Rod/Bulb Stiffened Concept -...

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COLLIER RESEARCH CORPORATION HyperSizer Rod/Bulb Stiffened Panel Family

HyperSizer User’s Manual

Rod/Bulb Stiffened Concept

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C O L L I E R R E S E A R C H C O R P O R A T I O N

HyperSizer Rod/Bulb Stiffened Panel Family

User's Manual Edition 5.9 Collier Research Corporation

Phone 757.825.0000 Fax 757.825.9988

Website: www.hypersizer.com E-mail: [email protected]

mailto:[email protected]�

Copyright HyperSizer® Software Copyright 1996-2010 Collier Research Corporation. Unpublished - All rights reserved under the copyright laws of the United States. Portions Copyright 1996 NASA. All Rights Reserved. HyperSizer® Rod/Bulb Stiffened Panel Family User’s Manual Copyright 2010 Collier Research Corporation. All Rights Reserved. This book and software product are both copyrighted and all rights are reserved by Collier Research Corporation. No part of this document may be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Collier Research Corporation. Any reproduction in whole or in part is strictly prohibited. The distributions and sale of this product are intended for the use of the original purchaser only and for use on only the computer system specified. The software product may be used only under the provisions of the license agreement that was delivered with the software. Unless otherwise stated, you may only use this software on a single computer, by one person, at one time. For additional copies of the software, please contact Collier Research Corporation.

Trademarks In this manual, and in the software, you will see references to many other applications and trademarks which are the property of various companies. HyperSizer is a registered trademark of Collier Research Corporation. ST-SIZE is a trademark of NASA. MSC/, MSC/NASTRAN, MSC/PATRAN, and P3 are trademarks of The MacNeal-Schwendler Corporation. FEMAP is a registered trademark of Enterprise Software Products, Inc. NASTRAN is a registered trademark of NASA. SDRC, SDRC I-DEAS, and I-DEAS are registered trademarks of Structural Dynamics Research Corporation. ANSYS is a registered trademark of ANSYS, Inc. Windows, Windows 95, Windows 98, Windows NT, Windows 2000, Windows, Windows XP, Windows Vista are registered trademarks of Microsoft Corporation.

I N T R O D U C T I O N

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Introduction

The purpose of this user manual is to demonstrate the steps required to set a Rod/Bulb stiffened panel optimization in HyperSizer. This panel concept will be demonstrated using two examples, a test configuration and a full cylindrical NASA vehicle. For users unfamiliar with HyperSizer, the HyperSizer Basic and Material Manager manuals should be studied and several of the tutorial examples worked before attempting this example. Additional details describing the HyperSizer analysis process not covered in this example are presented in the HyperSizer Material Manager and Basic users manuals.

This User Manual is intended for users that are familiar with HyperSizer Basic. Users should be comfortable with setting up running their own workspace analyses.

H Y P E R S I Z E R R O D / B U L B S T I F F E N E D U S E R M A N U A L

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Sizing Variables Sizing Variables for the Stringer

Geometric Variables Sizing Variable Symbol Top Face - Thickness t1 Stringer Web - Thickness t3 Stringer Height hstr Stringer Spacing Sstr Stringer Flange Width wnt,str Stringer Flange Thickness t2 Stiffening Rod - Diameter Drod Stringer Clear Span* Fw,str * Dependent Variable

Material Variables Sizing Variable Symbol Material Type Top Face - Material M1 Metal, Layup, Effective or Discrete Laminate Stringer Web - Material M3 Metal, Layup, Effective or Discrete Laminate

(HyperLaminate) Stiffening Rod - Material M6 Metal, Effective Laminate

M3

t2 M1, t1

hstr

M6,Drod t4

wnt,str

t3

Notes: • If M3 is a HyperLaminate, the layup and

thickness of the stringer flange (t2) is a function of the thickness and layup of the stringer web variable (t3).

• If M3 is an Effective Laminate, then the stringer flange thickness (t2) is an independently sized variable with the same material as M3.

• The Rod overwrap is always assumed to be ½ the thickness of the stringer web.


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Sizing Variables for the Frame

Geometric Variables Sizing Variable Symbol Frame Web - Thickness t5 Frame Height hfra Frame Spacing Sfra Frame Flange Width wnt,fra Frame Flange Thickness t7 Frame Foam - Thickness t8 Stiffening Rod - Diameter Drod Frame Clear Span* Fw,fra * Dependent Variable

Material Variables Sizing Variable Symbol Material Type Frame Web - Material M5 Metal, Layup, Effective or Discrete Laminate

(HyperLaminate) Frame Foam - Material M8 Foam

wnt,frame

M5

M8, t8

hfra

t7

t5 2

Notes: • Layup and thickness of the frame web

(t5) includes material on both sides of the foam core, each wall has thickness = t5/2.

• If M5 is a HyperLaminate, the layup and thickness of the frame flange (t7) is a function of the thickness and layup of the frame web variable (t5).

• If M5 is an Effective Laminate, then the flange thickness (t7) is an independently sized variable with the same material as M5.


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Sizing Variables for the Panel

Sframe

Sstr

Fw,frame

Fw,str

Spacing Span for Local Buckling


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HyperLaminates for the Stringer Flange

Note: For the Rod/Bulb stiffened panel concept the stringer web overwrap is not explicitly specified in the software, rather the overwrap is assumed to be 1/2 the L3 laminate of the stiffener web object.


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HyperLaminates for the Frame Flange

Stack 2 (7 Plies) Active for L2 and L3



Stack 4 (7 Plies) Active for L3 Only

Frame Flange (L2) Total Plies: 21

Frame Flange (L3) Total Plies: 28


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Material Orientation Axis The material orientation vector defines the 0 degree fiber direction for each panel object. The material direction for each Rod/Bulb stiffened panel object are shown in the graphic below:

HyperSizer - PRSEUS Material Orientation Axis For the this panel concept the top facesheet, stringer web and stringer flange are consistent with all other stiffened panel concepts in HyperSizer, where the 0 degree fiber direction is parallel to the stringer. However the frame, frame flange and frame cap have material orientation vectors in the transverse direction like a ringframe.


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Analysis Objects Each panel object and the corresponding failure methods are listed in the table below: Object Applicable Failure Modes Open Span Material Strength (Max Strain, stress, Tsai-Hill, etc) Bonded Combo - Stringer

Material Strength

Bonded Combo - Frame

Material Strength

Stringer Web Material Strength Local Buckling (Long., Shear, Interaction) - Simple-Simple-Simple-Simple Boundary Condition

Frame Web Material Strength Foam Sandwich Wrinkling Local Buckling (Long., Shear, Interaction) - Simple-Clamped-Simple-Free Boundary Condition

Stiffening Rod Flexural Torsional Buckling Max Stress/Strain

Frame Core Sandwich Wrinkling Spacing Span Local Buckling (Biaxial, Shear, Interaction)

- Simple-Simple-Simple-Simple Boundary Condition Frame Span Panel Buckling Between Frames

- Flat Panel Unsymmetric - S-S-S-S BC - Curved Panel Rayleigh Ritz - Any BC - Full Cylinder NASA SP-8007 - with and without transverse shear flexibility

Panel Span Panel Buckling of Full Panel Span - Flat Panel - Curved Panel Rayleigh Ritz - Any BC - Full Cylinder NASA SP-8007


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Local Buckling Objects

Spacing Span

By default the spacing span has simple boundary conditions on all edges. Using this assumption, HyperSizer may produce slightly conservative buckling results because the stringer can provide some fixity at the +Y, -Y edges. This effect increases as the stringer becomes stiffer. For this reason a backdoor flag for Percent Fixity is provided which may be used to 'tune' the spacing span buckling results. Enter a value between 0 and 1 (0 = Simple, 1 = Fully Fixed) to alter the local buckling results for this analysis.


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Stringer Web

The stringer web is also a local buckling object. The local buckling analysis for this object is also performed with simple-simple boundary conditions. Some rotational fixity is provided by the skin. This may produce slightly conservative local buckling results in HyperSizer.

Stiffening Rod (Simple BC)

Panel (Simple BC)

Frame Span Simple BC

Panel Span Simple BC


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Frame Web

The frame web is another local buckling object for this panel concept. Frame Web object includes both the right and left frame laminates as well as the foam separator For local buckling, this object is fixed at the panel because the stringers won't let the panel rotate at the frames A simple boundary condition is assumed at the +X, -X frame edges.

Free Edge (Free BC)

Panel (Clamped - zero rotation edge)

Simple BC Simple BC


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In addition to local buckling, a "facesheet wrinkling" analysis is also included for the frame web, to ensure that the facesheets do not size to be too thin and foam core is not too flimsy.

( )31

1 ccfwr GEEk=σ

Where: • Ec = Through the thickness elastic modulus of core • Ef = Elastic flexural modulus of facesheet • Gc = In-plane shear modulus of core • k1 = Symmetric mode wrinkling factor (HyperSizer = 0.63

Without this failure mode, the foam could be size to be very light and not substantial enough to maintain separation of the facesheet.


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Frame Span Buckling vs Full Panel Buckling The Rod/Bulb stiffened panel concept distinguishes two different kinds of panel buckling, frame span buckling and panel buckling.

Rod/Bulb stiffened panel buckling is a buckling wave which spans the entire length of the X and Y Span. Frame Span buckling is buckling between the frames. It is still considered a panel buckling failure mode because it includes both the facesheet and stringers, however this kind of panel buckling does not cross the frames. The lowest buckling mode shape is up and down over the frame and the proper symmetry boundary condition is simple-simple since the frame is not torsionally stiff enough to provide a rotational constraint to the skin.


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Thermoelastic Verification The first step in characterizing any HyperSizer panel concept is in formulating the strain response of a panel to an applied load or thermal environment. All HyperSizer failure analysis are built on this foundation. HyperSizer analyzes stiffened panels composed of arbitrary composite laminates through stiffener homogenization, or “smearing”, techniques. The result is an effective constitutive equation for the stiffened panel that is suitable for use in a full vehicle-scale finite element analysis. The thermoelastic formulation of the Rod/Bulb stiffened panel extends existing methods for all other panel types. FEA verification of HyperSizer's approach is presented in the following pages. The purpose of this Verification is to verify (1) the homogenization of the panel into a panel level ABD response is accurate and (2) the localization of panel level loads to object level loads is accurate.


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Global Panel ABD Matrix Response The ABD matrix verification is performed by constructing a discrete FEM model of a PRSEUS panel and applying four separate loads to obtain load-strain and moment-curvature response to back-out panel level ABD matrices

Case 1: Applied Nx

Case 2: Applied Ny


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Case 3: Applied Mx

Case 4: Applied My


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Panel Level Load-Strain Comparisons

FEA Total X Deformation, LC1: Applied Nx = 2381lb/in ( = 100kips) Average Translation Y = -0.1248in Panel Length = 80in Average Panel ex = -1561µin/in HyperSizer Computed Average Panel ex = -1591μin/in

FEA Total Y Deformation, LC2: Applied Ny = 142lb/in Average Translation Y = -0.0357in Panel Width = 42in Average Panel ex = -850μin/in HyperSizer Computed Average Panel ey = -879μin/in


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The panel strain response to the 4 load cases are listed below for HyperSizer and FEA:

LC 1 - Applied NxFEA HyperSizer Difference

Nx (lb/in) 2,381 2,381 0.0%Ny (lb/in) 261 252 3.4%ex (µin/in) 1,561 1,591 -1.9%

LC2 - Applied NyFEA HyperSizer Difference

Nx (lb/in) 142 137 3.4%Ny (lb/in) 1,250 1,250 0.0%ey (µin/in) 850 879 -3.4%

LC 3 - Applied MxFEA HyperSizer Difference

Mx (lb-in/in) 1,000 1,000 0.0%kx (x 106 in-1) 1,176 1,175 0.2%

LC2 - Applied NyFEA HyperSizer Difference

My (lb-in/in) 1,000 1,000 0.0%ky (x 106 in-1) 144 142 1.3%


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ABD Calculations: The force and moment resultants from the four load cases are compared to the strains and curvatures to derive panel level ABD terms

LC # Formula FEA HyperSizer DifferenceA11 1 Nx/ex 1,525,408 1,496,577 1.9%A12 1 Ny/ex 167,155 158,401 5.2%A22 2 Ny/ey 1,471,330 1,422,520 3.3%A21 2 Nx/ey 167,155 158,401 5.2%

B11 1 Mx/ex 753,385 746,099 1.0%B22 2 My/ey 1,797,302 1,789,474 0.4%

D11 3 Mx/kx 849,881 851,322 -0.2%D22 4 My/ky 6,953,642 7,044,432 -1.3%


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Object Load Comparison The HyperSizer computed object loads are compared to the FEA computed element loads. The FEA loads are extracted from the center of the panel to eliminate any boundary condition effects so a more accurate evaluation of HyperSizer's load calculation is achieved.

A summary of the internal load comparison between FEA and HyperSizer is shown below: Object Nx Loads FEA HyperSizer

Open Span (lb/in) -458 -440

Bonded Combo, Stringer -2097 -2150

Bonded Combo, Frame -939 -1115

Stringer Web -1570 -1561

Stiffening Rod (lb) -4267 -4334

These object forces are used for performing local buckling, crippling, and material strength analysis.

Note: Object Names listed in the Object Loads frame are generic names that are not concept dependent. For example, "Bonded Combo, Stringer" represents the combined laminate of stringer flange to facesheet. This represents a perfect bond between the flange and facesheet. Although the objects in your concept may be co-cured rather than bonded, this same object name is used.


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HyperFEMGen for Rod/Bulb Stiffened Panels

HyperSizer's HyperFEMgen capability is used to create local, discretely meshed FEMs to verify the local and panel buckling results provided by HyperSizer. As shown in the NASTRAN buckling solution, the first buckling mode occurs in the open span at an Eigenvalue of 0.85.

HyperSizer's spacing span margin of safety indicates and Eigenvalue of 0.83. In this case HyperSizer is slightly conservative.

Eigenvalue = MS + 1

= -0.163 + 1

= 0.83


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Example Problem 1: Analysis of a PRSEUS Test Article

As-fabricated test from Dec 2009, NASA Langley

The PRSEUS panel concept is a specific combination of sizing variables that incorporates pre-defined laminate sequences. The following example will demonstrate HyperSizer's analysis capability with the new Rod/Bulb stiffened panel family using the dimensions from the PRSEUS test article (Dec 2009 - NASA Langley). The purpose of this example is to demonstrate the accuracy of HyperSizer's Rod/Bulb stiffened panel failure methods and how to derive test predictions from HyperSizer results.


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Setting up the Workspace

Setting up Materials and Laminates Begin by creating the primary PRSEUS laminate.

1a Create a [+45/-45/0/_90]s laminate material named 'T1 C72 (one stack) skin'. Apply the orthotropic material "Gr/Ep AS4 Compression Properties" to all plies in the laminate.

Notice when you apply the material to the plies, the material thickness (0.0053 in) and density (0.057 lb/in^3) are automatically populated with the values stored for the material.

1b To modify the thicknesses right click on the individual plies and select 'Set Thickness' then enter the corrected thickness. Repeat the process until the ply thicknesses are stored as shown in the laminate above.


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2a. Now create a [-45/+45/90/_0]s laminate material named 'T1 C72 (one stack) skin - reversed'. Apply the same orthotropic material "Gr/Ep AS4 Compression Properties" to all plies in the laminate.

2b. Again modify the thicknesses by right clicking on the individual plies and select 'Set Thickness' then enter the corrected thickness. Repeat the process until the ply thicknesses are stored as shown in the laminate above.


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3a. Now create a [+45/-45/0/90/0/-45/+45]s laminate material named 'T1 C72 (two stack) skin'. Apply the same orthotropic material "Gr/Ep AS4 Compression Properties" to all plies in the laminate.

3b. Again modify the thicknesses by right clicking on the individual plies and select 'Set Thickness' then enter the corrected thickness. Repeat the process until the ply thicknesses are stored as shown in the laminate above.

There should be 3 new laminates in your database, these laminates are listed below:

Laminate Name Layup

T1 C72 (one stack) skin [+45/-45/0/_90]s

T1 C72 (one stack) skin - reversed [-45/+45/90/_0]s

T1 C72 (two stack) skin [+45/-45/0/90/0/-45/+45]s


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Creating the Workspace We will optimize the PRSEUS panels in the workspace environment using user-specified loads. First we should create a workspace and select the available materials.

4a. Create a new workspace named 'PRSEUS User Manual Example'

4b. Expand the database and right click on Available Materials and select the three laminates we just created to make them available for use in the new workspace.

4c. Now open the sizing form and browse to the 'Rod/Bulb Stiffened Panel

Family'. Create a new group named 'PRSEUS One Stack Test Configuration'.

4d. Add a component to the group and name the component 'Uniaxial Test Load (100 kips)'. The group/component definition in the sizing form should be the same as shown below:


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Assigning Sizing Variables The PRSEUS panel concept has many variables to define. We will now assign materials, thicknesses and widths to all panel objects.

5a. Start with the top facesheet, select the 'laminate' radial button and assign

the 'T1 C72 (one stack) skin - reversed' laminate to this variable.

Note: The PRSEUS test panel drawings are configured with facesheet 0 degree fiber direction parallel to frames (transverse panel direction), which is 90 degrees different than of HyperSizer's reference, therefore the 'reversed' panel T1 C72 laminate configuration is applied to this variable (ref: HyperSizer - PRSEUS Material Orientation Axis, p. 7):


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5b. Next enter the Stringer Height as 1.148in and enter 1 permutation. No material is assigned to this variable

Note: The stringer height dimension in HyperSizer slightly different from the callout in original drawing. Remember in HyperSizer the stringer height dimension is measured from the IML of the facesheet to the center of the stiffener. In the original drawing the stiffener height is measured from the OML of the facesheet to the tip of the stiffener, which includes the thickness of the facesheet.

5c. Continue by assigning the stiffener spacing as 6in with one permutation. No material is assigned to this variable.


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5d. Assign the Frame Height as 6in with one permutation. No material is assigned to this variable.

Note: The Frame Height variable is defined from the top facesheet to the top of the frame and includes the frame flange and frame cap thicknesses.

5e. Now define the frame spacing as 20" with one permutation. No material is assigned to this variable.

If the 'Frame Span Buckling failure methods are active, the Frame spacing defines the X-Buckling span for the panel.


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5f. Now define the Frame Foam Thickness as 0.5in with one permutation. Also assign the 'PRSEUS Rohacell Foam: Density 0.004, Dry' material to this variable.

5g. Assign a Stringer Flange Width of 3.37in with one permutation. No material is defined for this variable.

Note: The Stringer Flange Thickness is a dependant variable. Since the stringer web is defined with a HyperLaminate, the flange thickness is dependent on the stringer laminate definition.


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5h. Define the Frame Flange Width as 4in with one permutation. No material is defined for this variable.

Note: The Frame Flange Thickness is a dependant variable. Since the Frame web is defined with a HyperLaminate, the flange thickness is dependent on the web material.

5i. Now define the Stiffening Rod material and Rod diameter. Assign the "PRSEUS Composite Rod, Dry" Effective laminate material to the stiffening rod.

Since the rod is defined as an orthotropic (continuous) material that represents a laminate with a set ply percentage, the diameter may be defined as a range like an isotropic material.


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5j. Enter a diameter of 0.375in with one permutation. To view the properties of this material, right click on the material in the available materials window and select 'Edit This Material...', the orthotropic material form will appear. The stiffness values entered for the rod material are shown below:

Notice the high stiffness in the 1 direction relative to the 2 direction.

5k. Click on the 'Effective Laminate' tab to view the relative ply percents.

Notice the 'Treat this Orthotropic Material as Effective Laminate' option is toggled on. This option allows the user to treat this material as continuous and apply a user defined thickness variable.


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HyperLaminate for Stringer Web and Flange Material/Thickness Now we will create a HyperLaminate based on the 'T1 C72 (two stack) skin' laminate and assign it to the Stringer Web - Thickness variable.

6a. Open the 'T1 C72 (two stack) skin' laminate, we will create a "HyperLaminate" based on the T1C72 stack.

6b. Press the 'Hyper' button to activate this material as a HyperLaminate and

expose the L2, L3 and L4 objects.

6c. Turn off all of the L4 objects and change the name of the laminate to 'T1 C72 (two stack) stringer web and flange'.

6d. Press the "Save As New" button to save this as a new laminate definition.


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Note: The objects L2 and L3 represent the Stringer Flange and Stringer Web objects respectively.

In this case the web (L3) consists of 14 plies, two T1C72 stacks. The stringer flange is made up of a 7 ply tear strap, one T1C72 stack, added to 7 plies from the Stringer Web, a second T1C72 stack that is the left and right half of the flange. This means when defining the HyperLaminate for the stringer web the flange object (L2) is also made up of 14 plies or two T1C72 stacks, which includes both the tear strap and stringer flange. So when turning objects on and off for the stringer web and flange laminate, all fourteen plies should be turned on for objects L2 and L3. The L4 object is not currently being used for the PRSEUS concept. The stiffener rod overwrap is always assumed to be 1/2 the stringer web laminate.


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6e. We will now add this material into our workspace available materials and then add this material into the 'Stringer Web - Thickness' sizing variable.

Tip: A quick way to do this is to leave the Laminate Form open and return to the Sizing form. Then change the variable to the "Stringer Web - Thickness" variable and select the 'Laminate' radial option. Now with the sizing form open return to the laminate form and press the 'Add to Variable' button. Pressing this button will add the material to the workspace available materials and add the material to the active variable on the sizing form in one step.


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HyperLaminate for Frame Web and Flange Material/Thickness Now we will define the Hyperlaminate for the Frame Web. The laminate for the frame web is the entire laminate representing the left and right halves of the frame (on either side of the foam).

For the test setup, there are a total of 28 plies in the frame web (L2), 14 plies on either side of the foam. The flange (L2) is made up of one T1C72 stack (7 ply) frame cap bonded to two T1C72 stacks (14 plies) from the frame web, which totals 21 plies for the flange.


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6f. Now to create the laminate for the frame web and flange, open with the laminate previously created for the stringer web, 'T1 C72 (two stack) stringer web and flange'

6g. Copy the 14 plies and paste them over the 14th ply in the stack to create a 28 ply symmetric laminate.

6h. Now, turn off the L2 (Flange) object for the first 7 plies as shown below.


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This leaves 21 plies for the flange object L2 (7 ply frame cap + 14 plies from the divided frame web) and 28 plies for the frame web object L3. Once again, the L4 object is not used for the PRSEUS panel.

6i. Change the name of the laminate to 'T1 C72 (two stack) frame web and

flange' and press the "Save As New" button.

Add this laminate to the Frame Web - Thickness sizing variable and be sure to select "Laminate" rather than "Continuous" as the material type.

6j. After all variables have been specified, press the 'Save' button on the sizing form.

Note: If all materials and variables were entered the following in the Group Design Bounds. There will be a single candidate design with a unit weight of 2.149 psf.

If this is not what is shown in the Group Design Bounds and Component Result window, please review the variables entered for this group.


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Mechanical Loads and Panel Dimensions We will now enter the design-to loads and dimensions on the 'FBD' tab.

7a. For the a and b buckling length, enter the test panel overall dimensions of 80" and 42" respectively.

As a starting point, we want to enter a total panel compressive load of 100 kips. As a unit load, this is entered as Nx = (total load) / (width) = (-100,000lb) / (42in) = -2381 lb/in.

7b. Enter -2381 for Nx.

7c. Then set Ny and Nxy to "Free" and leave Mx, My and Mxy as constrained.

Setting Ny and Nxy to 'Free' allows the panel to expand . This eliminates Poisson's effect and no panel Ny loads will to be developed. Note: The image portrayed in the "Point Free Body Diagram" frame is not specific to the Rod-Stiffened Panel Family. It is a generic picture that depicts the sign convention for overall panel loads. For example Nx is in the direction of the stringers and Ny is perpindicular to the stringers (in the case of PRSEUS, Ny is the overall panel load in the Frame direction).


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Since this is a test analysis rather than a sizing, we want to set the Limit and Ultimate factors to 1.0 to ensure the design-to loads are not scaled up by any mechanical factor.

7d. Set the Mechanical Limit and Mechanical Ultimate factors to 1.0 on the

Design-to Loads tab.


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Active Failure Modes We will now specify the active failure methods in the Failure Tab. By activating the failure method you are prompting HyperSizer to return a margin of safety for that method during analysis. We will start by turning off all composite failure theories except for Max Strain.

8a. In the Failure Analysis Categories section of the failure tab, select "Material Strength, Composite Ply"

If nothing appears in the Available Failure Analysis window, click on the text "PRSEUS" to activate all analysis objects.

8b. Turn off all of the composite analyses for every object using the "Toggle"

button and then turn on max strain 1, 2 and 12 for every object.

Make sure that you have the three max strain analyses turned on for all analysis objects. Tip: Press the "Hide Unselected" button to hide all failure analyses that are not active. This will make the following steps easier by not showing the failure methods that are inactive.


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8c. Next click on "Crippling" under Failure Analysis Categories

8d. Turn off the isotropic crippling analyses and the "Johnson-Euler Buckling

Interaction" margin of safety so that Crippling-Composite is the only active Crippling failure analysis.

8e. Now isolate the stiffener buckling failure analysis by clicking on "Buckling, Stiffener" under Failure Analysis Categories

8f. Then turn on the "Stiffener Buckling, Flat, Stiffener Flexural Torsional Stability failure mode.

If no failure analysis are displayed, deselect the 'Hide Unselected' option.


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Review the Analysis Results

9a. Press the "Analyze" button to analyze the PRSEUS panel.

HyperSizer will return a minimum margin of safety of -0.2079, which is displayed in red on the Component results section of the sizing form. This margin of safety indicates first failure at (100 kips) * [1 + (-0.2079)] = 79 kips. Although this shows up as a "failure", we will see that this is not actually a catastrophic failure, but rather it is local buckling of the "Spacing Span". Recall the spacing span includes both the facesheet and stiffener flanges. With the PRSEUS concept, we expect the panel to exhibit substantial post-buckling strength. We will review HyperSizer's post buckling capability in the following pages.


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9b. On the Failure tab, make sure that all of the margins of safety are visible by

clicking all of the categories under Failure analysis categories.

9c. Next press the "Sort" margins checkbox to show the minimum margins of safety at the top of the window.

Since we know for PRSEUS that local buckling of the spacing span should not be considered a "catastrophic failure" we can enter a "required" margin for this failure mode so that HyperSizer will not consider it to be failure. We will enter a required margin of -0.5. By entering this value, we are saying that local buckling of the spacing span is allowable up to 50% of the user entered limit load (if using an ultimate factor of 1.5, then local buckling would be allowed up to 33% ultimate load). In this case, we are saying that local buckling is allowed for any load above 50 kips.


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9d. Right click on the -0.2079 margin and select "Required Limit Margin of

Safety".

9e. Enter a required margin of -0.5. Repeat this for both the Longitudinal and the Interaction failure modes.

Notice the margins of safety immediately turn blue indicating that this is no longer considered a failure. If you do not specify a required margin, HyperSizer will consider any facesheet buckling margin below 0 to be a catastrophic failure and as described in the next section, no post-buckling analysis will be performed. To determine the final failure prediction(s), look at the other margins of safety returned on the Failure tab. Behind the two local buckling margins, the next lowest margin is the stiffener Flexural-Torsional stability margin of 0.98. This margin indicates torsional buckling or "rolling" of the stiffener. This failure mode is predicted at a load of:

FT Buckling Load = (100 kips) * (0.98 + 1) = 198 kips

HyperSizer Flexural-Torsional Stability is a new failure mode in HyperSizer and is described in detail in the HyperSizer Methods and Equations document: "AID 016 Stiffener Flexural-Torsional Stability.HME" Additional Failure mechanisms are predicted at the following failure loads: Failure Mode Margin Panel Load

(kips) Strain (x106 in/in)

Flexural Torsional Buckling 0.98 198 3291 Crippling 1.696 270 4480 Frame Span Buckling with TSF 2.324 332 5520 Frame Span Buckling w/o TSF 2.943 394 6550 Material Strength (Max Strain) 3.97 497 8250 Panel Buckling (full 80x42 panel) with TSF

4.551 555 9210


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Generate a Local FEM using HyperFEMGen Local FEMs with discretely meshed stiffeners and frames are used to verify HyperSizer's smeared load determination and local buckling results. By using HyperFEMgen these models are easily created with the correct boundary conditions and enforced displacements. For these verification models each panel object is represented with a PCOMP property where the layups are discretely defined so HyperSizer's smeared approach may be verified with FEA.

10a. To create the local model open the Backdoor Data file for this workspace.

10b. Set the FEMgen Create option to 'True'

10c. Also set the FEMgen Minimum Segment option to '3'

10d. To ensure the proper load eccentricity is captured from the property offsets, set the FEMgen Midplane Laminates to 'False'.

For a more detailed description of the HyperFEMgen options, ref: '0451_+HyperSizer-Training-HyperFEMGen_Discrete-Panel_FEM_Generation_2009-03-17.ppt'


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Verify HyperSizer Local Buckling results The NASTRAN and Abaqus FEMs are created by HyperSizer and saved to the 'Temp' directory in the project working folder. The FEM containing the NASTRAN buckling run deck (solution 102) is saved as 'PRSEUS_User_Manual_Example001_Eigen.nas'. The proper loads and boundary conditions have automatically applied to this local FEM by HyperSizer.

10e. Run the local FEM and compare the buckling Eigenvalues

FEA Buckling Eigenvalue Solution (1st Mode Shape)


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HyperSizer Buckling Margin of Safety Calculation

10f. Use the following equation to determine the HyperSizer computed buckling Eigenvalue

Since the ultimate load factor = 1.0, then:

Eigenvalue Buckling Mode HyperSizer 0.79 Open Span FEA 0.85 Open Span

HyperSizer's local buckling Eigenvalue is slightly more conservative because the assumed boundary conditions for the open span are simple-simple. In reality the stiffener supplies the skin with some rotational fixity which effectively increases panel's critical buckling load. Currently the local buckling results for the spacing span can be 'tuned' by changing the PRSEUS Spacing Span Local Buckling Coefficient, in the Backdoor data file. However new buckling methods are being developed for the Rod/Bulb stiffened panel concept that will capture the rotational fixity between the stiffener web and skin.


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Post Buckling Behavior Note that the margins of safety that have been presented so far assume that the panel has a linear-elastic response to the loading, from the onset of local buckling up through the additional failure modes. In reality, when local buckling in the spacing span occurs, a portion of the buckled spacing span becomes non-effective and will carry no additional load. HyperSizer can calculate this reduction in effective area with its local post-buckling capability.

11a. To activate this capability, go to the Buckling tab and select "Local Post Buckling" then re-analyze the component.

Notice the 'Resulting Effective Width' that is returned as a result of the local post buckling analysis is displayed in this frame.


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This effective width is the width of the spacing span that is capable of carrying additional load after the skin local buckles which is shown in the figure below.

This figure illustrates the sequence of local buckling. First an initial bifurcation local buckling mode occurs denoted by the green line. Then the additional load causes the 2nd mode shape amplitude to be greater, blue line. Finally, as the full local post buckling strength is realized, the mode shape becomes its largest, red line. As load is increased, the buckling mode shape becomes larger, and the effective width of the remaining stable skin becomes narrower. HyperSizer assumes that immediately upon post-buckling, the effective width is immediately reduced to 1/2 the total width of the span. Immediately after facesheet buckling, the panel begins picking up load and there is a kink in the stress-strain curve where the stiffness is reduced. Note that the effective width is dynamic and does not necessarily have to intersect the end of the flange taper. For more details on the post-buckling methodology, see the following paper which can be downloaded from the HyperSizer website: "Local Post Buckling: An Efficient Analysis Approach for Industry Use" 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, May 2009.


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Local Post Buckling Analysis Details The analysis details for local post buckling are found in the Material Analysis Detail file.

12a. Click on the 'Options' drop down menu on the Project Sizing form, then select Material and Analysis Detail

A text box containing the detailed calculations for every active failure analysis will appear.

12b. Search the file for the term 'Local Post'

The effective width is recalculated for each local buckling bifurcation and listed for each iteration. For this analysis the load only causes one buckling bifurcation so a single effective width is calculated and listed in the .MTL file. Note: It has been observed during FEA verification of this approach that the effective width of the spacing span is never greater than ½ the stiffener spacing so this will always be the first effective width used in the HyperSizer local post buckling analysis.


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A look back at the failure tab reveals an increase in post-buckling load capability:

The critical failure mode is still Flexural-Torsional stability, but the margin of safety has increased to 1.22 for a total post-buckled load prediction of 222 kips.

Margins of Safety in Post-Buckling Failure Mode Margin Panel Load

(kips) Flexural Torsional Buckling 1.224 222 Crippling 1.874 287 Frame Span Buckling with TSF 2.13 313 Frame Span Buckling w/o TSF 2.13 313 Material Strength (Max Strain) 3.6 460 Panel Buckling (full 80x42 panel) with TSF 4.487 449


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The overall load in the panel is only 1/2 the story. The second half of the story is that the strain at this load level is quite different than the strain in the linear analysis. As the panel goes further into post buckling, it is has a lower overall stiffness at post buckled loads which causes the panel to strain more as the load is increased. This is behavior is observed in the linear vs. non-linear response plot below.

Plot of linear elastic Load-Strain vs non-linear post buckling load-strain

After local buckling, the load – displacement plot is non-linear. Notice the strain response of the linear curve is much lower than the non-linear curve at the same panel load. As shown in the figure above, both the analytical method (HyperSizer) and Abaqus FEA predict the same slope which provide an independent verification of HyperSizer's analysis. It should also be noted that the test collapse was initiated by the damage imposed on the panel prior to test.


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FEA Verification In order to verify any postbuckling result, linear static and eigenvalue FEA is no longer sufficient. The user must rely on a geometric non-linear finite element analysis in order to verify any post-buckled results.

When running HyperFEMGen, in addition to Nastran models of the panel, ABAQUS finite element models are also generated. These ABAQUS models are set up to do either linear static, linear eigenvalue or non-linear postbuckling analysis. In this case we will be using the "_PostBuckle.inp" file in ABAQUS.

Note that substantial effort has been made to make sure that the boundary conditions of the FEA analysis models match the design intent, however, it is always a good idea to review these boundary conditions in the FEA file to ensure that the FEA matches the design intent of your particular problem. For example, in this case the boundary conditions were chosen so that they match the conditions of the test article.


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The first results to show for the post-buckling result is Load vs. Strain. In non-linear postbuckling analysis, it is difficult to ascertain what constitutes a "buckling" event. In the results shown here, two events are used to determine when buckling occurs. First, negative eigenvalue buckling refers to the solver reporting negative eigenvalues while decomposing the stiffness matrix for inversion. The first negative eigenvalues shown in the following figure indicate the onset of local buckling. A secondary event that indicates the presence of local buckling is a change in the panel stiffness matrix. These are shown below and indicate secondary buckling events such as a mode change, or the final panel collapse.

In the current results, three principle responses were detected. First, local buckling onset occurred at approximately 2572 lb/in (108 kips). This is slightly higher than the linear eigenvalue load of 85 kips predicted from the FEA. (Notably, a linear eigenvalue analysis in ABAQUS returns an eigenvalue load of 76 kips, so it is apparent that this local buckling mode is a challenge even for FEA). A secondary event occurs when apparently the local buckling modes change from two to three half waves at approximately 3783 lb/in (159 kips). Finally the panel continues loading to a final collapse load of 5466 lb/in (229 kips). This compares favorably to the postbuckled HyperSizer Flexural-Torsional value of 222 kips.

Linear/Static Response

Local Buckling Onset

Panel Collapse Apparent Local

Mode Change


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The ultimate failure mode from the non-linear analysis can be determined from examining the deflected mode shapes. First, the initial local buckling mode shape at a load of 108 kips. The local buckled shapes can be seen in the second and fourth bays and are beginning to develop in the third. These mode shapes match the linear eigenvalue results. The contours represent the magnitude of out-of-plane deflection.

The second event is the mode shift that occurs at approximately 159 kips. Notice that there are now 3 half waves in the 2nd and 4th span and 2 half waves in the center span. Also notice that we are starting to see a slight perturbation of the stiffener.


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The final result snapshots for this analysis are at a point just before final collapse. This result is at 227 kips. Notice that there is substantial deformation of the straight stiffener path as the stiffeners are starting to substantially tip.

Also of note is the deformed shape of the panel shown from the side. As the stiffeners tip over the load that they are carrying is beginning to offload from the very stiff rod into the facesheet. As this happens the effective bending stiffness of the panel is rapidly diminishing and the panel is beginning to take on a flexural (i.e. panel) buckling mode shape.

So, in summary, the non linear FEA shows a torsional buckling mode of the stiffeners which leads very quickly to panel collapse by overall panel buckling. The load level of collapse is 229 kips which compares very favorably to HyperSizer's predicted collapse of 222 kips.


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Example Problem 2: Sizing PRSEUS for a Large Cylindrical Space Structure with Ringframes

Since the frames of the PRSEUS panel act like ringframes, the PRSEUS panel is ideal for large axially loaded structures where ringframes are needed for buckling stability. Since the frames are an innate sizing variable within the software the entire structure can be sized in HyperSizer using a simple workspace approach. This optimization approach requires no iterations between HyperSizer and FEA to determine the required ringframe stiffness to prevent global buckling or the transverse (hoop) compression load caused by ringframe pinching, these panel behaviors are captured within HyperSizer. In the following example we will enter a range of materials and variable bounds to explore the optimization capability of the new HyperSizer - PRSEUS concept. We will allow HyperSizer to optimize to user defined design-to loads that were determined with a simple FBD and finally compare the final weight estimate to an optimized honeycomb sandwich concept under the same load conditions.


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Description of Geometry, Loads and Load Factors

Structure Geometry The vehicle geometry is entered on the Buckling Tab.

Since the frames will be considered ringframes and the panel buckling X-Span will be the entire panel span, the X-Span buckling span is entered as the full barrel length (570in). The maximum allowable Y-Span is entered, (1/2 circumference).

Internal, Y Curvature is chosen and the radius of curvature is entered on the buckling tab (198in).


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Design-to Loads The loading for the workspace approach is based on the assumption that the maximum axial load from the flight conditions is to be clocked around the circumference of the structure and at preliminary stages of design the structure should be uniform from top to bottom. The derivation of the axial line load from the flight loads is shown below:

By following this design criteria the maximum line load (Nx = -4560 lb/in) will be applied to the entire cylinder and thus the effective line load will be a constant load used in the HyperSizer workspace environment. The two critical load cases for this vehicle are listed in the table below:

Load Case Nx Ny Load Description 1 -4500 990 Axial Compression + Internal Pressure 2 -4500 -495 Axial Compression + Crush Pressure

These loads are entered on the FBD diagram as user loads.


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Mechanical Load Factors Since this is a sizing/optimization rather than a test analysis, we want to set the Limit and Ultimate factors to appropriate values. Limit loads were derived and entered on the FBD tab so the mechanical limit factor is set to 1.0. The limit loads are scaled up by 1.4 for ultimate loads.

Curved Panel Knockdown Factor For this vehicle sizing a cylindrical buckling knockdown factor of 0.65 is applied.


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Active Failure Analysis The active failure analysis for this optimization are listed in the table below:

Panel Object Failure Analysis All Objects Material Strength (Max Strain 1, 2, 12) Panel Curved Panel Buckling, All BC, w/TSF Panel Crippling Bonded Combo Local Buckling Stringer Web Local Buckling Spacing Span Local Buckling (LPB) Frame Span Curved Panel Buckling, All BC, w/TSF

Local Post Buckling For this analysis local post buckling is active and the skin is allowed to local buckle at 75% limit load.


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Optimization Bounds:

Dependant Variable when DLs are assigned to corresponding object Always a Dependent Variable

Panel Object Min Max Perm Material Top Face - Thickness

N/A N/A N/A

Stringer Web - Thickness

N/A N/A N/A

Stringer Height 2.0 2.2 3 N/A

Stringer Spacing 6.5 7 5 N/A

Frame Web Thickness

N/A N/A N/A

Frame Height 6.75 7.25 5 N/A

Frame Spacing 48 52 2 N/A

Frame Foam - Thickness

0.5 0.5 1 PRSEUS Rohacell Foam

Stringer Flange Width

3.5 3.75 2 N/A

Stringer Flange Thickness

N/A N/A N/A N/A

Frame Flange Width

4 4 1 N/A

Frame Flange Thickness

N/A N/A N/A N/A

Rod Diameter 0.55 0.65 3 PRSEUS Composite Rod - EL

Stringer Clear Span

N/A N/A N/A N/A

Frame Clear Span

N/A N/A N/A N/A


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The combination of sizing variables has created a total of 72000 candidate designs which may be considered during this optimization.

Optimum Variable Dimensions

Panel Object Thickness (in)

Material

Top Face - Thickness 0.1026 PRSEUS Skin IM7 (Two Stack) Real - 18 plies

Stringer Web - Thickness 0.0798 PRSEUS Stiffener and Foot IM7 14 ply symmetric Stringer Height 2.1 N/A Stringer Spacing 6.625 N/A Frame Web Thickness 0.1026 PRSEUS Frame, foot and tear strap IM7 18 plies Frame Height 7 N/A Frame Spacing 48 N/A Frame Foam 0.5 PRSEUS Rohacell Foam Stringer Flange Width 3.5 N/A Stringer Flange Thickness 0.0798 N/A Frame Flange Width 4 N/A Frame Flange Thickness 0.1026 N/A Rod Diameter 0.60 PRSEUS Composite Rod - EL Stringer Clear Span 4.125 N/A Frame Clear Span 44 N/A


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Chosen Laminates Stiffener Web, Flange and Tear Strap:

The stiffener web (L3) has two stacks of seven plies. The stringer foot has the same seven stack plus the same stack repeated as the tear strap. Frame Web, Flange and Frame Cap:

The frame web (L3) has two stacks of nine plies. The tear strap and foot both have the same nine stack (L2).


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Top Facesheet:

The top facesheet is 18 plies consisting of two 9 ply stacks that are 44% 0s, 44% 45s and 12% 90s.


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Margins of Safety

There are many failure analyses performed that control the sizing. For this particular sizing, the lowest MS is panel buckling, followed closely by frame span buckling then local buckling of the skin (post buckling), flexural torsional buckling of the stiffener (ultimate), crippling, then composite material strength (max strain limits). Notice by freezing the design then turning off local post buckling and re-analyzing, the margins for panel buckling are negative. A comparison of the buckling margins with and without local post buckling active is shown below.

Failure Analysis Margins of Safety Local Postbucked Non Local Postbuckled

Panel Buckling 0.00 -0.10 Flexural Torsional Buckling 0.05 0.03


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Weight Comparison Comparing the unit weight of the PRSEUS panel design to the fully optimized Honeycomb Sandwich design, we see the PRSEUS design is weight competitive concept for this application and is just 7% heavier than honeycomb sandwich.

Since honeycomb sandwich panels have fewer sizing variables they are easy to optimize but this leaves little opportunity for weight reduction. For this reason as the design maturity of this vehicle increases, the honeycomb sandwich may not be sized any lighter whereas the PRSEUS is likely to be re-optimized for lighter weight. The optimum non-post buckled PRSEUS design is shown on the chart. Notice the large weight savings from optimizing the PRSEUS panel to with local post buckling. Also notice there is no added ringframe weight to the PRSEUS concept. A major advantage of using HyperSizer to optimize the PRSEUS, is the ringframes are an innate sizing variable. This makes the optimization process easier by eliminating the need to iterate with FEA and reducing the time required to perform vehicle level trade studies.


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