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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
PATRAM 2013 4Olaf Schilling
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
PATRAM 2013 5Olaf Schilling
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
PATRAM 2013 6Olaf Schilling
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
PATRAM 2013 7Olaf Schilling
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
PATRAM 2013 8Olaf Schilling
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
PATRAM 2013 9Olaf Schilling
� 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
PATRAM 2013 10Olaf Schilling
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
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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
PATRAM 2013 11Olaf Schilling
� 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)
PATRAM 2013 12Olaf Schilling
� 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
PATRAM 2013 13Olaf Schilling
� 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
PATRAM 2013 14Olaf Schilling
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
PATRAM 2013 15Olaf Schilling
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
PATRAM 2013 16Olaf Schilling
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
PATRAM 2013 17Olaf Schilling
� 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