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.

What is the U*?(Cont.)

UUU

11*

Case (1)

Eq.1 Definition of U*

(1) (2)

Case (2)

U U’

What is the U*?(Cont.)

• Contour of U* value

U*=1 at Loading point

U*=0 at Constraint point

What is the U*?(Cont.)

• Identification of load paths through U*Contour

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