KEPIC WEEK 2017

동적하중이 부가되는 구조에 대한 KEPIC 붕괴하중적용법에 대한 고찰

2017. 09. 07

유용균, 유제용

Contents

Motivation

Stress Limit for KEPIC Linear Analysis

KEPIC Plastic Analysis

Case Study

Alternative approaches

Our suggestion

Conclusions

Motivation

소성해석 방법론 (MNB3228)

• 극한해석 (MNN 3228.1) 및 소성해석 (MNB3228.3)

• 일반막응력강도(MNB 3221.1), 국부막응력강도(MNB 3221.2), 1

차 막응력+1차 굽힘응력강도(MNB 3221.3) 면제

• 셰이크다운 해석 (MNB 3228.4)

• MNB 3222.5 및 MNB 3227.3 면제

• MNB 3221.2, 3222.2, 3222.5, 3227.3 면제

• 일반적으로 선형해석방법에 비해 더 큰 설계마진을 가질 수 있음.

• MNB 3213.25(소성해석-붕괴하중), MNB 3213.28 (극한해석-붕괴하

중)방법은 동하중에 적용하기 애매함

• 동하중에 대해서 탄소성 해석방법을 적용할 수 있는가?

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KEPIC MNB 3000

Design by Rule

Design by Analysis (MNB-3200)

• Linear Analysis

• Limit Analysis (MNB-3228.1)

• Experimental Analysis (MNB-3228.2)

• Plastic Analysis (MNB-3229.3)

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Stress Limits for Linear Analysis (1)

Stress Limit

• Design

• Level A : normal condition

• Level B : upset condition

• No damage to the component that requires repair.

• Level C : emergency

• Permit large deformations in areas of structural discontinuity which may necessitate the removal of the component or support from service for inspection or repair of damage.

• Level D : faulted

• Permit gross general deformations with some subsequent loss of dimensional stability and damage requiring repair, which may require removal of the component or support from service.

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Stress Limits for Linear Analysis (2)

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Sm for Design Load= 2/3 Sy yield (excessive deformation)or 1/3 Su ultimate tensile strength (plastic instability or burst)

Sm for Level D= 2.4 Syor 0.7 Su ( factor of safety : 1.43)

[1]

Stress Limits for Linear Analysis (3)

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Only for rectangular section![1]

Stress Limits for Linear Analysis (4)

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Stress Limits for Linear Analysis (5)

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Stress Limits for Linear Analysis (6)

Primary & Secondary Stress

• Primary stress

• Required for equilibrium with an applied “mechanical” load.

• Pressure -> hoop stress

• Self-weight -> primary bending stress

• Secondary stress

• Developed by the constraint of adjacent materials or by self-constraint of the structure

• Self-limiting

• Thermal expansion stress

• mechanical load (including gross structural discontinuity)

• Peak stress

• Increment of stress which is additive to the primary + secondary stresses by reason of local discontinuities or local thermal stress.

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Secondary Stress Limit

Ratchet

Shakedown to Elastic Action

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Is It Primary or Secondary stress?

• The fallback position seem to be to consider all stresses as

primary. -> unreasonable.

• The key is that primary stress is required for equilibrium with

an applied mechanical load.

• The shear and moment at the discontinuity are secondary in

nature

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Disadvantage of Linear Analysis

• Primary? or Secondary?

• Stress is not real

• Require to construct stress classification lines(SCLs)

• Time-consuming

• Overly-conservative for some complex 3-D structure.

• Entire structure can not be assessed simultaneously

• Analyst select the most onerous locations for SCLs.

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Plastic Analysis

• Elastic-plastic material model

(including strain hardening

effects)

• Geometric nonlinearity (large

displacement theory)

• 2/3 of collapse load

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Limit load analysis

• Requirements for protection against plastic collapse

• Elastic-perfectly plastic model. (not elastic-plastic analysis)

• Small displacement theory

• nonlinear geometric effects are not considered!

• equilibrium is satisfied in the unreformed configuration.

• Pallowable = 2/3 maximum load

• Method

• Discontinuity layout optimization

• Maximum load achieved directly prior non-converge.

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PVRC Bust Disk Test (1)

• PVRC Burst Disk Test with Comparison to the ASME Code [2]

• 304 SS Burst Disk – 46.9 MPa

• Failure at the center of the disk by ductile rupture

• ABS-C Burst Disk – 25.9 MPa

• Failure at the center of the disk by ductile rupture

• A-533-B Burst Disk – 36.5 MPa

• Failure at the built in edge of the plate by cracking

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PVRC Bust Disk Test (2)

• PVRC Burst Disk Test with Comparison to the ASME Code [2]

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SSSD – small strain small displacement (limit analysis)LSLD – large strain large displacement (elastic-plastic analysis)

PVRC Bust Disk Test (3)

• Increase in structural strength due to strain hardening

• Geometric strengthening as the plate deforms into a spherical

shape

• And more?

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PVRC Bust Disk Test (4)

• Linear Analysis

• 0.5MPa * 2/3 = 0.33MPa

• Limit Analysis

• 1.2MPa * 2/3 = 0.8MPa

• Elastic-Plastic Analysis

• 1.1MPa x 0.5 x 2/3

= 0.73MPa

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FEA and DBA stress criteria

• When DBA(Design by Analysis) was developed, shell analysis was the

standard method for determining stresses in a vessel. With shell

analysis, membrane stress and bending stress are a direct output of the

analysis

• Identification of primary stresses versus secondary stresses is

relatively straightforward but still requires judgement.

• Stress intensity do not represent single quantities, but set of six

quantities representing the six tress components

• Some people say that design-by-analysis stress criteria are not

applicable for FEA.

• Many papers about stress criteria and linearization method -> not clear.

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Nozzle-to-shell junctions example

• A Comparison of design by analysis techniques for evaluating

nozzle-to-shell junctions per ASME section VIII division 2 [3]

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Limit analysis vs. Linear analysis

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• Axial load

• Limit load: 1600N

• Linear : 1440N

• Bending moment

• Limit load : 1576 N.mm

• Linear : 1595 N.mm

• Axial load + Bending moment

• Limit load = 0.8125(<1!!)

x Maximum load of linear analysis

Limit Load Analysis under Dynamic Load

• Requires the limit load be compared to the equivalent static load

• But, not explicit guidance on representing dynamic loads in static

equivalent.

• Limit load analysis to dynamic problem is not clear

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Static load can NOT represent above 2nd mode response

Alternative approach

• M. R. Booth, Applying Finite Element Based Limit Load Analysis

methods to Structures under Dynamic Loads [4].

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Our Suggestions (1)

• Load – Strain/Deformation curve

• Max. over time / Residual value

• No clear limit loads

• Material after yield can absorb the energy through permanent

deformation and does not show any collapse

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1.0 x P(t)1.1 x P(t)1.2 x P(t).....2.0 x P(t)

Our Suggestions (2)

• For Level A or B load,

• No permanent deformation -> Limit analysis

(assume no strain hardening)

• For Level C or D load,

• Allow permanent deformation ->plastic analysis

(assume stain hardening)

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Max. Strain or Deformation Based

Approach?

• NB-3213.25 Plastic Analysis – Collapse Load

The collapse load is the load at the intersection of the load–deflection or load–

strain curve and the collapse limit line. If this method is used, particular care

should be given to ensure that the strains or deflections that are used are

indicative of the load carrying capacity of the structure.

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For strain based approaches,

At Collapse limit load, plastic strain = elastic strain

Load-deformation(stain) curve & Limit load

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Deformation Based Approach?

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What is maximum deformation for limit analysis?

1st mode

3rd mode

Load – Strain/Deflection/Compliance Curve

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mmJ

Mesh Dependency of Strain

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0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 0.2 0.4 0.6 0.8 1 1.2

Mesh Size - Maximum elastic - plastic strain

elastic plastic total

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 20 40 60 80 100 120

Mesh Size-1 - Maximum elastic/ plastic strain

elastic plastic total

0.0005

0.005

0.01 0.1 1

Mesh Size - Maximum elastic - plastic strain

elastic plastic total

0.0005

0.005

1 10 100

Mesh Size-1 - Maximum elastic/ plastic strain

elastic plastic total

Mesh Dependency of Strain

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0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

0 20 40 60 80 100 120

Mesh Size-1 – elastic strain

Mesh dependency of Strain Energy

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0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 1/mesh size

Maximum Strain Energy

Residual Strain Energy Approach

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Strain energy

Stress

Summary of Our Suggestion

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1.0 x P(t)1.1 x P(t)1.2 x P(t).....2.0 x P(t)

For Design, Level A,BNo strain hardeningMeasure: Strain energy (or Strain)

1. Maximum over time2. Residual after loading

For Level A,B Secondary stress-> Shakedown analysis(plastic)

For Level C -> Limit load analysis

For Level D -> Plastic analysis

Conclusions

• KEPIC의 선형 해석 방법은 오랫동안 검증된 훌륭한 방법론임.

• 하지만, 복잡한 3차원 형상에 적용하는 경우 과도하게 보수적으로 설계될 수

있음.

• 탄소성 해석을 이용하면 선형해석 방법보다 합리적으로 설계가 가능하나 현재

KEPIC 규정상에서는 동하중을 적용하기가 모호함.

• 기존의 등가정적하중을 적용하는 방법은 시스템&하중의 고유진동수의 관계

에 따라 큰 오류를 가질 수 있음.

• 동적하중이 부가되는 경우에도 탄소성 과도해석을 수행하여 건전성 평가가 가

능함. 이때 Strain 뿐만 아니라 Strain energy를 기준으로 Limit Load를

계산하는 것이 가능함.

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References

• [1] G. C. Slagis, ASME Section III Design-By-Analysis Criteria

Concepts and Stress Limits, Journal of Pressure Vessel Technology,

2006

• [2] D. P. Jones 외, Elastic-Plastic Analysis of the PVRC Burst Disk

Tests with Comparison to the ASME Code Primary Stress Limits, Bettis

Atomic Power Laboratory, 1999

• [3] P. E. Prueter 외, A Comparison of Design by Analysis Techniques for

Evaluating Nozzle-To-Shell Junctions per ASME Section VIII Division 2

• [4] Martin R. Booth, Applying Finite Element Based Limit Load Analysis

Methods to Structures under Dynamic Loads, Proceedings of the ASME

2014 PVP Conference.

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