Improved Tornado Missile Risk Analysis Using Nonlinear ...psa.ans.org/wp-content/pdf/21892_PSA_2017_Present_ARA_21892.pdf · Improved Tornado Missile Risk Analysis ... • Insulation

11

INNOVATIVE SOLUTIONS TO COMPLEX PROBLEMS

www.ara.com

© 2017 Applied Research Associates, Inc. ARA Proprietary

PSA 2017 Paper 21892

Improved Tornado Missile Risk Analysis Using Nonlinear Finite Element Analysis of Nuclear Power Plant Structures

September 25, 2017

www.ara.com © 2017 Applied Research Associates, Inc. ARA Proprietary


Authors:Claudia Navarro-NorthrupRobert T. Bocchieri, Ph.D.Virginia PhanJeffrey C. SciaudoneLawrence A. Twisdale, Ph.D.

Applied Research Associates, Inc.95 1st Street, Suite 100, Los Altos, CA 94022

Improved Tornado Missile Risk Analysis Using Nonlinear Finite Element Analysis of Nuclear Power Plant Structures

2



TORMIS computer code

• Developed to estimate the probability of damage to nuclear power plant structures from debris

missile impacts in extreme winds.

• Relies on calculations for critical damage to a structure.

Critical damage to power plant structures

• Results in loss of function to the plant structure (e.g., crimping of exhaust).

• Each type of missile causes critical damage at a different impact velocity.

• Knowing this critical velocity is an important component of performing this risk analysis.

Analytical methods (e.g., SDOF) for damage analysis

• For some target/missile combinations, test data and simple analytical methods exist to predict

damage.

• Can require many conservative assumptions.

• May result in unnecessarily low critical velocities.

Nonlinear dynamic FEA

• More accurate analysis of impact damage.

• Higher critical velocities are calculated, leading to lower risk numbers.

• Now a practical and cost-effective part of TORMIS risk analysis.

Overview

3



Nonlinear finite element analysis (FEA) can model the complex, dynamic target-

missile interaction to determine accurate critical missile velocities.

‘Soft’ missiles are hard to assess with simplistic loading methods.

• These missiles crush significantly during impact, affecting the load applied to the target.

• Target response affects the missile crushing and trajectory.

• Important because they can have a high hit frequency.

Real targets often have complex boundary conditions (BCs) that affect the

target-missile interaction.

• Ignoring or simplifying the BCs can lead to much lower critical missile velocities.

Many target-missile configurations can be analyzed to determine the critical

impact location and velocity.

• Crimping is critical failure mode that can be assessed with FEA.

Overview

4



‘Soft’ missiles are missiles that are

weak compared to the target.

• Experience significant deformation during

impact.

• Generally higher hit frequencies.

• Examples include metal siding, steel

grating, and wood planks.

‘Hard’ missiles are comparable to or

stiffer/stronger than the target.

• Hard missiles have little deformation.

• Examples include a wide flange beam and a

channel section beam.

Soft Missiles

5

Metal Siding

(Soft Missile)

Steel Grating

(Soft Missile)

Wide Flange Beam

(Hard Missile)

MissileDepth

(in)

Width

(in)

Length

(ft)

Weight

(lb)

Metal Siding 24 3.6 20 255

Steel Grating 24 1.3 6 74

Wide Flange 14 5.0 15 390



Crimping is an important failure mode for

exhaust pipes.

• Exhausts from diesel generators and steam lines.

• These exhaust pipes have minimum required flow

rates to function properly.

Target description:

• 16-in diameter exhaust pipe with a rigid constraint

at the bottom.

• Pipe is in contact with a deformable roof sleeve.

• The concrete roof penetration is modeled as rigid.

Exhaust Pipe Crimping

6

16-in Exhaust Pipe

Roof

Sleeve

Roof

Penetration

Constraint

Exhaust

Pipe



Metal siding impact of

16-in exhaust pipe at

540 fps.

• Pipe shown as semi-

transparent.

Soft Missile Impact Response

7



At 8 ms:

• Max crimping has occurred.

• Missile has 65% of its original KE.

• Significant, non-uniform crushing of

missile.

o The crush shape conforms to the

deformed shape of the pipe.

• Large deformation/buckling of the

missile away from the crush zone.

At 20 ms:

• Pipe moves away from the missile.

• A plastic hinge has formed in the pipe

at the roof sleeve interface.

o Crimping in the pipe at the roof

sleeve interface.

At 76 ms:

• The missile continues to push the

exhaust pipe until the missile slides off

the pipe.

Soft Missile Impact Response

8

t = 8 ms

t = 20 ms

t = 76 ms



Wide Flange at 170 fps

Three missiles resulted in very different

crimping of the exhaust pipe.

• Missile configurations are those that resulted in

the greatest crimping at the given velocity.

• Images shown are for the time of maximum

crimping.

Steel grating:

• Similar behavior to the metal siding.

• Significant crushing at the target interface.

• Plastic deformations/buckling away from missile

crush zone.

Wide flange beam:

• Small amount of damage to missile.

o Localized bending of the flanges at the impact

interface.

o Slight bending along the missile length.

Soft vs. Hard Missile

9

Metal Siding at 540 fps

Steel Grating at 515 fps



Wide Flange 𝝋 = 0.38

The open area fraction, 𝝋, is:

𝝋 =𝑶𝒑𝒆𝒏 𝑨𝒓𝒆𝒂 𝒂𝒇𝒕𝒆𝒓 𝑰𝒎𝒑𝒂𝒄𝒕

𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑶𝒑𝒆𝒏 𝑨𝒓𝒆𝒂

Metal siding:

• Initially denting was narrow, matching missile profile.

• As the missile deformed, the load spread out

laterally, resulting in a wider crimp zone.

Steel grating:

• The crimp zone remains narrow.

• The missile deformed significantly vertically but not

laterally (the stiff direction).

Wide flange beam:

• The crimp zone remains wide.

• The missile front end does not deform significantly

and the crimp zone does not become localized.

Target Crimping Response by Missile

10

Metal Siding 𝝋 = 0.30

Steel Grating 𝝋 = 0.44

Open Area Before

Impact 𝝋 = 1



Real targets have complex shapes and boundary conditions.

• Difficult to represent in simplified analyses without large conservative assumptions.

Target constraints (even at a distance) can affect the response at the impact location.

• Soft missiles take a relatively long time to impart load.

• Target deforms and moves prior to time of maximum crimping.

• Ignoring or simplifying soft constraints (e.g., insulation) changes the target-missile interaction.

Complex Targets

11

Roof Sleeve

Exhaust Pipe and

Cover Plate

Roof Penetration

Roof sleeve and penetration shown as semi-transparent.

Insulation

Exhaust Pipe with Angled Exit

and Cover Plate.

• Insulation in the roof penetration

modeled with crush response and

lock up of the material.

• Cover plate and angle irons are

attached with welds.

• Bottom of pipe model extends

37.5 ft below the roof line (not

shown).



Metal siding impact of angled exit exhaust pipe with cover plate at 240 fps.

• Pipe shown as semi-transparent.

• Missile rebounds at late time.

Complex Target Impact Response

12



At 6 ms:

• Missile is engaged with pipe and cover plate.

o Localized crushing at the interface with target.

• Localized deformation of the exhaust pipe and

cover plate.

• Most of the welds are still intact.

At 20 ms:

• The front of the metal siding has started to buckle.

• The exhaust pipe has begun to sway back.

• Maximum crimping has occurred and the front of

the exhaust pipe has impacted the back of the

pipe.

At 34 ms:

• Significant buckling of the missile.

• All welds in the target have failed.

At 82 ms:

• The missile has buckled along its length, well away

from the target interface.


13

t = 6 ms t = 20 ms

t = 34 ms t = 82 ms

Partial missile shown.



Cover plate inhibits deflection

of the metal siding away from

the exhaust pipe.

The buckling of the missile at

multiple missile locations has

changed loading on the target.

• Buckled regions reduce load

applied and deceleration of

missile.

• Missile buckling, and target

deformation, has affected the

missile trajectory, allowing the

missile to deflect vertically and

laterally.


14

t = 82 ms

Side View

Top View



In previous simulation, a deformable

insulation constitutive model was

used for the crush response and

lock up of the material.

• Conservatively modeling the insulation as

rigid provides a stiff constraint that

maximizes crimping.

• Ignoring the insulation results in less

crimping

o The air gap allows the pipe to sway out

of the way during impact.

Impacts to 3 models with a wide

flange beam at 112 fps give very

different responses.

Insulation Modeling

1515

t = 6 ms

t = 20 ms

t = 34 ms

t = 82 msPartial missile shown. The roof penetration, roof sleeve,

and insulation are all shown as semi-transparent.

No

InsulationRigid

Insulation

Insulation 𝝋

Rigid 0.29

Deformable 0.50

None 0.57

Deformable

Insulation

t = 34 ms

t = 24 ms



Many different target-missile

configurations can be analyzed.

• Critical location for complex targets and soft

missiles depends on the target-missile

interaction.

• Not known a-priori.

Configuration A:

• Lowest missile impact location without impacting

roof sleeve.

Configuration B:

• Exhaust pipe rotated so the missile impacted the

exhaust pipe to the side of the angle irons.

Configuration C:

• The missile was rotated 90˚.

Configuration D:

• Missile impacts the tallest side (rear) of the

angled pipe.

Complex Target – Critical Impact Location

1616

Configuration A Configuration B

Partial missile shown.

Configuration C Configuration D



1717

Configuration A Configuration B

Pipe shown as semi-transparent.

Configuration C Configuration D

Complex Target – Critical Impact Location



Plots of open area fraction (𝝋) versus

velocity highlight the critical configurations.

Configuration A:

• Analyzed at 240 fps and 250 fps with little change

in 𝝋.

• At 240 fps, the missile has pushed the front of the

exhaust pipe against the back of the pipe, not

allowing for any more crimping.

Configuration B:

• Less crimping than Configuration A.

• Impacting higher on the pipe on more of the curved

exhaust face reduces the amount of crimping at

the same velocity.

Configuration C:

• The least effective at pipe crimping.

Configuration D:

• Most effective at crimping.

Critical Impact Location

1818

A B C D



Nonlinear FEA using LS-DYNA was demonstrated to accurately model complex target-

missile interaction

• Many of the behaviors shown cannot be easily, if at all, modeled with simple analytical methods.

Soft missiles crush and deform affecting the target response.

• Soft missiles have a longer impact duration allowing the target to respond and affecting the overall target-

missile interaction.

• Critical impact location varies by missile type.

Constraints and adjacent structures surrounding a target can also affect the target-

missile interaction.

• In particular, soft boundary conditions, such as insulation, result in a very different target response.

LS-DYNA was used for all the FEA shown here.

• LS-DYNA is commercially available (developed by Lawrence Livermore National Laboratory).

• LS-DYNA has an extensive user community that helps validate the code for a variety of applications

including crash, blast, and impact.

Nonlinear dynamic FEA is now a practical and cost-effective part

of TORMIS risk analysis.

Summary

19



Questions?

20

A category 2 hurricane has

maximum sustained winds

of 129 mph (189 fps).

Documents

Improved Tornado Missile Risk Analysis Using Nonlinear ...psa.ans.org/wp-content/pdf/21892_PSA_2017_Present_ARA_21892.pdf · Improved Tornado Missile Risk Analysis ... • Insulation