composite structural analysis and design issues

Composite Structural Analysis and Design Issues

ME 7502 – Lecture 14

Dr. B.J. Sullivan

1

Finite Element Analysis of Composite Structures

Lamina stress analysis in FEA of composites Considerations in selection of element types Modeling individual layers with orthotropic elements FEA model construction Boundary conditions in FEA of composite plates and

shells Thermal and Thermo-Structural Analysis Methods Assessment of Calculated Stresses and Strains Determination of Allowable Stresses and Strains Calculation of Margins and Safety FEA Assessment of Delamination Growth in

Composite Structures

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Lamina stress analysis in FEA of composites

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Some public domain FEA codes have at least the capabilities a), b) and c) above;

Capability d) can be user-dependent; i.e., the user may wish to be very specific about how lamina level stresses are combined within a failure criterion to make judgments regarding failure

6

Lamina stress analysis in FEA of compositesANSYS, ABAQUS, NATRAN public domain FEA codes all have laminated composite plate and shell elements

Required input includes:a. Lamina (ply) properties in local material directionsb. Orientation of ply relative to laminate (global) coordinate

directionc. Lamina (ply) thicknessd. Lamina failure algorithm (e.g., Hashin, Puck, etc.) and

associated parameters

Output features:e. Stresses in each ply in local material axesf. Stress contour plots within plies across continuous

elementsg. Margin of safety contour plots within plies across

continuous elements, based on failure criterion and its parameters

Considerations in Selection of Element Types Three basic questions in element selection:

Should elements be represented by plate elements or solid elements?

Plate elements do a good job of capturing bending behavior and will require far fewer elements to simulate response

Solid elements provide a much better assessment of the interlaminar stresses

If plate elements are selected, should homogenous orthotropic properties be used, or should individual ply properties be used?

Homogenous orthotropic properties require single plate/shell elements through the thickness

Use of individual ply properties in FE analysis requires use of layered plate/shell elements through the thickness

Should elements with transverse shear deformation be employed?

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Considerations in selection of element types

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Laminate approximated by homogeneous orthotropic plate properties (average properties throughout)

Considerations in selection of element types

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Laminate approximated by homogeneous orthotropic plate properties (average properties throughout)

Modeling Individual Layers with Orthotropic Elements

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Modeling Individual Layers with Orthotropic Elements

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FEA Modeling of Laminated Plates

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FEA Modeling of Laminated Plates

Use of Elements with Transverse Shear Deformation

Most general purpose FEA codes provide plate and shell elements with transverse shear capability

As we have seen, this can be an important aspect of composite structural analysis in two cases:

The ratio of in-plane Young’s modulus to through thickness shear modulus is relatively large (in some cases as low as 5; for metals, E/G < 3 is typically)

The span-to-thickness ratio is small (~25 or less) If you are not sure if shear deformation is important, try to

perform identical analyses with and without this effect Near identical results will indicate shear deformation is not

important Different results will indicate the importance of this feature in

your analysis

14

FEA Model Construction Typical FEA model

construction practice is not substantially different from metallic parts Shell / flat plate elements

for thin gauge members, e.g. facesheets

3D solid elements for thicker parts, e.g. solid leading edge materials and core material of sandwich structure components

3D solids or 3D beam elements for longerons and ribs

T-300/SiC facesheets

P-30X/SiC leading edge

Carbon Foam Core Metallic

Spar or Spindle

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FEA Model Construction One area of difference between FEA analysis of

metallic parts and FEA analysis of composite parts is that more submodels are needed to accurately assess responses of composite parts, since interlaminar strengths of these materials are typically low This is particularly true for refractory (e.g.,

Carbon-Carbon and Ceramic Matrix Composites) Submodeling effort is accomplished by creating

a smaller model of the components where overstress in the full scale model is calculated More elements through the thickness and better

aspect ratio elements used16

Cut Boundary Interpolation is performed by taking the resulting displacements from the full scale model that occur at the cut boundary of the sub model and applying them to the sub model (shown with bright blue arrows in picture on right)

Submodel temperatures are applied using a Body Force interpolation, where temperatures are taken from the full scale model and applied to the submodel

Submodel is composed of volumes outlined in orange.

Submodel shown with applied temperatures and displacements from full scale model

Example of FEA Submodel

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Boundary Conditions in FEA of Composites For isotropic plates and shells, we frequently use symmetry

B.C.’s to avoid having to analyze the entire body For example, a plate under a load symmetric about one or two

axes parallel to the edges can frequently be analyzed with a reduced model by employing symmetry B.C.’s:

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Here, the pressure load p is symmetric about both X and Y axes

For loads and edge B.C.’s symmetric about both X and Y axes, an isotropic plate can be analyzed with a quarter segment and the following B.C.’s:

where Edge #1 could be simply-supported (uZ = qX = qZ = 0) or clamped (uZ = qX = qY = qZ = 0) and Edge #2 could be simply-supported (uZ = qY = qZ = 0) or clamped (uZ = qX = qY = qZ = 0)

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Boundary Conditions in FEA of Composites

For composite plates, the elements of the A, B and D matrices must be examined before deciding if symmetry B.C.’s such as those used above can be employed to make the model smaller

For example, even if the load and edge B.C.’s are symmetric about the X and Y axes, if the laminate has shear-extensional coupling (i.e., if A16 and A26 are not zero), then symmetry B.C.’s are the type shown above cannot be used, since

uY is not zero across the X-axis cut, and uX is not zero across the Y-axis cut

If the laminate has no shear extensional coupling (i.e., if A16 = A26 =0) but does have bending twisting coupling (i.e., if D16 and D26 are not zero), then qZ is not zero across either axis cut, so that here again symmetry B.C.’s could not be used

In either case, the entire plate would have to be analyzed.

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The same conclusion can be drawn for plates with bending-extensional coupling (i.e., non-zero Bij coefficients) since any loads causing bending would mean

uY would not be zero across the X-axis cut, and uX would not be zero across the Y axis cut

Suppose we have a balanced and symmetric laminate (A16 = A26 = Bij = 0) making up a plate which has loads and edge boundary conditions symmetric about one or both axes

Typically, we will have bending-twisting coupling (i.e., D16 and D26 will be non-zero), so that, strictly speaking, the model cannot be made smaller by employing symmetry B.C.’s across the X-axis or Y-axis cuts

Practically speaking, however, if there are many plies and the plies are well dispersed within the laminate, the magnitude of D16 and D26 relative to the other Dij will be small

In these cases we treat the laminate as if it were specially orthotropic and employ symmetry B.C.’s

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Examples of laminate stack-ups and associated bending-twisting coupling coefficients:

The greater the number of plies and the more dispersed the plies within the laminate, the smaller the D16 and D26 coefficients relative to the others, the better the representation of the plate as Specially Orthotropic, and the more appropriate

the use of symmetry B.C.’s if loads and edge B.C.’s are themselves symmetric


The same concepts apply to the analysis of composite shells

For example, the half-symmetry model of the cylindrical shell shown on the next page would not be appropriate if

The laminate contained shear-extensional coupling, or If loads causing bending were present and there was

substantial bending-twisting coupling

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Thermal and Thermo-Structural Analysis Methodology

In assessment of composite components on vehicles subjected to time-varying thermal loads, both transient heat transfer and thermal stress analyses are performed

Stress analyses typically require greater discreteness in the FE grid than what is required for thermal analyses

Displacement, strain and stress spatial gradients are typically much greater than spatial temperature gradients

Nevertheless, same FE model is used for both transient heat transfer and thermal stress analyses

Elements selected for the FE analyses must be capable of switching from thermal to stress types

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Transient heat transfer analyses must usually be performed for some period of time beyond the cruise/re-entry period

Thermal soak must be permitted to occur

Highest temperatures in thermal protection system (TPS) components often do not occur until after “wheel stop”

CPI Time History

0

200

400

600

800

1000

1200

1400

0 2000 4000 6000 8000 10000 12000 14000 16000

Time (s)

Tem

pera

ture

(R)

NetworkBaselineLighteningScalloped

Wheel Stop

Period of thermal soak may actually be 2-3 times as long as period of aerothermal heating


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“Snap shot” thermal stress analyses are performed for a few discrete times of flight

Times corresponding to peak thermal gradients

These times will lag time of peak gradient(s) in aero-thermal heating

Times corresponding to peak temperatures of different materials in CMC components

These times will lag time of peak aero-thermal heating

Time-Temperature Profile of TPS Surface Temperature for FS877 (STS-5 Flight)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 500 1000 1500 2000 2500 3000 3500

Time (Sec)

Tem

pera

ture

(°F)

SPAR CalculationsSTS-5 Flight DataAnsys Baseline CalcsAnsys calculations with TORC

Candidate times for thermal stress analyses


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Measured stress-strain curves of composite material used in structural components will dictate type of analysis performed

Non-linear response requires nonlinear material analysis and strain allowable assessments

Linear response permits linear material analysis and allowable stress assessments


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Assessment of Calculated Stresses and/or Strains

Peak stresses or strains appearing on FEA contour plots are not appropriate for realistic assessment of component performance

When failure is initiated within a composite test specimen, the initial failure occurs over a region containing several (3-5 at a minimum) textile unit cells

A textile unit cell is defined as the “smallest volume of the fiber reinforcement containing all unique fiber orientations in the preform” (i.e., longitudinal, lateral, and through thickness)

In-plane, hoop stress: 9.7ksi MOS: 1.60

In-plane, hoop stress: 9.7ksi MOS: 1.60

In-plane stress in torque tube of flaperon EDU resulting from mechanical loading

In Plane Stress σx (6.3ksi)

In Plane Stress σy (6.0ksi)

ILT and ILS are localized stresses σz (6.0ksi)

Stress Contours in access panel of flaperon EDU resulting from mechanical loading

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Accordingly, in the comparison of FEA calculated strains or stresses, an average of any given strain or stress component over a volume of at least three (3) unit cells should be compared to the measured failure strain or stress of the material

This approach definitely makes the structural analysis more time consuming

One textile unit cell


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Photomicrographs of Composites and Definition of Unit Textile Cells


One textile unit cell

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Generation of design properties through

material property testing

How are the thermo-elastic properties used in the material models of the composite FE analyses determined?

How are the composite strength or strain-to-failure values measured?

How are the measured strengths used to define allowable values for the comparison with calculated stresses/strains?

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Design Properties

Most basic element of design properties database is material thermo-elastic properties themselves

Young’s moduli (tension and compression) Axial shear modulus Poisson’s ratios Coefficients of thermal expansion Thermal conductivities

Thermo-elastic moduli and thermal conductivities are typically temperature-dependent

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For full three-dimensional orthotropic materials, all properties (e.g., through thickness Young’s and shear moduli) cannot be measured

Micromechanics models are correlated using measurable data and then used to predict properties that cannot be measured

Temperature-dependent strengths are frequently measured at same time as moduli

Axial tensile and compressive In-plane shear strengths

Through thickness strengths (tensile, compressive, shear) are measured alone

Design Properties

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Tension Specimen

This specimen is used to measure the composite in-plane axial tensile modulus and strength

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Compression Specimen

This specimen is used to measure the composite in-plane axial compressive modulus and strength

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Rumanian Shear Specimen

This specimen is used to measure the composite in-plane axial shear modulus and strength

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Double Notch Shear Specimen

This specimen is used to measure the composite through thickness or interlaminar shear strength

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Curved Beam Specimen

This specimen can be used to measure the composite through thickness tensile strength

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Thermal Expansion Specimen

This specimen can be used to measure the composite in-plane coefficients of thermal expansion (CTE)

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Design Properties

Definition of A-basis allowable property: Design property for which there is a 95 percent

confidence that 99 percent of the tested material samples will exceed this value

B-basis allowable property defined as property for which there is a 95 percent confidence that 90 percent of the tested material samples will exceed this value

Guidelines for composite material test programs to achieve A-basis or B-basis allowable properties are provided in MIL-HDBK-17

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A-basis Allowable Test Matrix from MIL-HDBK-17

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Allowable Material Properties A statistical software package known as

STAT17, a by product of the MIL-HDBK-17 Working Group, is available for calculating A-basis and B-basis allowable properties from measured material property test data

A-basis and B-basis properties for polymer matrix composites used in military aircraft exist

Reinforced Carbon-Carbon used on Space Shuttle is the only refractory composite material for which A-basis properties exist

B-basis properties for specific material properties exist for ACC-6 and CVI C/SiC

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Other Critical Design Properties

Tensile strength of specimens with butt-joint plies

Strength of notched specimens (i.e., specimens containing open holes)

Strength of specimens containing loaded holes Bearing strength Net tension and/or compressive strength Shear tear-out strength

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Calculation of Margins of Safety Margins of safety (MOS) are used to quantify the

state of stress or strain relative to design allowable values

Margins of safety must be calculated using either calculated stresses or strains

In expression below, substitute eAllowable and eActual for corresponding stress quantities, if strain allowable design approach is used

Typically for composite stresses calculated via FEA, the MOS for one component at a time is calculated

1

FOSFOSFOSMOS

Actual

Allowable

Actual

ActualAllowable

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Example of a typical MOS table:

This approach ignores potential adverse affects of stress or strain interaction

Calculation of Margins of Safety

ANSYS Predicted Predicted Temp Dep Temperture Temperture ANSYSStress Strength Strength Predicted at at Calculated

Component 70.00 2000.00 Strength Peak Stress Peak Stress Stress Factor Of Safety Margin Of Safety(ksi) (ksi) (ksi) °R °F (ksi)

σXXT 37.9 46.5 39.73 945.00 486.33 6.19 1.0 5.42

σXXC 51.7 53.7 52.61 1423.00 964.33 -25.31 1.0 1.08

σYYT 37.9 46.5 39.78 956.00 497.33 6.03 1.0 5.60

σYYC 51.7 53.7 52.63 1439.00 980.33 -12.62 1.0 3.17

σZZT 1.5 2.0 1.58 904.00 445.33 0.50 1.0 2.13

σZZC 14.382 13.94 14.17 1435.00 976.33 -3.52 1.0 3.03

tXY 28.9 35.5 31.86 1400.00 941.33 7.63 1.0 3.18tYZ 1.6 3.0 1.89 961.00 502.33 0.90 1.0 1.09tXZ 1.6 3.0 1.75 779.00 320.33 0.78 1.0 1.24

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Interlaminar Strain Interaction

ginterlaminar

einterlaminar tensile Failure surface without diminishing

effects of strain interaction

This (or a similar) failure surface is more likely

Material characterization testing to define interaction curves for all relevant components and at all

temperatures of interest can be costly

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Comments on Load Factors and Factors of Safety Load factors and factors of safety are used to amplify loads and

calculated stresses, respectively, prior to determining MOS values Load factors are a reflection of the degree of uncertainty in the applied

loads Factors of safety are intended to reflect the degree of uncertainty in the

calculated stresses due to the complexity of the structure and/or the uncertainty in the math model representation of physical structure

Typical factors of safety for composite structures (from NASA-STD-5001: Structural Design and Test Factors of Safety for Spaceflight Hardware)

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Hot Structure / TPS ComponentsLoad Factors and Factors of Safety

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VehicleLimit Load Factors Factor of Safety

Margin of Safety CalculationMechanical Thermal Mechanical Thermal

AHW ~1.2 1.25 1.25

X-33 1.25 1.0 1.25 1.25 Estimated B-Basis Allowables



X-51 2.0 1.2 1.5 / 2.0* 1.0 Estimated B-Basis Allowables

Space Shuttle 1.4 1.4 1.4 1.0 True A-Basis

Allowables

NASA Depends on uncertainty (NASA-STD-5002)

1.5 1.5 A-Basis allowables if man-rated; B-basis allowable otherwise(NASA-STD-5001A)

* 1.5 if tested; 2.0 if not tested

FEA Assessment of Delamination Growth Delaminations can occur in composite structures from

Residual stresses from processing Overstress conditions from operation of composite structure

Computational, finite element based methods are available to make an assessment of the likelihood of the delaminations to grow in an unstable fashion

The strain energy release rate (SERR) is calculated at the “front” of the delamination or crack

SERR is then compared to the critical strain energy release rate (i.e., the Fracture Toughness) within a specific fracture mode (GXc) of the material

If SEER > GXc, delaminations will grow If SEER < GXc, delaminations are stable and will not

continue to grow under the applied loads

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FEA Delamination Growth Analysis Methods

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Initially developed FEA method was Finite Crack Extension Technique for calculating dU/da (or SERR).

This method requires two FE analyses: one using the original flaw size, and another using a marginally increased flaw size (+1%).

The strain energy U is calculated for both cases dU = U(2) – U(1). U is a solution quantity calculated by the FE code.

The change in the flaw size is known da = a(2) – a(1). Subsequently, theVirtual Crack Closure Technique** (VCCT)

was developed, which is more robust, requires only one FE analysis, does not require user-defined quarter-point elements, and has been shown to yield good agreement with the closed form solution for a plate with a central crack.

VCCT essentially replaced Finite Crack Extension Technique

R. Krueger, “The Virtual Crack Closure Technique: History, Approach and Applications,” ICASE Final Report No. 2002-10, NASA/CR-2002-211628.

**

Delamination Growth Analysis Method

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Delaminations in composite structures frequently result from excessive ILS stresses.

Accordingly, fracture propagation (if it occurs) would most likely occur in Mode II, but could also occur in Modes I or III.

Delamination grows if SERRX ≥ GX,c where SERRX = strain energy release rate in Mode X and GX,c = Mode X critical strain energy release rate.

While Mode II ILS may be the primary mode of concern, VCCT allows SERR to be easily calculated for all three modes to obtain a more complete assessment of the likelihood of propagation.

Delamination Growth Analysis Method VCCT uses the forces at the crack front (red arrows) and relative crack

opening displacements (green arrows) immediately behind the crack front to enable direct calculation of SERR for each mode, for each node along the crack front.

baA

vvYA

SERR

uuXA

SERR

wwZA

SERR

LlLlLiIII

LlLlLiII

LlLlLiI

where

)(2

1

)(2

1

)(2

1

*

*

*

Therefore, VCCT readily provides SERR for all three modes.

If SERRX ≥ GX,c, delamination is expected to propagate.

If SERRX < GX,c, delamination is stable.

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Figure from Krueger

VCCT vs. Closed Form Solution

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Simple Plate with Central Crack Plate Dimensions: 5” x 8” x 1” Crack Width (a): 0.50” Applied Load: 100 psi (on top face) Material: Aluminum (E = 10 Msi) Closed Form Solution:

a = 0.50”

2

2

0357.1in

lbinEE

aSERR

Two Mesh Sizes Model 1: All elements are 0.1” x 0.1” x 0.1”

11 Nodes through-the-thickness Model 2: All elements are 0.25” x 0.25” x 0.25”

5 Nodes through-the-thickness

Schematics of Model 1

100 psi

Take Y-dirn displacements from these nodes…

Take Y-dirn forces from these nodes…For each pair of nodes TTT, complete the SERRI calculation defined previously on slide 12.

VCCT vs. Closed Form Solution

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VCCT results agree very well with closed form solution Model 1 (10 elements TTT) yields a maximum error of 6.4%. Model 2 (4 elements TTT) yields a maximum error of 12.7%.

1.20E-03

1.25E-03

1.30E-03

1.35E-03

1.40E-03

1.45E-03

1.50E-03

1.55E-03

1.60E-03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Stra

in E

nerg

y Re

leas

e Ra

te (i

n-lb

/in2 )

Distance Through-the-Thickness (in)

Closed Form

Model 1

Model 2

Example: Finite Element Model OverviewOriginal GTOR Plate Model

Submodel of Hole

Cross Section of Submodel

Applied boundary conditions derived from full GTOR plate model.

Coupled nodes representing the edge of the delamination (nodes inside this boundary at the midplane are unmerged).

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Location and Size of Delamination in GTOR

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Delamination is centered at the location of maximum ILS stress predicted in the global analysis.

Duplicate unmerged nodes are used at the mid-plane of the cross section over the appropriate region to physically represent the delamination.

Approximate size of the delamination is shown at right (previous work performed by S. Caperton of NASA JSC)

~0.10” circumferentially x ~0.067” radially.

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RT Case (Hole 5) – GTOR Plate Results

q

From FE analysis of GTOR plate, peak ILS stress is found to occur at Hole 5 create submodel for this location.

First, identify the angle at which the peak ILS stress occurs center the delamination at this location.

Next, use the GTOR plate solution to obtain the applied displacements for the boundary of the submodel.

Peak ILS stress occurs at q = 325° Displaced shape

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RT Case (Hole 5) – Submodel Details Submodel details are shown below.

Image on left shows outline of delamination, centered about the location of the peak ILS stress.

Image on right shows correct application of boundary conditions as derived from complete GTOR plate model.

Delamination centered at q = 325° Displaced shape (boundary conditions interpolated from GTOR plate model)

q

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Calculation of SERR along the Crack Front As discussed previously, VCCT uses forces at the crack front

and relative crack opening displacement behind the crack front to calculate SERR.

All calculations are made in the appropriate coordinate system (normal to the crack front) as discussed below.

Delamination Nodes

There is a pair of duplicate, unmerged nodes in each green circle.

There is a pair of duplicate, coupled nodes in each red circle.

Coordinate System X Black Line Y Yellow Line Z Out of the page

For each green-red circle pair (boxed in black above), calculate the relative distance between the pair of nodes in the green circle, calculate the force between the two coupled nodes in the red circle, for each direction (X, Y, Z), then complete the SERR calculations discussed previously on slide 14.

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RT Case (Hole 5) – SERR Calculations As shown in the following tables, the SERR in all three

directions along the entire crack front is at least five orders of magnitude lower than the lowest C/SiC fracture toughness at any temperature. Minimum C/SiC fracture toughness: 40.4 in-lbf/in2. Maximum SERR: 1.785∙10-4 in-lb/in2.

Radial (X-Direction) SERR Data – Mode IINode 1 UX1 Node 2 UX2 Node 3 FX3

Opening Displacement

SERR Angle

(-) (in) (-) (in) (-) (lb) (in) (in-lb/in2) (deg)74985 -0.000031629 88335 -0.000031484 73917 -0.001761873 1.45E-07 2.907E-06 31874986 -0.000033272 88336 -0.000033329 73918 0.001767423 5.70E-08 1.146E-06 31974987 -0.00003493 88337 -0.000035124 73919 0.00452624 1.94E-07 9.990E-06 32074988 -0.000036575 88338 -0.000036895 73920 0.006861568 3.20E-07 2.498E-05 32174989 -0.000038205 88339 -0.000038638 73921 0.008904464 4.33E-07 4.387E-05 32274990 -0.000039818 88340 -0.000040351 73922 0.01067952 5.33E-07 6.476E-05 32374991 -0.000041413 88341 -0.000042033 73923 0.0122195 6.20E-07 8.620E-05 32474992 -0.000042987 88342 -0.000043682 73924 0.013549083 6.95E-07 1.071E-04 32574993 -0.000044538 88343 -0.000045297 73925 0.014686059 7.59E-07 1.268E-04 32674994 -0.000046064 88344 -0.000046876 73926 0.015643895 8.12E-07 1.445E-04 32774995 -0.000047563 88345 -0.000048417 73927 0.016431721 8.54E-07 1.597E-04 32874996 -0.000049034 88346 -0.000049919 73928 0.017047772 8.85E-07 1.717E-04 32974997 -0.000050478 88347 -0.000051378 73929 0.017433227 9.00E-07 1.785E-04 33074998 -0.000051902 88348 -0.000052782 73930 0.017522437 8.80E-07 1.754E-04 33174999 -0.000053283 88349 -0.000054153 73931 0.016683104 8.70E-07 1.651E-04 332

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RT Case (Hole 5) – SERR Calculations

Hoop (Y-Direction) SERR Data – Mode III

Through-Thickness (Z-Direction) SERR

Data – Mode I

Node 1 UY1 Node 2 UY2 Node 3 FY3Opening

DisplacementSERR Angle

(-) (in) (-) (in) (-) (lb) (in) (in-lb/in2) (deg)74985 -0.000000279 88335 -0.000000295 73917 0.028844339 1.60E-08 5.251E-06 31874986 -0.000000272 88336 -0.000000297 73918 0.040741854 2.50E-08 1.159E-05 31974987 -0.000000266 88337 -0.000000297 73919 0.050167658 3.10E-08 1.769E-05 32074988 -0.00000026 88338 -0.000000296 73920 0.057723796 3.60E-08 2.364E-05 32174989 -0.000000255 88339 -0.000000294 73921 0.063541154 3.90E-08 2.819E-05 32274990 -0.000000249 88340 -0.000000292 73922 0.067579139 4.30E-08 3.306E-05 32374991 -0.000000244 88341 -0.000000288 73923 0.069838479 4.40E-08 3.496E-05 32474992 -0.000000239 88342 -0.000000284 73924 0.070341709 4.50E-08 3.601E-05 32574993 -0.000000235 88343 -0.000000278 73925 0.069116838 4.30E-08 3.381E-05 32674994 -0.000000231 88344 -0.000000272 73926 0.066189976 4.10E-08 3.088E-05 32774995 -0.000000227 88345 -0.000000265 73927 0.061595415 3.80E-08 2.663E-05 32874996 -0.000000223 88346 -0.000000257 73928 0.055392728 3.40E-08 2.143E-05 32974997 -0.000000219 88347 -0.000000249 73929 0.047694142 3.00E-08 1.628E-05 33074998 -0.000000216 88348 -0.000000239 73930 0.038437423 2.30E-08 1.006E-05 33174999 -0.000000213 88349 -0.000000229 73931 0.027455381 1.60E-08 4.998E-06 332

Node 1 UZ1 Node 2 UZ2 Node 3 FZ3Opening

DisplacementSERR Angle

(-) (in) (-) (in) (-) (lb) (in) (in-lb/in2) (deg)74985 -0.027618148 88335 -0.027618148 73917 -0.000000741 0.00E+00 0.000E+00 31874986 -0.027632134 88336 -0.027632134 73918 -0.000000843 0.00E+00 0.000E+00 31974987 -0.027645731 88337 -0.027645731 73919 -0.00000083 0.00E+00 0.000E+00 32074988 -0.027658947 88338 -0.027658947 73920 -0.000000761 0.00E+00 0.000E+00 32174989 -0.02767181 88339 -0.02767181 73921 -0.000000682 0.00E+00 0.000E+00 32274990 -0.027684359 88340 -0.027684359 73922 -0.000000627 0.00E+00 0.000E+00 32374991 -0.02769664 88341 -0.02769664 73923 -0.00000062 0.00E+00 0.000E+00 32474992 -0.027708698 88342 -0.027708698 73924 -0.000000676 0.00E+00 0.000E+00 32574993 -0.027720578 88343 -0.027720578 73925 -0.000000795 0.00E+00 0.000E+00 32674994 -0.027732324 88344 -0.027732324 73926 -0.000000964 0.00E+00 0.000E+00 32774995 -0.027743978 88345 -0.027743978 73927 -0.000001154 0.00E+00 0.000E+00 32874996 -0.027755582 88346 -0.027755582 73928 -0.000001326 0.00E+00 0.000E+00 32974997 -0.027767171 88347 -0.027767171 73929 -0.000001433 0.00E+00 0.000E+00 33074998 -0.027778769 88348 -0.027778769 73930 -0.000001411 0.00E+00 0.000E+00 33174999 -0.02779038 88349 -0.027790379 73931 -0.000001189 1.00E-09 1.353E-11 332

Summary FEA modeling and analysis of composite structural

components must be sensitive to relatively poor interlaminar properties, especially for refractory composites

Submodeling is frequently necessary Nonlinear material elastic analysis is more appropriate

for certain types of composite materials, e.g. particular types of refractory composites, high strain-to-failure composites

Strain based design criteria applies in this case Post-processing of calculated stresses and strains must

account for textile reinforcement architecture effects 3-5 unit textile cell volume averaging

Interaction criteria are important in calculation of MOS values, primarily for interlaminar components

Finite element analysis methods (VCCT) may be conveniently applied to the numerical assessment of delamination growth in composite materials and structures 64

composite structural analysis and design issues

Documents

thicknessshould elements

fewer elements

responsesolid elements

lamina ply properties

fea of composite plates

fe analysis

single plateshell elements

element selection