buckling fatigue analysis
DESCRIPTION
FEMTRANSCRIPT
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Failure Analysis
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• STATIC (LINEAR & NON-LINEAR)
• BUCKLING FAILURE
• FATIGUE FAILURE
• IMPACT FAILURE
• CREEP FAILURE
• FRACTURE FAILURE
Analysis Types Covered
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BUCKLING ANALYSIS(STRUCTURAL ANALYSIS)
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For an intermediate length compression member,kneeling occurs when some areas yield beforebuckling.
However, when a compression member becomes longer, the role ofthe geometry and stiffness (Young's modulus) becomes more andmore important. For a long (slender) column, buckling occurs waybefore the normal stress reaches the strength of the column material
The failure of a short compression member resulting fromthe compression axial force (YS or UTS Limit):
Compression Member
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In practice, for a given material, the allowable stress in a compression memberdepends on the slenderness ratio Leff / r and can be divided into three regions:short, intermediate, and long.Short columns are dominated by the strength limit of the material. Intermediatecolumns are bounded by the inelastic limit of the member. Finally, long columnsare bounded by the elastic limit (i.e. Euler's formula).
Yield Strength
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Buckling
Structures subject to compression load that
haven’t achieved material strength can show
failure mode called buckling.
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Buckling Failure | Model Examples
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Buckling Loads for Various BCs
CLASSICAL EULER SOLUTIONS
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Buckling Failure | Model Examples
The demand for automobiles with less consumption of
fuel and less emission is increasing continuously.
Besides the light weight design, the increasing
usage of optimization software leads to thin walled and
slender components which tend to buckle under
compressive/lateral loading.
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Buckling Failure | Model Examples
An interesting variation arises in the case of
automotive applications. In the case of front end
collision, the hood is expected to crumple (buckle) in
order to absorb the energy of collision, as well as to
save the passenger compartment.
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How FE Analysis will help us?
If a structure has one or more dimensionsthat are small relative to the others (slender orthin-walled), and is subjected to compressiveloads, then a buckling analysis may benecessary.
From an FE analysis point of view, a bucklinganalysis is used to find the lowest buckling loadand to find the shape of the buckled structure.
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FE Domain | Pre-Processing
• Geometry: 1-D, 2-D, 3-D
• Element: Structural: 1-D, 2-D, 3-D
• Material Prop: Structural (E, , )
• Geometrical Prop: Area, MI (I)
ν ρ
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FE Domain | Solution
• Boundary Conditions:
Structural nodal constraints and Load Application
(depends upon Analysis Types)
• Solution Parameters:
Depends upon Analysis Type: Linear or Non-
Linear
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How to Carry out Buckling FE Analysis Buckling loads are critical loads where certain typesof structures become unstable. Each load has an associated buckled mode shape.This is the shape that the structure assumes in abuckled condition. There are two primary means to perform a bucklinganalysis:
1. Eigen-value (Linear Analysis)Buckling is an Eigenvalue problem that is a functionof the material & geometric stiffness matrices.
2. Non-Linear (Non-Linear Analysis)(Geometrical Non-Linearity)
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Eigen-value (Linear Analysis) Eigenvalue buckling analysis predicts the theoretical buckling
strength of an ideal elastic structure. This is known as classicalEuler buckling analysis.
This method is not recommended for accurate, real-worldbuckling prediction analysis.
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Eigenvalue buckling analysis predicts the theoretical buckling strength (thebifurcation point) of an ideal linear elastic structure. (See Figure (b).) This methodcorresponds to the textbook approach to elastic buckling analysis: for instance,an eigenvalue buckling analysis of a column will match the classical Eulersolution. However, imperfections and nonlinearities prevent most real-worldstructures from achieving their theoretical elastic buckling strength. Thus,eigenvalue buckling analysis often yields unconservative results, and shouldgenerally not be used in actual day-to-day engineering analyses.
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T1 | Buckling Analysis | Column
Theoretical Solution (Euler’s Formula)
Eigenvalue Solver (ANSYS) to get theoretical value
Non-Linear Analysis (ANSYS) to get more accurate value
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Steel column (10X10 mm cross-section) is constrained atthe bottom. Objective is to calculate the required load tocause buckling.
T1 | Buckling Analysis | Column
E = 2E5
L = 100 and C/S: 10X10
I = 833.333 = [(10X103)/12]
P= (π2E*I)/4L2 = 41,081.65 Unit
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T1 | Buckling Analysis | Column
BEAM3 ELEMENT
3 DoF = Ux, UYand RotZ
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T1 | Buckling Analysis | Column
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/TITLE,Eigenvalue Buckling Analysis
/PREP7 ! Enter the preprocessor
ET,1,BEAM3 ! Define the elt of the beam to be buckled
R,1,100,833.333,10 ! Real Consts: type 1, area (mm^2), I (mm^4), height (mm)
MP,EX,1,200000 ! Young's modulus (in MPa)MP,PRXY,1,0.3 ! Poisson's ratio
K,1,0,0 !Define the geometry of beam K,2,0,100L,1,2 ! Draw the lineESIZE,10 ! Set element size to 1 mmLMESH,ALL,ALL ! Mesh the lineFINISH
T1 | Buckling Analysis | Column
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/SOLU ! Enter the solution mode
ANTYPE,STATIC ! Before you can do a buckling analysis, ANSYS! needs the info from a static analysis
PSTRES,ON ! Prestress can be accounted for - required! Eigenvalue buckling analysis
DK,1,ALL ! Constrain the bottom of beam
FK,2,FY,-1 ! Load the top vertically with a unit load.! The eignenvalue solver uses a unit force to
! determine the necessary buckling load.
SOLVEFINISH
T1 | Buckling Analysis | Column
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/SOLU !Enter the solution mode again to solve bucklingANTYPE,BUCKLE !Buckling analysisBUCOPT,LANB,1 !Extraction Method (Block Lanczos) for mode-ISOLVEFINISH
!Check with General Postprocessor, List Results, Detailed Summary
T1 | Buckling Analysis | Column
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Buckling Load = ~41,123 N
T1 | Buckling Analysis | Column
41,081.65 Unit
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Buckling Load = 41,123 N
The eignenvalue solveruses a unit force todetermine the necessarybuckling load.
LINEAR ANALYSIS
T1 | Buckling Analysis | Column
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T2NON-LINEAR ANALYSIS
Ensure that you have completed the Linear Analysis or Eigenvalue
Buckling Analysis before going for a Non-Linear Analysis
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Non-Linear Analysis) Buckling loads for several configurations are readily available
from tabulated solutions. However, in real-life, structuralimperfections and nonlinearities prevent most real-worldstructures from reaching their eigenvalue predicted bucklingstrength; ie. it over-predicts the expected buckling loads
This method is not recommended for accurate, real-worldbuckling prediction analysis.
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A more practical approach is to carry out a large displacement analysis,where buckling can be detected by the change of displacement in themodel.
A large displacement problem is non-linear in nature. Geometric non-linearity arises when deformations are large enough to significantly alterthe way load is applied, or load is resisted by the structure.
The approach to a non-linear buckling solution is achieved by applyingthe load slowly (dividing it into a number of small loads increments).
The model is assumed to behave linearly for each load increment, andthe change in model shape is calculated at each increment.
Stresses are updated from increment to increment, until the full appliedload is reached.
T2 | Buckling Non-Linear Analysis | Column
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/TITLE,Non-Linear Buckling Analysis
/PREP7 ! Enter the preprocessor
ET,1,BEAM3 ! Define the element of the beam to !be buckled
R,1,100,833.333,10 ! Real Consts: type 1, area (mm^2), I (mm^4), height (mm)
MP,EX,1,200000 ! Young's modulus (in MPa)MP,PRXY,1,0.3 ! Poisson's ratio
K,1,0,0 ! Define the geometry of beam (100 !mm high)
K,2,0,100L,1,2 ! Draw the lineESIZE,10 ! Set element size to 1 mmLMESH,ALL,ALL ! Mesh the lineFINISH
T2 | Buckling Non-Linear Analysis | Column
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/SOLUANTYPE,STATIC !Static analysis (not buckling)NLGEOM,ON ! Non-linear geometry solution OUTRES,ALL,ALL ! Stores bunches of outputNSUBST,20 ! Load broken into 20 load stepsNEQIT,1000 ! Use 20 sub-steps to find solutionAUTOTS,ON ! Auto time stepping
/ESHAPE,1 ! Plots the beam as a volume rather than !line
DK,1,ALL,0 ! Constrain bottomFK,2,FY,-50000 ! Apply load slightly greater than predicted
! buckling load to upper nodeFK,2,FX,-250 ! Add a horizontal load (~0.5% FY) to initiate
! Buckling (Thumb Rule)SOLVEFINISH
T2 | Buckling Non-Linear Analysis | Column
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SOLUTION IS ON
T2 | Buckling Non-Linear Analysis | Column
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View the deformed shapeT2 | Buckling Non-Linear Analysis | Column
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View the DoF solution UYT2 | Buckling Non-Linear Analysis | Column`
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In Time History: ADD UY at Node-2 (Top End) and FY (Reaction force)at Node-1 (Bottom-Node)
T2 | Buckling Non-Linear Analysis | Column
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Force on X- axis and Deflection on Y Axis
T2 | Buckling Non-Linear Analysis | Column
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Beam became UNSTABLE and BUCKLED with anapproximate load of 38,000 N.
T2 | Buckling Non-Linear Analysis | Column
Theoretical P = 41081 N
ANSYS P = 41,123 N
Non-Linear = 38,000 N
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Buckling Features Buckling is a critical state of stress and deformation, atwhich a slight disturbance causes a gross additionaldeformation, or perhaps a total structural failure of the part. Structural behaviour of the part near or beyond'buckling' is not evident from the normal arguments ofstatics. Buckling failures do not depend on the strength of thematerial, but are a function of the component dimensions &modulus of elasticity. Therefore, materials with a high strength will buckle justas quickly as low strength ones.
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FATIGUE ANALYSIS(EXTENSION OF TRANSIENT
DYNAMIC ANALYSIS)
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S-N curve – A material property
Where, Su is the ultimatestrength and Se is theendurance limit (fatiguelimit). Assume the ratioSe/Su is equal to 0.5.
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Miner’s rule
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Miner’s rule• It states that if there are k different stress levels and the
average number of cycles to failure at the ith stress, Si, is Ni
(from S-N curve), then the damage fraction, C, is:
ni is the number of cycles accumulated at stress Si.
C is the fraction of life consumed by exposure to the
cycles at the different stress levels.
• When the damage fraction (C) reaches 1, failure occurs.
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FE Domain | Pre-Processing
• Geometry: 1-D, 2-D, 3-D
• Element: Structural: 1-D, 2-D, 3-D
• Material Prop: Structural (E, ) and S-N curve
• Geometrical Prop: Area, MI (I)
ν
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FE Domain | Solution• Boundary Conditions:
Structural nodal constraints and Load steps
• Solution Parameters:
General structural solution
• Post processing:
Miner’s rule the simplest and the most widely usedcumulative damage models for fatigue failure.
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Problem definition | Geometry and applicationA flat leaf spring has been machined from AISI 1050 steel cold-drawn steel (Young’s Modulus is 210 GPa, Poisson’s ratio is 0.3,Yield Strength is 580 MPa and the Ultimate Strength is 690 MPa).
A cyclic load of ±100 N acts for 5,00,000 cycles and another cyclicload of ± 150 N acts for 5000 cycles at the free end of the leafspring. Assume one cycle of 20 seconds.
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Fatigue Failure | Model Example
5 x 105 cycles
-100 N force in
Y direction
5 x 105 cycles
+100 N force in
Y direction
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Fatigue Failure | Model Example
5 x 103 cycles
-150 N force in
Y direction
5 x 103 cycles
+150 N force in
Y direction
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Problem definition | Type of loading
5 x 105 cycles
+100 N force in
Y direction
5 x 105 cycles
-100 N force in
Y direction
Load case 1
Load case 2
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Problem definition | Type of loading
5 x 103 cycles
+150 N force in
Y direction
5 x 103 cycles
-150 N force in
Y direction
Load case 3
Load case 4
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S-N table defined in ANSYS (POST-PROCESSOR)
ASSUMPTION: S-N DATA IS AVAILALE TO US
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/PREP7ET,1,PLANE182
MP,EX,1,2.1E5MP,PRXY,1,.3
RECTNG,0,60,0,1
ESIZE,0.5
AMESH,1SAVEFINI
Pre-processing
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/SOLUANTYPE,4 TRANSIENT DYNAMICDL,4,1,ALL!Define Time Intervals (10,20,30,40) for loading
TIME,10 !DEFINE LOAD STEP 1 AT TIME=10FK,2,FY,100LSWRITE,1,
FKDELE,ALL,ALL
TIME,20 !DEFINE LOAD STEP 2 AT TIME=20FK,2,FY,-100LSWRITE,2,
Solution
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FKDELE,ALL,ALL
TIME,30 !DEFINE LOAD STEP 3 AT TIME=30FK,2,FY,150LSWRITE,3,
FKDELE,ALL,ALL
TIME,40 !DEFINE LOAD STEP 4 AT TIME=40FK,2,FY,-150LSWRITE,4,
LSSOLVE,1,4,1,
FINI
SAVE
Solution
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/POST1 !DEFINE S-N TABLE (5 S-N VALUES)FP,1,10,1000,10000,100000,1000000 !5 KEY CYCLESFP,21,62100,62000,51200,42200,34800 ! Corresponding S values
FL,1,65 !STORE RESULTS AT A NODE IN FIXED END
Fatigue Analysis | Post-processingEvent
(Type of Cycle)
Load No.
Load Step No. Load Value No. of Repititions
(Cycles)
1 1 1 100 N 500,000
1 2 2 -100 N 500,000
2 1 3 150 N 5,000
2 2 4 -150 N 5,000
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SET,,, ,,, ,1 !CALLS LOAD STEP 1 (Event-1, Load-1)!Defines the data set to be read from the results file!SET, Lstep, Sbstep, Fact, KIMG, TIME, ANGLE, NSET, ORDER!Data set number of the data set to be read. If a positive value!for NSET is entered,Lstep, Sbstep, KIMG, and TIME are ignored.
FSNODE,65,1,1 !Calculates and stores the stress components at a node for fatigue.
SET,,, ,,, ,2 !CALLS LOAD STEP 2 (Event-1, Load-2)FSNODE,65,1,2 !Calculates and stores the stress components at a node for fatigue
SET,,, ,,, ,3 !CALLS LOAD STEP 3 (Event-2, Load-1)FSNODE,65,2,1 !Calculates and stores the stress components at a node for fatigue
SET,,, ,,, ,4 !CALLS LOAD STEP 4 (Event-2, Load-2)FSNODE,65,2,2 !Calculates and stores the stress components at a node for fatigue
FE,1,500000 !ASSIGNS 500000 CYCLES TO EVENT NO.1FE,2,5000 !ASSIGNS 5000 CYCLES TO EVENT NO.2
FTCALC,1 !CALCULATES FATIGUE AT LOCATION 1 (NODE NO.65)FINISAVE
Fatigue Analysis | Post-processing
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By Miner’s rule, Damage criteria (C = 0.73 < 1So, Fatigue failure will not occur in the model
Result for 2 Events [±100 & ±150]