) (auto or T). (required). d Overlap or gap in time between windows for this Event (real) (+ means overlap)

(optional - default = 0). ti,tj Used to specify sections (defined by pairs of time values t1-t2, t3-t4, t5-t6, t7-t8) to

delete from Event files before FFT process is applied (optional – default = none).

www.caefatigue.com

t1

t2 t3

t4

t5

t6

T δ

number of blocks determined by integer((Ttotal/(T-δ)) +1

Conventional example

need an automatic way to calculate T If number of stationary intervals is greater than 1 then the original samples would be split into NSI samples and then the whole of the above approach would be applied independently to each sample.

www.caefatigue.com

!200$

!150$

!100$

!50$

0$

50$

100$

150$

200$

1.99$ 2.09$ 2.19$ 2.29$ 2.39$ 2.49$

!200$

!150$

!100$

!50$

0$

50$

100$

150$

200$

1.99$ 2.09$ 2.19$ 2.29$ 2.39$ 2.49$

t1

t2

T - δ

number of blocks determined by integer((Ttotal/(T-δ)) +1

SAE575 example T

- δ

number of blocks determined by integer((Ttotal/(T-δ)) +1

CAEfatigue Control File

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