Y. S. Yang and S. H. HsiehNational Taiwan University,

Taipei, Taiwan

December 8, 2000

FE2000: An Object-OrientedFramework For Parallel Nonlinear Dynamic Finite Element Analysis

Develop a parallel FEA test bed

– High performance

– Parallel computing (substructure method)

– Good extensibility & maintainability

Introduction (1/2)

Introduction (2/2)

FE2000– Object oriented– Linear / Geometric nonlinear analysis– Static / Implicit dynamic analysis– Sequential / Parallel computing

Key classes (1/3)

feAssemblage– Uses dynamic arrays for FE objects

• vector<feNode*>• vector<feElement*>

• ANSI C++ Supported• Useful for adaptive mesh refinement

Key classes (2/3)

Hierarchy of feElement

feElement

feB8Element

feB20Element feBCElement

feTrussElement

feSuperElement

Key classes (3/3)

2D-frame structure examplefeA ssemblage

O b jec t

E lem en t # 2E lem e n t # 1N o d e # 2

N o d e # 1 N o d e # 3

feNodeO b jec t # 1

feNodeO b jec t # 1

feNodeO b jec t # 3

feBCE lementO b jec t # 1

feBCE lementO b jec t # 2

(a ) A f in ite e lem n e t a n a ly s is ex am p le (b ) O b je c t re la tio n sh ip in F E 2 0 0 0

Substructure analysis

Multi-level substructure hierarchy

Iterative mesh partitioning approach– Improved Hsieh-Yang-Tsai (IHYT) approach

for better computational load balance (Yang, 2000)

(a ) In it ia l m es h(lev e l 0 )

(b ) S u b s tru c tu re A(lev e l 1 )

(c ) S u b s tru c tu re B(le v e l 1 )

(d ) S u bs tru c tu re A A(lev e l 2 )

(e ) S u b s tru c tu re A B(lev e l 2 )

(f ) S u b s tru c tu re B A(lev e l 2 )

(g ) S u b s tru c tu re B B(lev e l 2 )

Proc 0

Proc 1

Proc 2

Proc 3

Proc 0

Proc 2

Proc 0

Matrix libraries (1/2)

For solving [K]{d}={f}– Extended SPARSPAK (George and Liu, 1981)

• Direct, sequential• Linear system solution/matrix condensation

– SPOOLES (Ashcraft et al., 1999)

• Direct/Iterative, sequential/parallel– PETSc (Balay et al., 1997)

• Iterative, sequential/parallel

Matrix libraries (2/2)

Interface between FE2000 and matrix libraries

Validation tests

Static nonlinear analysis

P

V

U

0.01 P

0

1

2

3

0 0.2 0.4 0.6 0.8 1

Displacements V/L

P/Pc

r

BCB20

Dynamic analysis

F

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1T (sec)

D/Do

BCB20

Numerical experiments (1/2)

Nonlinear dynamic analyses– Analysis methods

• Newmark method (avg. accel.) • Total t = 0.2 sec., Δt = 0.01 (20 time steps)• Geometric nonlinearity• Sequential / Parallel multi-level substructure method

– Computing environment• 4 PCs (Pentium II 350) + 100 Mbps network• Linux Redhat • FE2000 + Extended SPARSPAK

Numerical experiments (2/2)

2165

675

Seq. Par.

H5-1211,568 BCs25,344 DOFs

4057

1605

Seq. Par.

O1-1235,904 BCs181,152 DOFs

19679

4370

Seq. Par.

M12BD-24,032 B20s64,809 DOFs

2509

9113

Seq. Par.

B20P64162,048 BCs34,767 DOFs

S=2.89 S=2.48 S=3.60 S=3.15

Conclusions & future works

FE2000– An efficient object-oriented parallel nonlinear dynamic

FE package. Future works

– More element types (plate, shell, etc.)– More material models– Adaptive mesh refinement– Pre/post processing