Nafems_composites_ply_calculator_handbook_ (1).ppt
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Nafems_composites_ply_calculator_handbook_ (1).ppt as PDF for free.
More details
- Words: 2,742
- Pages: 40
Composite Ply Calculator This is an Excel spreadsheet used to perform Classical Laminate Theory calculations in support of the e-learning course and also to provide a means of completing the homework in some sections without the use of FEA software. The calculations have been exposed as much as possible, and can be investigated in detail. For this reason the number of plies has been kept to 10 sets. A version containing Macros is also available to help simplify some calculations, but the non-macro version does contain all required functionality. The calculator is provided ‘as is’ and no warranty is made as to its accuracy.
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 1
Material Data Input Material Stiffness and Strength Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units The label ‘Units’ is just to remind you, along with the description at top right, no checking is done on units
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 2
Loading Data Input Loading Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units The loading is load/unit length on an infinitesimally small section of layup The layup datum direction is along the x axis, so a load applied in-plane in x, to a single 0 degree ply, will be uniaxial, along the fibers.
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 3
Ply Data Input
Loading Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units Ten ply variations are available, but the number of plies per ‘layer’ can be varied to give some versatility The layup datum direction is 0 degree aligned along the x axis
In this example a [0/90/45/-45/]s layup is used. Each ply is 1e-4 m thick, but ply 1 and 8 have 4 times the number of plies, i.e. a thickness of 4e-4 m each. Ply 9 and 10 are ignored in the calculation as the number of plies is set to 0. Total Layer and Layup thickness is checked, don’t overwrite the yellow summary cells NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 4
Calculations – summary output
Total Layup thickness and upper and lower z distance is checked. The untransformed material stiffness matrix Q is calculated – used in ply Q bar The material Invariants U1 to U6 are calculated – used in ply Q bar The total in-plane and bending strains for the whole layup are output in length/length and percentage strain. These are in global x-y coordinates
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 5
Calculations – summary output
Ply local stresses and the ply FI and SR using Tsai-Wu are tabulated. The calculations for these are all exposed on the backing sheets.
The critical FI and SR is highlighted The effective, or equivalent, layup stiffness properties are summarized on the main page
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 6
Calculations – ‘calculations’ sheet
The Qbar and A, B, D matrix terms are calculated ply by ply and summed
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 7
Calculations – ‘calculations’ sheet
The [A, B, D] matrix is assembled Its inverse is calculated and the load vector aligned with it
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 8
Calculations – ‘stress-strain’ sheet
Ply stresses and strains are calculated in the local ply coordinate system Results are passed back to the main page
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 9
Calculations – ‘FI’ sheet
FI using Tsai Wu is calculated, and the corresponding quadratic roots give the SR, ply by ply. These values are passed back to the main page.
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 10
Calculations – ‘Plots’ sheet Ply stresses and strains are calculated, and ply strains are also calculated in the global xy coordinate system Plots are produced through thickness
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 11
Optional Macro – Force Scaling of applied load This macro forces the worst SR and FI to be 1.0, by scaling all terms in the loading vector by 1.0 It is a convenient tool to use with Homework 1, for instance
The macro is invoked by clicking on the button
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 12
Optional Macro – Force Percentage of various plies into a layup This macro forces the a pattern of symmetric plies onto a layup.
It overwrites any existing ply definition In this example, 30% of 0 degrees, 10 percent of 20 degrees and 60 percent of a balanced 45/-45 are requested. The total layup thickness is input. If the percentage does not total 100%, a warning is given. The value t’ is used to check the thickness contribution either side of the symmetry surface. The total should be t/2.
The macro is invoked by clicking on the button NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 13
Optional Macro – Force Percentage of various plies into a layup The results of definitions are shown:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 14
Section 1 Homework Review
Using FEA to simulate a test coupon
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 15
Section 1 Homework Use the following material properties to create a single ply FEA test coupon. Carbon/Epoxy (AS4/3501‐6)
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 16
Section 1 Homework The coupon dimensions are 4 inches wide by 20 inches long (0.102m by 0.508m). Thickness is 0.15 inch (0.00381 m) The coupon is loaded in the long direction with an axial load of sufficient value so as to just fail the coupon. (Hint: if your solver has a SR output option it will be easier to scale the load to failure) The ply end is held axially, but free to shrink due to Poisson’s effect The ply orientation is varied from 0 degrees (aligned with the long axis) to 90 degrees ( aligned with the short axis) Plot the failing load against ply angle, using the Tsai-Wu criterion Plot the sigma1, sigma2 and sigma12 stresses against ply angle Repeat the exercise using the Maximum Stress Criterion
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 17
Section 1 Homework Alternatively use the stress terms given below if you do not have access to an FEA solver P cos 2 A P 2 sin 2 A P 12 sin cos A
1
Another alternative is to use the Ply calculator to calculate stresses, load and FI terms
Experiment with values of F12 term between 0.5 and -0.5 in the Tsai Wu criterion, ensuring you normalize the whole term NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 18
Section 1 Homework – Answer Using Ply Calculator Metric Version
Step 1. In ply calculator enter material properties and ply 1 data (theta = 0.0 t = 0.00381m)
Step2. Enter arbitrary load/width in x
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 19
Step2. Investigate SR and scale load by this to get SR 1.0
Step3. First data point Px total = Load/width* width = 711175 N Sig1 = 1.830E9 Pa Sig2 = 0.0 Pa Sig12= 0.0 Pa
Now repeat for theta = 1,2,3,4,5,10,15,20,25,30,45,75,90 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 20
Resultant Loads, Stresses and Tsai-Wu Terms
Dominant terms highlighted in Tsai-Wu
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 21
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 22
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 23
t1 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
t2
t3
t4
t5 Composite Analysis
Ply Calculator V5.0 Page 24
LAMINATE ANALYSIS – IN PLANE The terms are tedious to calculate so we will use part of the Ply Calculator Spread Sheet to evaluate an example from reference [1].
A single dummy ply is input, with the defined Stiffness values E1 19.981GPa
E2
11.389GPa
G12
3.789 Gpa
12
0.274
The reduced stiffness matrix is calculated
Note > E1 Note > E2
[1] Introduction to Composite Material Design. Barbero. CRC 1999, page 115 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 25
LAMINATE ANALYSIS – IN PLANE We now want to consider off-axis plies, where the with-fiber angle can be arbitrary.
The stiffness in the reference directions has to be resolved as shown
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 26
LAMINATE ANALYSIS – IN PLANE The resultant is the transformed reduced stiffness matrix.
Q11 Q21 Q16 Q Q12 Q22 Q26 Q16 Q26 Q66 Note that there can now be coupling terms between in-plane direct and shear. We will explore this later. Using the example in Reference [1], by including angle theta -55 degrees:
Q matrix is shown for the single ply Note Q11 is less than E1
The
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 27
LAMINATE ANALYSIS – IN PLANE For arbitrary coordinates the Stress-Strain relationship for kth ply of a layup are:
k Q k k
x Q11 Q21 Q16 x y Q12 Q22 Q26 y Q Q xy Q xy 16 26 66 k k k
Following ref [1] page 125
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 28
LAMINATE ANALYSIS – IN PLANE As an example a 6 ply layup is shown, the ply stack is:
[-55/55/0/0/55/-55] or [-55/55/0]symm The layup is symmetric and balanced
The A matrix calculations are shown for each ply:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 29
LAMINATE ANALYSIS – IN PLANE The A matrix summation is shown. Notice that the shear coupling terms go to zero, as the layup is balanced
An axial loading will show no shear coupling
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 30
LAMINATE ANALYSIS – IN PLANE The ply 1 and 6 angles are changed to remove the balanced condition
The A matrix now shows signs of coupling:
Shear strains are now induced with axial loading
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 31
LAMINATE ANALYSIS – IN PLANE The balance is further altered by changing all plies
The resultant A matrix is shown
And the increased shear strain:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 32
LAMINATE ANALYSIS – IN PLANE For a balanced symmetric layup an equivalent laminate moduli can be calculated and used for engineering calculations, sizing etc.
The Moduli represent the stiffness of an equivalent orthotropic plate under in-plane loading. The moduli are defined in terms of the A matrix.
A11 A22 A212 Ex tA22 A11 A22 A212 Ey tA11 A66 t A 12 A22
Gxy
xy
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 33
Balanced and symmetric plies used
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 34
In-plane and bending coupling terms are zero
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 35
Balanced, but not symmetric, in plane decoupled
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 36
Not balanced, or symmetric, full coupling
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 37
Buckling in Composites Typical plate simply supported on all edges Layup is 0/90/90/0 Ply thickness = 0.0001m = 0.1 mm Plate length = .0125m = 12.5 mm Plate width = .01m = 10 mm
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 38
Buckling in Composites Nominal load = 10 N EigenValue = 21.38 Pcr = 213.8 N
365 N
214 N NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
668 N Composite Analysis
Ply Calculator V5.0 Page 39
Buckling in Composites
Hand Calculation 2 2 D 2 D D22 2 D11 b 1 a 12 66 2 m 2 2 b D22 a D22 m b 2
N x cr N x cr
Load per unit width
N x cr 288N This assumes one half wave as per the FEA, but is quite innacurate However relative buckling loads are acceptable, based on D11, D22, D66,D12 estimates
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 40
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 1
Material Data Input Material Stiffness and Strength Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units The label ‘Units’ is just to remind you, along with the description at top right, no checking is done on units
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 2
Loading Data Input Loading Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units The loading is load/unit length on an infinitesimally small section of layup The layup datum direction is along the x axis, so a load applied in-plane in x, to a single 0 degree ply, will be uniaxial, along the fibers.
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 3
Ply Data Input
Loading Data is Input in the green cells as shown. Units are user-defined, so it is up to you to work in consistent units Ten ply variations are available, but the number of plies per ‘layer’ can be varied to give some versatility The layup datum direction is 0 degree aligned along the x axis
In this example a [0/90/45/-45/]s layup is used. Each ply is 1e-4 m thick, but ply 1 and 8 have 4 times the number of plies, i.e. a thickness of 4e-4 m each. Ply 9 and 10 are ignored in the calculation as the number of plies is set to 0. Total Layer and Layup thickness is checked, don’t overwrite the yellow summary cells NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 4
Calculations – summary output
Total Layup thickness and upper and lower z distance is checked. The untransformed material stiffness matrix Q is calculated – used in ply Q bar The material Invariants U1 to U6 are calculated – used in ply Q bar The total in-plane and bending strains for the whole layup are output in length/length and percentage strain. These are in global x-y coordinates
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 5
Calculations – summary output
Ply local stresses and the ply FI and SR using Tsai-Wu are tabulated. The calculations for these are all exposed on the backing sheets.
The critical FI and SR is highlighted The effective, or equivalent, layup stiffness properties are summarized on the main page
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 6
Calculations – ‘calculations’ sheet
The Qbar and A, B, D matrix terms are calculated ply by ply and summed
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 7
Calculations – ‘calculations’ sheet
The [A, B, D] matrix is assembled Its inverse is calculated and the load vector aligned with it
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 8
Calculations – ‘stress-strain’ sheet
Ply stresses and strains are calculated in the local ply coordinate system Results are passed back to the main page
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 9
Calculations – ‘FI’ sheet
FI using Tsai Wu is calculated, and the corresponding quadratic roots give the SR, ply by ply. These values are passed back to the main page.
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 10
Calculations – ‘Plots’ sheet Ply stresses and strains are calculated, and ply strains are also calculated in the global xy coordinate system Plots are produced through thickness
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 11
Optional Macro – Force Scaling of applied load This macro forces the worst SR and FI to be 1.0, by scaling all terms in the loading vector by 1.0 It is a convenient tool to use with Homework 1, for instance
The macro is invoked by clicking on the button
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 12
Optional Macro – Force Percentage of various plies into a layup This macro forces the a pattern of symmetric plies onto a layup.
It overwrites any existing ply definition In this example, 30% of 0 degrees, 10 percent of 20 degrees and 60 percent of a balanced 45/-45 are requested. The total layup thickness is input. If the percentage does not total 100%, a warning is given. The value t’ is used to check the thickness contribution either side of the symmetry surface. The total should be t/2.
The macro is invoked by clicking on the button NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 13
Optional Macro – Force Percentage of various plies into a layup The results of definitions are shown:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 14
Section 1 Homework Review
Using FEA to simulate a test coupon
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 15
Section 1 Homework Use the following material properties to create a single ply FEA test coupon. Carbon/Epoxy (AS4/3501‐6)
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 16
Section 1 Homework The coupon dimensions are 4 inches wide by 20 inches long (0.102m by 0.508m). Thickness is 0.15 inch (0.00381 m) The coupon is loaded in the long direction with an axial load of sufficient value so as to just fail the coupon. (Hint: if your solver has a SR output option it will be easier to scale the load to failure) The ply end is held axially, but free to shrink due to Poisson’s effect The ply orientation is varied from 0 degrees (aligned with the long axis) to 90 degrees ( aligned with the short axis) Plot the failing load against ply angle, using the Tsai-Wu criterion Plot the sigma1, sigma2 and sigma12 stresses against ply angle Repeat the exercise using the Maximum Stress Criterion
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 17
Section 1 Homework Alternatively use the stress terms given below if you do not have access to an FEA solver P cos 2 A P 2 sin 2 A P 12 sin cos A
1
Another alternative is to use the Ply calculator to calculate stresses, load and FI terms
Experiment with values of F12 term between 0.5 and -0.5 in the Tsai Wu criterion, ensuring you normalize the whole term NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 18
Section 1 Homework – Answer Using Ply Calculator Metric Version
Step 1. In ply calculator enter material properties and ply 1 data (theta = 0.0 t = 0.00381m)
Step2. Enter arbitrary load/width in x
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 19
Step2. Investigate SR and scale load by this to get SR 1.0
Step3. First data point Px total = Load/width* width = 711175 N Sig1 = 1.830E9 Pa Sig2 = 0.0 Pa Sig12= 0.0 Pa
Now repeat for theta = 1,2,3,4,5,10,15,20,25,30,45,75,90 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 20
Resultant Loads, Stresses and Tsai-Wu Terms
Dominant terms highlighted in Tsai-Wu
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 21
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 22
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 23
t1 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
t2
t3
t4
t5 Composite Analysis
Ply Calculator V5.0 Page 24
LAMINATE ANALYSIS – IN PLANE The terms are tedious to calculate so we will use part of the Ply Calculator Spread Sheet to evaluate an example from reference [1].
A single dummy ply is input, with the defined Stiffness values E1 19.981GPa
E2
11.389GPa
G12
3.789 Gpa
12
0.274
The reduced stiffness matrix is calculated
Note > E1 Note > E2
[1] Introduction to Composite Material Design. Barbero. CRC 1999, page 115 NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 25
LAMINATE ANALYSIS – IN PLANE We now want to consider off-axis plies, where the with-fiber angle can be arbitrary.
The stiffness in the reference directions has to be resolved as shown
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 26
LAMINATE ANALYSIS – IN PLANE The resultant is the transformed reduced stiffness matrix.
Q11 Q21 Q16 Q Q12 Q22 Q26 Q16 Q26 Q66 Note that there can now be coupling terms between in-plane direct and shear. We will explore this later. Using the example in Reference [1], by including angle theta -55 degrees:
Q matrix is shown for the single ply Note Q11 is less than E1
The
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 27
LAMINATE ANALYSIS – IN PLANE For arbitrary coordinates the Stress-Strain relationship for kth ply of a layup are:
k Q k k
x Q11 Q21 Q16 x y Q12 Q22 Q26 y Q Q xy Q xy 16 26 66 k k k
Following ref [1] page 125
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 28
LAMINATE ANALYSIS – IN PLANE As an example a 6 ply layup is shown, the ply stack is:
[-55/55/0/0/55/-55] or [-55/55/0]symm The layup is symmetric and balanced
The A matrix calculations are shown for each ply:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 29
LAMINATE ANALYSIS – IN PLANE The A matrix summation is shown. Notice that the shear coupling terms go to zero, as the layup is balanced
An axial loading will show no shear coupling
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 30
LAMINATE ANALYSIS – IN PLANE The ply 1 and 6 angles are changed to remove the balanced condition
The A matrix now shows signs of coupling:
Shear strains are now induced with axial loading
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 31
LAMINATE ANALYSIS – IN PLANE The balance is further altered by changing all plies
The resultant A matrix is shown
And the increased shear strain:
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 32
LAMINATE ANALYSIS – IN PLANE For a balanced symmetric layup an equivalent laminate moduli can be calculated and used for engineering calculations, sizing etc.
The Moduli represent the stiffness of an equivalent orthotropic plate under in-plane loading. The moduli are defined in terms of the A matrix.
A11 A22 A212 Ex tA22 A11 A22 A212 Ey tA11 A66 t A 12 A22
Gxy
xy
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 33
Balanced and symmetric plies used
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 34
In-plane and bending coupling terms are zero
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 35
Balanced, but not symmetric, in plane decoupled
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 36
Not balanced, or symmetric, full coupling
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 37
Buckling in Composites Typical plate simply supported on all edges Layup is 0/90/90/0 Ply thickness = 0.0001m = 0.1 mm Plate length = .0125m = 12.5 mm Plate width = .01m = 10 mm
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 38
Buckling in Composites Nominal load = 10 N EigenValue = 21.38 Pcr = 213.8 N
365 N
214 N NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
668 N Composite Analysis
Ply Calculator V5.0 Page 39
Buckling in Composites
Hand Calculation 2 2 D 2 D D22 2 D11 b 1 a 12 66 2 m 2 2 b D22 a D22 m b 2
N x cr N x cr
Load per unit width
N x cr 288N This assumes one half wave as per the FEA, but is quite innacurate However relative buckling loads are acceptable, based on D11, D22, D66,D12 estimates
NAFEMS. The International Association for the Engineering Analysis Community FETraining - Your Partner in FEA Training and Consultancy www.fetraining.com
Composite Analysis
Ply Calculator V5.0 Page 40
More Documents from "hung nguyen"
Adverse Effects Of Statins.docx
December 2019 32
Duoi Nang Troi Chau Au - Hoang Yen Anh.pdf
December 2019 25
Book1 (autosaved).xlsx
December 2019 28
Nafems_composites_ply_calculator_handbook_ (1).ppt
December 2019 18
Langzeitvisumantrag.pdf
October 2019 18