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© 2012 Armand J. Chaput

University of Texas VSP Structural

Analysis Module Update - Demonstration

VSP Workshop, San Luis Obispo, CA

Hersh Amin

Armand J. Chaput

Department of Aerospace Engineering and

Engineering Mechanics, University of Texas at Austin

7 August 2013

http://vspsam.ae.utexas.edu/

http://vspsam.ae.utexas.edu/

Today’s Lineup

• Overview of VSP SAM Process

• VSP Model

• Grumman A6E Intruder Wing

• VSP SAM

• Version 1

• Overview

• Tutorial:

• Shrenk’s Approximation (Air Loads)

• Load Factor: 9.75 g

• Version 2

• Overview

• Tutorial:

• Shrenk’s Approximation (Air Loads)

• Load Factor: 9.75 g

• Wing fuel

• External stores (external fuel tanks)

• Note: corresponding files can be found at:

http://vspsam.ae.utexas.edu/archieve/VSPWorkshop2013



Overview of VSP SAM Process

UT Input Executable (Java)

Boundary Conditions and Load Cases

CalculiX Input File

Vehicle Sketch Pad

External and Internal Mesh

Generation

Parametric

External Geometry

Parametric

Internal Geometry

CalculiX

FEM Solution

FEM Input

FEM Post Process

and Graphics

Output Files

UT Convergence Executable

(Java)

Solution Files

Thickness Calculation

Stress Convergence

Thickness and Material Properties

Mass Calculation

Wing Trim

VSP process through mesh generation

Vehicle Sketch Pad

External and Internal Mesh

Generation

Parametric

External Geometry

Parametric

Internal Geometry

Overview of VSP SAM Process – Vehicle Sketch Pad



CalculiX Input File


Wing Trim • Deletes non-primary load carrying structure

- Typically leading and trailing edge devices

• Deletes non-load carrying skin panels

- To represent typical fabric or film skin sections

Overview of VSP SAM Process – UT Input Executable




CalculiX Input File


Wing Trim

Spars, Ribs and Skins can be defined as different

materials

Required Thickness

defined by input

Design Nominal

Stress (DNS)

objective and

Minimum Gauge



CalculiX Input File


Wing Trim


• 2D linear load – at defined constant chord fraction

- Input based on root and tip running load

• 2D elliptical and Schrenk approximations

- Input based on flight design gross weight and nz

• Discrete point loads (Fxx, Fyy, Fzz, Mxx, Myy, Mzz)

- GUI inputs at defined % span and % chord locations

• Discrete mass loads (nz) (v2+ feature)

- GUI inputs at defined spar # and % span or rib # and % chord

locations with multiple attachment points on ribs and/or spars

• Multiple Load Cases (v2+ feature)

- GUI inputs for multiple 2D linear, elliptical or Schrenk

approximations with varying angle of attacks and varying load

distributions on spars

• Fuel Loads (v2+ feature)

- GUI inputs for adding fuel tanks between ribs and spars

- Applies pressure loads and inertial loads on the skin

Boundary conditions define which rib is fixed from

translation in the x, y and z axis



CalculiX Input File


Wing Trim

CalculiX

FEM Solution

FEM Input

FEM Post Process

and Graphics

Output Files

Overview of VSP SAM Process – CalculiX Solutions

Users can see status messages while VSP SAM

is running. Messages can have information on

VSP SAM’s current stress convergence iteration,

Load cases and/or Wing trim operation.

Solution

viewing

area

Mouse commands

rotate and zoom

solution

CalculiX

FEM Solution

FEM Input

FEM Post Process

and Graphics

Output Files

Left click in

white area

brings up menu

Menu provides

range of stress

& displacement

viewing options

Option shown

is von Mises

stress

Overview of VSP SAM Process – CalculiX Solutions

Simple Von Mises stress-based structural

thickness resizing algorithm developed

• An enabling capability for FEM based

structural mass property estimation

• Node thickness resizing is based on

user defined design nominal stress (DN)

or minimum gage, whichever larger

VSP SAM iterates stress to mass convergence

UT Convergence Executable

(Java)

Solution Files

Thickness Calculation

Stress Convergence

Mass Calculation

Overview of VSP SAM Process – UT Convergence Executable

Summary of theory and method used to back out required Nodal thicknesses

Background

Part of the objective of the project is to be able to determine the optimized thickness of each part of the

wing for a given working stress. This backing out the thicknesses aims to do that. The procedure used

by our team and the theory behind it is described.

Theory

We begin with an arbitrary 3D element as shown below:

The blue plane represents a plane lying in one of the 3 principal axes, showing that the element can be

arbitrarily oriented. We can then describe the stress acting on this plane as follows:

We know seek to find the required thickness for a given working stress as defined by the user:

Solving equation (1) for the force, and plugging into equation (2) it can be shown that we get:

By using the max principal stress in any given element for we can ensure that the element is sized for

the worst case scenario. This is the theory behind the procedure used.

Thickness

(1)

(2)

t’i = (/DN) ti

Build VSP Model

• Use actual Area, Taper Ratio, Dihedral, Thickness, and Span

• Model the actual Spar locations.

• Model the actual Rib locations.

Generate Mesh

• Choose mesh size depending on wing size. Typically 100 elements spanwise (Half-Span/100).

• Generate meshes.

• If mesh size > 5 Mb, increase mesh size.

Mass Convergence Minimum Gauges & DNS

• Constant Minimum Gauge

• Initial Design Nominal Stress (DNS) = Initial guess

• Vary DNS for ribs, spars and skins until final wing structure weight matches expected value.

Overview of VSP SAM Process – Mass Calibration Method

Overview of VSP SAM

VSP Model Information

VSP Model – A6E Intruder

Intermediate & Outer sections Only

No Center Section

VSP Model – Why A6E Intruder ?

• Available in Metal and Composite

• Good Mass Properties

• Internal Fuel and External Stores

• Larger Operating Flight Envelope

• Good for the purpose of Software Calibration

VSP Model – A6E Planform

All locations and linear

dimensions in inches

BL

30

5

BL

31

8

33”

BL

14

4

56”

B

L 7

8

B

L 6

6

0.05 c

0.70 c

29.5

28

BL

38

.9

Sweep: 29.5

Root Chord (BL 66):

~156.53” = 13.04’

Tip Chord (BL 305):

62.125” = 5.18

NOTE: Currently VSP SAM does not

support Multi-Section Wing which

limits this analysis to intermediate

and outer sections only which will be

combined into single wing section

VSP Model – A6E Airfoil

NACA-6 Series

Airfoil

t/c (BL 66):

~0.0885 t/c (BL 305):

~0.0612

NOTE: Only Root and Tip t/c ratios

will be used since adding additional

t/c ratios need multi-section wing

which is not currently supported by

VSP SAM

All locations and linear

dimensions in inches

BL

30

5

BL

31

8

FS 228.2

FS 283.9

33”

BL

0

0.70 c?

182.6

BL

14

4

FS 0

56”

0.83 c

0.15 c

57”

318”

B

L 7

8

B

L 6

6

0.05 c

0.70 c

29.5

28

1

17”

Drawing warped L/R B

L 3

8.9

VSP Model – A6E Spars

VSP Model – A6E Ribs

Rib 0

Rib 8

9 Ribs

including Root

and Tip Rib

Spar 0

Spar 1

NOTE: To further simply the

model, all ribs are placed parallel

to free stream.

VSP Model Information

Build A6E VSP Model

VSP Model – Adding a new wing

1

2

3

VSP Model – Modifying the new wing (A6E Planform)

2

3 6

4

1 5

Delete all sections

except section ID: 0

2

3

Set Tip Chord, Root

Chord, & Sweep

4

Set Span, &

Projected Span

6

VSP Model – Modifying the new wing (A6E Airfoil)

1

2

3

Airfoil ID: 0 1 Type:

(Dropdown

menu)

NACA

6-series

NACA

6-series

t/c ratio:

(“Thick” slider)

0.0885 0.0612

1

2

3

VSP Model – Modified A6E wing geometry

1

2

VSP Model – FEM Geometry

1

2

VSP Model – A6E FEM Geometry (Spars)

1

2

3

Spar ID: 0 1 Position:

(“Position:

Slider)

0.05 0.7

Sweep

Angle:

(“Rel”

checkbox)

Checked Checked

Relative

Sweep

Angle:

(“Sweep”

Slider)

0.00 0.00

3

VSP Model – A6E FEM Geometry (Ribs)

1

2

3

Rib ID: Position (“Position” Slider)

0 0.0

1 0.1

2 0.231

3 0.322

4 0.457

5 0.611

6 0.751

7 0.892

8 1.0

3

VSP Model – Finished A6E FEM Geometry

1

2 Location of Ribs and Spars

VSP Model – Generate A6E Mesh

1

2 3 4

Bigger element

size yields bigger

mesh and faster

run time.

VSP SAM – Required Files

1

• Geom File: <Wing_Name>_calculix_geom.dat

• Thick File: <Wing_Name>_calculix_thick.dat

• Copy the “Geom File” and the “Thick File” in a separate directory to run

SAM

• NOTE: SAM working directory (next slide) must not have any spaces in its

path.

VSP SAM – Import VSP Mesh

1 2 3 Set directory for VSP Mesh Files.

You can choose either

calculix_geom or calculix_thick file.

NOTE: having spaces in the

directory path will result in crash.

1

Set the directory of the CalculiX

folder

(use default with typical installation)

2

Open GUI inputs from previous

session or Save GUI inputs for

future sessions

3

1

2

3 Open

3 Save

VSP SAM – Sign Conventions

Y

Z

X X axis goes

chordwise

Y axis goes

spanwise

Z axis goes

normal to the

Datum

α

Origin is always at wing Apex

and parallel to the VSP

coordinate system.

Datum

Applies to all the load factors including nx, ny, and nz

NOTE: All Axis are parallel or

perpendicular to the Datum

regardless of wing sweep,

dihedral or angle of attack

Y axis

goes into

the page

Build A6E VSP Model

VSP SAM Version 1

VSP SAM – Version 1

Features:

• Skin Trim Feature

• Load Spar Approximations

• Boundary Condition

• Separate FEM Models

• Special Case: “Zero” Node Thickness

• Stress Convergence and Node Sizing

• Mass Calculation

VSP SAM – Skin Trim Feature

Remove non-load carrying skin

panels which can be fabric

sections of the skin, landing

gear hatches, etc.

Skin trim must be defined by

Inboard/Outboard rib and

Forward/Aft spar

VSP SAM – Load Spar Approximations

Planform Shape, Elliptical and Schrenk’s Approximations:

Schrenk’s Load distribution is equivalent to average of elliptical load distribution

and the actual planform shape distribution of the wing.

VSP SAM – Boundary Condition

Rib 0 is fixed from

translation in the x,y and

z axis as shown in the

CalculiX results file.

As a result, this particular

wing structure is a

cantilever beam with Rib

0 as the stationary plane.

Any Rib can be defined

as a fixed rib such as a

“Body Rib” as shown in

the figure below.

Rib 0 Body Rib

VSP SAM – Separate FEM Models

Version 0 contains Single FEM model results from original VSP’s output files

Version 1 Splits FEM into separate Skin, Rib, and Spar FEM models using “Rigid

Body Elements” to make connections at rib-skin, spar-skin, and rib-spar intersections

When node thickness is

resized to meet user defined

DNS objective, different node

thickness requirements at

intersections distort elements

which results in CalculiX error

Thicker

elements at rib-

skin, spar-skin,

and rib-spar

intersections

VSP SAM – Special Case: “Zero” Node Thickness

y

z

Set of vertical nodes from a spar, with the horizontal lines representing the

thickness of each node and the Red Arrow represents the force applied to this set

Before After

Thickness of

some nodes

approaches at

nearly zero after

convergence Solution: Apply average

thickness of the adjacent

nodes to the affected node

NOTE: Set of nodes from a

spar is only used as an

example, The same method

applies to any affected node

within the FEM model

VSP SAM – Stress Convergence and Node Sizing Summary of theory and method used to back out required Nodal thicknesses

Background

Part of the objective of the project is to be able to determine the optimized thickness of each part of the

wing for a given working stress. This backing out the thicknesses aims to do that. The procedure used

by our team and the theory behind it is described.

Theory

We begin with an arbitrary 3D element as shown below:

The blue plane represents a plane lying in one of the 3 principal axes, showing that the element can be

arbitrarily oriented. We can then describe the stress acting on this plane as follows:

We know seek to find the required thickness for a given working stress as defined by the user:

Solving equation (1) for the force, and plugging into equation (2) it can be shown that we get:

By using the max principal stress in any given element for we can ensure that the element is sized for

the worst case scenario. This is the theory behind the procedure used.

Thickness

(1)

(2)

t’i = (/DNS) ti

1 and Thickness1 corresponds to each node

VSP SAM – Mass Calculation

VSP SAM Version 1

A6E Tutorial for v1

VSP SAM (version 1) – A6E Wing Geometry

1 2

3

2

Initial Thickness definitions

Set boundary conditions

(Fixed Rib) which indicates

which Rib is fixed from

translation in x, y, and z

direction and Convergence

Tolerance which ends the

iterative process when the

mass difference between

previous iteration and

current iteration converges

to the user defined

tolerance

3

VSP SAM (version 1) – A6E Wing Trim

Before Trim After Trim

Wing Box of the A6E Intruder Wing

VSP SAM (version 1) – A6E Wing Trim (cont’d)

Leading Edge Trim Trailing Edge Trim

1 1 2 2

3 3

4 4

Device Trim definition to reveal the Wing Box of the A6E Intruder Wing

VSP SAM (version 1) – A6E Material Properties

1 2

3

Set Material Properties such as

Young’s Modulus, Poisson’s

Ratio, Yield Stress and Ultimate

Stress

Assign materials defined (2) to

each component and set the

Design Nominal Stress (DNS)

as well as Density and Minimum

Gauge (minimum thickness) for

each component

3

For this case, properties of 2024 T3

Aluminum Alloy is used which is a

nominal material for metal wings,

and Minimum gauge of typical

military aircraft wing is used.

MIL-HDBK-5, Table 3.2.3.0(d)

NOTE: Throughout VSP

SAM, ft and lbm will be the

nominal units.

VSP SAM (version 1) – A6E Aircraft Weight

Wing External Loads (distributed)

0

2000

4000

6000

8000

10000

12000

0.000 0.100 0.200 0.300 0.400 0.500

y/b

lbf/

ft

Running Load pFuel inertia relief

Wing External Load Fraction

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50

y/b

Lo

ad

fra

cti

on

External loadInertia relief

Load Fraction at BL66 (root):

0.73 of Flight DGW

26664 lbm

NOTE: Only 73 % of the

Flight DGW will be used

since this analysis only

involves the intermediate

and outer sections of the

A6E Wing

Flight Design Gross

Weight (DGW):

36526 lbm

VSP SAM (version 1) – A6E Load Case

1

http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html

2

3

4

NOTE: All of the Aircraft

Load will be placed on

Spar 0 Only due to VSP

SAM version 1 limitation

VSP SAM – Running SAM

1

2

Press Run button to initialize SAM

Press Stop button to quit SAM

1

2

A6E Tutorial for v1

A6E v1 Results

VSP SAM – Viewing CalculiX Results

1

NOTE:

These files can be

found in the same

directory where VSP

Mesh files are located

In version 2, “Wing1_N” represents

CalculiX results for Case ID 1 set

in “Load Case” tab at iteration N.

Highest “N” represents the final

iteration.

NOTE: In version 1, “Wing1” from “WingN” is used where “N”

represents the iteration number. “Wing_initial” represents the

initial iteration and “Wing_final” represents the final iteration.

VSP SAM – Viewing CalculiX Results (cont’d)

2 1

3

Translate Model:

Use Right Mouse

Button

Rotate Model:

Use Left Mouse

Button

Zoom in/out Model:

Hold scroll wheel

while dragging the

mouse

VSP SAM – Mass Results File

NOTE:

These files can be

found in the same

directory where VSP

Mesh files are located

“mass.csv” consists of mass values of each

component as well as volume and surface

area at each iteration.

NOTE: VSP SAM only outputs the mass

values in “mass.csv” file. It does not plot any

values as of right now.

VSP SAM (version 1) – A6E Mass Results

Skin Rib Spar Total

Mass (lbm): 652.9 162.8 237.5 1052.8

VSP SAM (version 1) – A6E Stress Results (Iteration 0)

DNS

Skin: 46.181 ksi

Spars: 16.875 ksi

Ribs: 12.361 ksi


DNS

Skin: 46.181 ksi

Spars: 16.875 ksi

Ribs: 12.361 ksi

A6E v1 Results

VSP SAM Version 2

VSP SAM – Version 2

Features:

• Multiple Load Spars & Angle of Attack

• Multiple Load Cases

• Wing Fuel Loads

• Discrete Mass Loads

VSP SAM – Multiple Load Spars & Angle of Attack

http://www.pilotfriend.com/training/flight_training/aero/pres_pat.htm

α > 0

α = 0

Red Arrow

represents

the resultant

force applied

on the wing

x

z

• Based on Angle of Attack (α), loads are split in x and z directions.

• Each spar can be assigned a load fraction of the Total Load in order to get

the resultant force applied on the wing.

VSP SAM – Multiple Load Cases

• More than one Load case can be assigned with varying Angles of Attack

and varying Load Spar Distributions.

• Constructs new FEM model from using Max Stress on each node and Max

Thickness of each node out of all the user-defined load cases.

• The new FEM model is used to calculate final mass estimate.

1 2

3 4

Positive High Alpha

1

Positive Low Alpha

2

Negative Low Alpha

Negative High Alpha

3

4

All 4 points of the flight envelope

can be analyzed

VSP SAM – Wing Fuel Loads

•

Fuel Tanks are defined by forward/aft spar and inboard/outboard rib

VSP SAM – Discrete Mass Loads

• Adds inertial loads on the spars and/or ribs with multiple attachment points.

• User defines spanwise/chordwise fraction along with spar/rib numbers and load fraction of the Total Load for a given attachment point.

• Adds load along the neutral axis of the rib or spar (figure 2). • Distributes loads based on the distance from user-defined spar/rib

location (figure 1).

Node 1 Node 2

Location

D1 D2

Loads are applied in the nz direction

figure 1

figure 2

VSP SAM Version 2

A6E Tutorial for v2

VSP SAM (version 2) – A6E Initial Inputs

1

Same inputs as version 1:

Wing Trim (Devices Tab)

Wing Geometry

1

VSP SAM (version 2) – A6E Material Properties

2

3

Same inputs as version 1

Different DNS for each

component. Same Minimum

Gauge and Density as version 1

1

VSP SAM (version 2) – A6E Load Case

1 2

3

4

5

6

7

Load

Parameters: 0 1

Spar #: 0 1

% of Load: 0.75 0.25

Fixed End

Moment:

0.0 0.0

4

http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html

VSP SAM (version 2) – A6E Wing Fuel Tanks

Fuel Tanks

78. Starboard Wing

Integral Fuel Tank

91. Outer Panel

Integral Fuel Tank

84. Outer Wing

Missile Pylon

201. Inboard Wing

Pylon

Top View

VSP SAM (version 2) – A6E External Stores

y

z

Rib 0 Rib 8

Rear View

y

x

Spar 0

Spar 1

Rib 1 Rib 4

Attachment

Points

Inboard Fuel Tank Outboard Fuel Tank

Pylon

Tank w/adapter External Stores: Inboard: Outboard:

Pylon (lbm): 96.3 91.7

Tank w/adapter (lbm): 199 199

Fuel (lbm): 2005 2005

Total Mass (lbm): 2300.3 2295.7

VSP SAM (version 2) – Adding A6E External Stores

1 2

3

4

5

6

Mass ID: 0 1

Mass(lbm): 2300.3 2295.7

Load Factor

(nz):

-9.75 -9.75

Rib #: 1 4

Chordwise

Fraction:

0.5 0.5

3

4

Note: All masses are

attached at ribs

4

VSP SAM (version 2) – Adding A6E Wing Fuel

1 2

3

4

5

Tank

ID:

Inboard

Rib

Outboard

Rib

FWD

Spar

Aft

Spar

0 0 1 0 1

1 1 2 0 1

2 4 5 0 1

3 5 6 0 1

4 6 7 0 1

5 7 8 0 1

4

A6E Tutorial for v2

A6E v2 Results

VSP SAM (version 2) – A6E Mass Results

Skin Rib Spar Total

Mass (lbm): 651.8 162.3 235.9 1050.0


DNS

Skin: 42.569 ksi

Spars: 15.069 ksi

Ribs: 9.028 ksi

Questions ?

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