A Novel Optimization Strategy for Composite Beam Type Landing Gear for Light Aircraft

8/11/2019 A Novel Optimization Strategy for Composite Beam Type Landing Gear for Light Aircraft

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A novel optimization strategy for composite beam type landing gear for light aircraft

Edwin Spencer *

United Technologies Aerospace Systems

850 Lagoon Drive

Chula Vista

Ca. 91910

Abstract

Composite beam type landing gear have applications in small light aircraft. A novel optimization

strategy using Nastran finite element models and sol 200 (optimization solution sequence) ispresented in this paper. The analysis criteria are to meet stiffness strength and weight

requirements for multiple landing load cases. The optimization analysis strategy is a novel two

stage approach. In the first stage a shape optimization is carried out on a tapered rectangular

hollow cross section beam finite element model . Each beam element had 8 design variables:

height, width, cap thickness and web thickness at each end of the beam. The design constraints

for the optimization analysis is a specified vertical deflection at the wheel attachment to meet

landing energy absorption criteria and stresses below allowable for all elements for all load

cases. The optimum cross-sections from the beam analysis are used to create a 3D composite

shell finite element model with multiple ply lay-up property regions for the second stage of theoptimization analysis. In the second stage a ply thickness optimization analysis was carried out

on the 3D composite shell finite element model. The design variables are the thicknesses of

zero degree, + / - 45 degree and 90 degree plies for the various property regions. The objective

function for both shape optimization and ply thickness optimization was to minimize weight.

*Currently employed at UTAS, work for this paper was carried out while the author wasformerly employed at MSC Software.


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Introduction

Landing gear for small light aircraft need to satisfy minimum weight criteria, strength criteria

with adequate margin of safety against failure and a precisely tuned stiffness or deflection on

landing to absorb the landing energy. Laminate composite structures are ideal for this

application because the material system can be tailored to meet the specific requirements in a

very predictable manner. To design the landing gear structure to meet these requirements

manually by trial and error will be very labor intensive and extremely time consuming. Finite

element laminate composite analysis coupled with optimization techniques offer a robust and

efficient methodology to design a beam type landing gear.

Optimization Concept

A novel two stage optimization strategy using Nastran finite element models and Sol 200

optimization solution sequence has been devised which can be used to design any generic

beam type landing gear for multiple landing load cases. In the first stage the landing gear

structure is modeled with tapered rectangular hollow cross section beam elements (seeFigure

1). Each beam has 8 design variables : height, width , cap thickness and web thickness at eachend of the beam which are initially set to nominal values and a shape optimization is carried out

whereby the cross sectional shape can change span-wise as shown onFigure 2 which is a 3D

rendering of the optimized beam structure.

The optimum cross-sections from the beam analysis (Figure 2)are used to create a 3D

composite shell finite element model with multiple ply lay-up property regions (Figure 3 and

Figure 4)for the second stage of the optimization analysis. In the second stage a ply thickness

optimization analysis was carried out on the 3D composite shell finite element model. The

design variables are the thicknesses of zero degree, + / - 45 degree and 90 degree plies for the

various property regions. The objective function for both shape optimization and ply thickness

optimization was to minimize weight.


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Figure 1Tapered Rectangular Hollow Cross Section Shape Optimization Beam Model


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Figure 23D Rendering of Shape Optimized Beam Model


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Figure 33D Composite Shell Finite Element Model Lofted from Optimized Shape Beam

Model


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Figure 4Ply Lay-Up Property Regions for Thickness Optimization


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Shape optimization Tapered Box Beam Finite Element Model:

This is a full model consisting of 32 tapered box section beam elements and 33 nodes. The MSCNastran solver solution sequence 200 was used. This model uses equivalent isotropic material

properties of a typical ply lay-up. This is a shape optimization analysis model the purpose of

which is to obtain an optimum shape while meeting the stiffness constraint of 14.5 in at loadapplication point for the 3g ult. vertical load case and also stress constraints of tensile,

compressive and shear stresses below the material allowable for the four load cases considered:

1. 3g. Ultimate Vertical load (Figure 5)

2. Max. Drag Load (Figure 6)

3. Max. Side Load (Figure 7)

4. Max. Vertical Load (Figure 8)

The loads and boundary conditions for each of the above four cases are shown onFigure 5to

Figure 8.Although the model is symmetric about the aircraft center line a full model has to be

used because the loading is un-symmetric for the side load case (case 3). Each beam crosssection has 8 design variables: width, height, cap & web thickness at ends A & B as shown on

Figure 1. The cross section of end B of each beam is constrained to be same as End A of

adjacent beam so that a smooth shape transition is created.Figure 2shows a 3d plot of the

optimized shape beam model. The cross sectional dimensions of this beam model is used tocreate the 3d lofted surfaces of the composite shell model which is optimized for ply thickness in

a further analysis step.


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Figure 5 - 3g Ultimate Vertical Load (lbf)


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Figure 6 - Max. Drag Load lbf (ultimate)


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Figure 7 - Max. Side Load lbf (ultimate)


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Figure 8 - Max. Vertical Load lbf (ultimate)


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Ply Thickness Optimization 3d Composite Shell Finite Element Model:

Figure 3shows the 3d composite shell finite element model lofted from the cross sections of the

optimized shape beam model shown inFigure 2.The model consists of 72136 predominantlyquadrilateral shell elements and 72610 nodes. The MSC Nastran solver solution sequence 200

was used, version 2008 R3 (or higher) of the software is required in order to use the compositefailure indices in the optimization routine. The main purpose of this model is to calculate the

optimum ply thicknesses while meeting the stiffness constraint of 14.5 in at load application

point for the 3g ult. vertical load case and a stress constraint of failure index below 0.95 for allelements for the four load cases considered:

1. 3g. Ultimate Vertical load (Figure 5)

2. Max. Drag Load (Figure 6)

3. Max. Side Load (Figure 7)

4. Max. Vertical Load (Figure 8)

The loads and boundary conditions for each of the above four cases are identical to that used for

the beam model as shown onFigure 5toFigure 8.The model was broken up into spanwise

regions and each span-wise region was further broken into cap region, corner region and web

region (Figure 4). There are 30 such property regions in the finite element model and they are

symmetrical about the aircraft centerline. Each of the thirty property regions was assigned anominal thickness 6 ply symmetric lay-up, [0/ + - 45 /90]s . The design variables are the

thicknesses of 0s, 45s and 90s plies, the optimization analysis calculates the required

thicknesses of 0s,45s and 90s from which the number of plies of each are backed out. Havingobtained the required number of plies in each orientation a reasonable stacking sequence and ply

drop off details have to be then determined.


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Nastran Sol 200 Cards For Design Response, Design Constraint, Design

Variable and Design Variable to Property RelationThe model has 30 property regions and 6 plies in each region. For each of 6 plies in each of 30 property

regions we need to set up 2 design responses , one for failure index based on normal stresses and the

other failure index based on interlaminar shear stress. Therefore there are 30*6*2 = 360 response

items to set up with Dresp1 cards.

DRESP1,1,FP, cfailure,PCOMP,,5,1,1

DRESP1,360,FP, cfailure,PCOMP,,7,6,30

All of these response items ( failure indices) are limited to max value 0f 0.95 with as many DCONSTR

cards ( 360 of them):

DCONSTR,200,1,,0.95

DCONSTR,200,3606,,0.95

Z Displacement of a certain node ( 248123) is set up with another Dresp1 card and constrained to have

max and min value set by another DCONSTR card.

DRESP1,999,ZDISP,DISP,,,3,,248123

DCONSTR,100,999,14.24,14.26

The weight is set up as response number 1000 :

DRESP1,1000, WEIGHT, WEIGHT,

This is a symmetric layup [ 0/ + - 45 /90]s and there are 30 regions , so there are 30*3 =90 design

variables to set up :

DESVAR,1,TPLY,0.006,0.006,1.0

DESVAR,90,TPLY,0.006,0.006,1.0

There are 90 DVPREL1 cards needed to relate each design variable to a property card ( Pcomp) field

DVPREL1,1,PCOMP,1,13,,,,,+

+,1,1.0

DVPREL1,90,PCOMP,30,23,,,,,+

+,90,1.0


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Figure 9Vertical Displacement


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Figure 10Max. Failure Index3G Ultimate Vertical Load Case


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Figure 11Max. Bond Failure Index3G Ultimate Vertical Load Case


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Figure 12 Max. Failure Index Max. Drag Ultimate Load Case


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Figure 13 - Max. Bond Failure Index Max. Drag Ultimate Load Case


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Figure 14- Max. Failure Index Max. Side Load Ultimate Load Case


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Figure 15- Max. Bond Failure Index Max. Side Load Ultimate Load Case


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Figure 16 - Max. Failure Index Max. Vertical Load Ultimate Load Case


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Figure 17- Max. Failure Index Max. Vertical Load Ultimate Load Case


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Figure 18Eigen Value buckling Load FactorMax. Side Load Ultimate Load Case


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FEA Results Versus Test Strain Correlation

Strain Gauge Location

Test Result Micro Strain

FEA Result Microstrain

SG 13 Bot. Cap, Y = 0.0

2500

2420

SG 11 Top Cap , Y= 0.0 -2230 -2050

SG 23 Bot. Cap, Y = 30.43

2818

3270

SG21 Top Cap. Y=31.1

-2500

-2490

SG 33 Bot. Cap, y= 41.99 3068 3840

SG 31 Top Cap , Y=43.08

-2700

-3260

SG53 Bot. Cap, Y= 60.3

1750

1830

Conclusions

A robust and easy to implement shape/composite ply thickness optimization strategy has been

developed for beam type landing gear to meet stiffness, strength and weight criteria for

multiple landing load cases. The predicted strains from the finite element analysis compared

favorably with strain gauge measurements on a test article. Eigen value buckling analysis was

carried out on the optimized structure independent of the optimization solution. For future

development, the buckling check could be also be included in the optimization routine.

A Novel Optimization Strategy for Composite Beam Type Landing Gear for Light Aircraft

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