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Application of Load path U* Analysis for
Vehicle Chassis by Natran new U* toolkit
May 17, 2011
MSC.Software Japan
Hiroaki Masaki
Agenda
• Introduction
• What is U*?
• Difficulties of U* calculation
• What is U* Toolkit?
• Example
• U* vs. conventional method
• Conclusion
Introduction
• Importance to understand load path
– To make sure a structure will perform properly.
– For optimum material utilization.
– To assess the overall integrity of structure.
– To check performance of structure when damaged
• Traditional indexes for load path
– Principal stresses and its direction
– Strain
– Strain Energy
• What is the problem of above method?
Introduction : Problems
• Simple plate with hole
– Major principal distribution
• Misleading
– More loads be transferred through concentration area?
What is the U*?
• U* has been introduced by Keio Univ. Prof. Takahashi.
• U* is a new index to express the connectivity between the
loading point and an arbitrary point in a structure.
– Based on the relative strain energy ratio
– Rather than local stress or strain energy
• We can understand the structure comprehensively from U*
distribution.
Difficulties of U* calculation
• Calculation Cost
– Need to calculate U* values at many nodes of FE model to
obtain U* distribution and the location of the load paths.
– Too many static load cases are required to calculate U*
distribution.
– Huge disk space
– Long CPU time
10 [sec/case] x 1,000,000 [case] = 10 M [sec] = 115.7 [days]
This is not applicable for customer’s daily use.
• U* can’t be calculated with standard FE program.
– Customized tool is required.
What is U* Toolkit?
• What is U* toolkit?
– U* calculation formulation is included.
– Specialize algorithm called for iterative Nastran static
analyses using DMAP to reduce calculation costs.
• Values
– The calculation time is reduced drastically.
– Required disk space is also reduced.
– Designer can understand the load transfer in body structure
and make better design and/or effective reinforcement.
What is the U*?(Cont.)
CACAAAA
B
dKdKp
d
0
AAAA
CB
dKp
dd
00
ACACAAA
AA
ddKdK
dpU
2
1
2
1
AAAA
AA
ddK
dpU
2
1
2
1
Eq.3(1) Strain Energy for case (1) Eq.3(2) Strain Energy for case (2)
(1) (2)
C
B
A
CCCBCA
BCBBBA
ACABAA
C
B
A
d
d
d
KKK
KKK
KKK
p
p
p K : Relative stiffness
p : Force vector
d : Displacement vector
Eq.2 : Load-Disp. relation
U* toolkit : Reduction of calculation costs
• Formulation
ACACAAA
AAAA
ddKdK
ddK
U
U
– U, dC and dA can be calculated in case(1).
– Necessary to calculate KAC for all point.
– U* calculation reduces to calculate KAC values.
• Original boundary condition
– In original definition, many SUBCASEs with different BCs are
needed.
– Decomposition cost is very high.
ACAC ddKUU 2
1
1
* 21
11
ACAC ddK
U
UUU Eq.4
U* toolkit :Reduction of calculation costs (Cont.)
• Boundary condition change for KAC calculation
– Convert
SUBCASEs for multiple BCs & one loading cond.
into
SUBCASES for one BC & multiple loading cond.
– Case (3) is used to calculate KAC ,.
(3)
C
B
A
CCCBCA
BCBBBA
ACABAA
C
B
A
d
d
d
KKK
KKK
KKK
p
p
p
1
00
CAAC
CACA
BA
dRK
dKR
dd
(2)
RA
U* toolkit :Reduction of calculation costs (Cont.)• Change of calculation flow
• Specialize to calculate KAC efficiently
• Elapsed time & disk usage reduced to 1/3 or less
Standard Nastan
commoditized1 Pre-Process
2 LU Factorization
3 FB Substitution
4 Quality Checking
5 Data Recovery
3 FB Substitution
5,6 Recovery & Export
7 U* Calculation
1 Pre-Process
2 LU Factorization
6 Data Exportaion
commoditized
omitted
omitted
speeding up
FASTUSTAR
Performance example
• Sample Model
– Grid 170,000
– Shell 164,000
• Used Software
– MD Nastran R3
– U* toolkit for MD Nastran R3
• Used computer
– Linux Red Hat EL5.5
– Intel Xeon CPU X5677 3.47GHz x 8 (2CPUs quad core)
– 96 GB memory
Performance Example (Cont.)
• Case 1
– Ordinary : 3,000 SUBCASEs
– U* method : 1,000 points (=3,000 DOF)
- 82% - 89%- 74%
Performance Example (Cont.)
• Case 2
– Ordinary : 30,000 SUBCASEs
– U* method : 10,000 points (=30,000 DOF)
- 91% - 97% - 90%
U* vs. Conventional Method
• Topology Optimization
– Implemented in most FEM codes, such as MD Nastran
– Enable to find out better design.
– This optimization tends to remain elements at the load transfer
path.
– Topology/topometry optimization show “a final result”.
U* vs. Conventional Method (advantage of U*)
• Shows current load path condition with current design.
• Users can change their design freely by
– Reducing material
– Adding some parts or reinforcement.
– Changing its shape
• Topology optimization can only remove elements.
• Load path based on U* toolkit is helpful information for
designer.
– This will be available in near future.
Conclusion
• Principal stresses and strain energy are used to find load
transfer path, but these are inadequate.
• U* is newly introduced parameter to express load transfer
path.
• U* distribution is very helpful to understand structures.
• With ordinary method, U* analysis might require huge
calculation costs, but U* toolkit can reduce them drastically.
• Users can change their design freely by
– Reducing material
– Adding some parts or reinforcement.
– Changing its shape
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