Analytical Approaches within the Assessment Strategy … · Analytical Approaches within the...

Analytical Approaches within the Assessment Strategy

of Numerical Analyses of RAM Packages

Olaf Schilling, TÜV Rheinland Industrial Services, GermanyLars Müller, Viktor Ballheimer, Steffen Komann, Frank Wille,

BAM Federal Institute for Materials Research and Testing, Germany

Session A Package Analysis: Structural Analysis - Modeling

Dr. Frank Wille - INMM 52nd Annual Meeting - 2

Analytical Approaches within the Assessment Strategy

of Numerical Analyses of RAM Packages

Olaf Schilling

TÜV RheinlandIndustrial ServicesBerlin, Germany

Lars Müller, Viktor Ballheimer, Steffen Komann, Frank WilleBAM Federal Institute for Materials Research and Testing

Berlin, Germany

PATRAM 2013 San Francisco, August 18-23

PATRAM 2013 3Olaf Schilling

� Aspects of mechanical safety assessment of RAM packages

� Competent authority in Germany is BAM Federal Institute for Materials Research and Testing

� TÜV experts are authorized from BAM for subtasks

� Demonstration of compliance with national and international transport

regulations required for each package design

� European PDSR-Guide assists in preparation of Package Design Safety Report

� BAM guidelines * regulate parts of mechanical design calculations

� BAM-GGR 011: Definition of safety objectives ** and classification ofcomponents

Overview

*) E.g. GGR 008: Numerical safety analysis; GGR 012: Lid systems and load attachment points**) Shielding, containment, integrity, prevention of criticality


Component Classification according BAM GGR 011and Analysis Approaches

� Other influences on design calculation effort:• Safety margin • Geometrical and structural (material properties) complexity

Componentclassification

examples Usual analysis approaches

Grade 3(low safety relevance)

Type plate, O-rings Sometimes analysis not necessary

Grade 2Shock absorber, closing plate, pressure springs

Often analytical calculations or estimations sufficient (nominal stresses)

Grade 1(high safety relevance)

Cask body, primary-, secondary lids, small lids, trunnions

Detailed numerical analysis(FEM, local stresses)

� Detailed numerical calculations recommended for Components with high safety relevance


Calculation Effort in Design and Assessment

De

sig

n

eff

ort

Grade 1 Grade 2 Grade 3C

1

B1

A1

C2

C3

A2

A 3

B2

B 3

Numericalcalculations

Analyticalcalculations

� Assessment effort proportional to design effort

� Design effort increases with safety relevance and component complexity

Safety relevance


Enhanced Assessment Strategy

� Purpose: optimized assessment strategy

Analyticalcomparison

Re-simulation

Pre / postcheck

Num

eric

al

calc

ulat

ions

A

naly

tical

ca

lcul

atio

ns

Design

Assessment

� Optimization options in check of numerical calculations higher

• Complete re-simulation

• Check of decisive load cases in detail,plausibility check for others

• Analytical comparative calculations

� Always check of applicability and plausibility

� Check of analytical calculations

• Own analysis


Values to calculate Analytical Numerical

Nominal stresses in cask components under applicable conditions of transport

Limited, depending on the geometrical shape of component

Local stresses in cask components under applicable conditions of transport

Limited, inaccurate Yes

Assembly pretension of bolts StandardNot practicable: high

modeling effort

Pretension changes due to temperature and relaxation

Yes

Nominal stresses in bolts under applicable conditions of transport

Limited Yes

Local stresses in bolts under applicable conditions of transport

NoNot practicable: high modeling efforts

Lack of any adequate assessment concepts

Scope of Analytical and Numerical Calculations

Possible use of analytical comparitive calculations


Theories of Structural Mechanics and Possible Applications on Components of RAM Packages

Beam

Friction / rigid body mechanics

Shell

Contact mechanics

Plate

Lids and closing plates under transversal loads(internal pressure, inertia, ...)

Package under puncture drop test (only estimation)

Bolts under assembly forces and lid displacement

Trunnion in a support Packages on cargo area,fuel assemblies in basket


� Internal forces above thread Axial force 200 kNLateral force 40 kNBending moment 928 Nm

� Nominal stresses pretension 288 MPamax. bending 633 Mpa

� Maximum displacement of bolt head0.11 mm

Example 1: Bolt Bending due to Lid Displacement /Numerical Model and Results

� Bolt M30x120 (DIN EN ISO 4762)

� Thread to cask tied contact

� Bolt head to lid friction (0.2)

� Loads: 200 kN pretension,1 mm lid displacement

(time)

dis

pla

ce

me

nt

lid

bolt head

Numerical model

Results


Example 1: Bolt Bending due to Lid Displacement /Analytical Approach and Comparison of Results

FP

FC

s

M0

dslsLateral force

Max. displacement of bolt head

Bending moment due to

Fp

Bending moment due to

Fc

Pretension stress

Bending stress

�� ∗ � � �� ∗ ��

�

�� ∗ ∗ ��

�� ∗ �

��

�� ∗ ��

��

��

�

��

��

Value Numeric Analytic

Axial force 200 kN = 200 kN

Lateral force 40 kN = 40 kN

Bending moment 928 Nm ~ 956 Nm

Pretension stress 288 MPa ~ 283 MPa

Max. bending stress 633 MPa ~ 644 MPa

Max. displacement of bolt head

0.110 mm > 0.044 mm

Basic approach: Bernoulli beam theory

Analytical formulas for bending

Comparison of results

in good accordance

discrepancy →→→→ further analysis required


� Results

• Scope of theories has to be considered

• Numerical results between analytical results for fixed and free support

Example 1: Bolt Bending due to Lid Displacement /Causes of Discrepancy in Displacement

Theory / model

Boundary condition

FixedPartiallyfixed

Free

Bernoulli 0,044 0,177

Timoshenko 0,081 0,212

FEM 0,110

Problematic area

Bolt head displacement in mm

� Boundary stiffness

• In numerical model small rotation of bolt head → bolt head partially fixed as in reality

• In analytical model realistic boundary stiffness difficult to realize→ bolt head either fixed or free

� Component stiffness

• Bolt thickness to length ratio 1:1.6

• Scope of Bernoulli theory (ratio < 1:5)

• Scope of Timoshenko theory (ratio < 1:3)


� Boundary conditions / loads• only axial loads → segment sufficient

• symmetry conditions on cut surfaces

• bottom side of cask cutout vertically fixed

• tied contact bolts to cask

• frictional contact between other parts

• bolt pretension

• line loads for compressed metallic gaskets

• ACT: consideration of 50 g (content and modeled components)

Example 2: Lid system / Properties and Numerical Model

� High requirements → detailed analysis

� Modeled area: primary and secondary lid, bolts, cask body cutout

� Of particular interest: widening in area of metallic gasket


� Basis: classical Kirchoff plate theory

� Special case: circular or annular plate, rotationally symmetric surface load

� Solution of differential equation contains four integration constants

� Primary lid: line load (metallic gasket), change in thickness→ three concentric areas of integration → 12 integration constants

� Adjustment of solution by 12 boundary and transition conditions

� Difficult to model: stiffness of bolt connection, rotation point

� Two limiting cases examined: (a) plate clamped in area of bolt pitch circle(b) simple supported at outer edge

Example 2: Lid system / Analytical Model


Example 2: Lid system / Comparison of Results

Displacement in vertical direction [mm]

� Numerical result in the limits of analytical results� Analytical approach helps to assess the numerical calculation


Example 3: Trunnion / Properties and Numerical Model

support,movable inload direction

symmetry plane

lifting load(remote force)

bolt pretension

Half model of trunnion

� High safety requirements → detailed analysis necessary� Usually local stresses required for fatigue analysis� Compact geometry


Example 3: Trunnion / Results

Equivalent stress (v. Mises) [MPa]

Total displacenment [mm]

� Analytical model?� Compact component → outside scope of beam theory

� No simple and verified analytical model for comparative calculation

� Confirmation by numerical results:� Nonuniform distribution of stress and deformation / local effects


� Possibilities and limitations of analytical approaches

• Applicable basic structural mechanical theories

• Fast localization of solution area (plausibility)

• Scope of theories has to be considered

• Usually not applied for calculations of local stresses

Conclusion

Analyticalcomparison

Re-simulation

Pre / postcheck

Assessment effort

� Assessment effort

• Depends on safety requirements, geometrical and structural complexity and safety margin

• Proportional to design effort

• Especially high for complex numerical calculations

• Sometimes analytical comparative calculations helpful


Thank you for your attention!

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