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Boundary Element Analysis at Caterpillar

Ling PanCaterpillar Inc.

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EZBEAEasy Boundary Element AnalysisOriginated from ‘70’s code at Kentucky State

Owned & enhanced significantly by Caterpillar

Model external boundary only Meshing is much easier, especially with

details & small holes Accurate with coarse triangles, quads

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StrengthExcels on Geometry with

Complicated DetailsLookingInside

Brake Stand for C9 Engine

IntersectingHoles

- Still difficult to tet-mesh

- “Easy” to surface-mesh

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ApplicationsEngine components

Fuel injector Crankshaft

Powertrain components Gear Shaft

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Challenges Longer solve time compared to FEA

analysisNonlinear (contact) analysis Not suitable with thin body

(fabricated) structures

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EZBEA+EZBEA+ - provides integration with

Pro/MeshEZBEA Menus

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EZBEA CapabilitiesAnalysis types

steady-state heat conduction

static thermoelasticity beam section

propertiesDomain types

planar axisymmetric general 3D

Material Isotropic, linear, 1 per

subregionSymmetry:

planes of geometric symmetry

planes of loading symmetry/anti-symmetry

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Loading and Boundary Conditions Only linear, static loads and boundary conditions

point load constraints edge pressure constraintssurface pressure constraints surface displacement constraints

Loads and boundary conditions in nature have area associated with them.

A true point load is impossibleA knife edge constraint is impossible These loads would result in infinite stress

EZBEA Capabilities

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An Example: 9881 nodes, 20 hours on HP C240

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Current Models size vs. Time Plot on HP C240

EZBEA V4.5 Elapsed Time vs Problem Size for HP C240

0

2

4

6

8

10

12

14

0 10000 20000 30000 40000

Degrees of Freedom

Elap

sed

Hou

rs

Elapsed time

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Speedup

EZBEA Elapsed Time vs Problem Size for Three Versions(Logarithmatic Scale Plot)

0.001

0.01

0.1

1

10

100

0 5000 10000 15000 20000 25000 30000 35000

Degrees of Freedom

Elap

sed

hour

s

v3.30 on HP9000/755

v4.00 on HP 9000/755

v4.50 on HP C240

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Future WorkEliminate the physical limit on

number of elements and nodes dynamic memory allocation scratch files accuracy issue when elements get

smaller(double precision)

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Future WorkSolver improvement (performance

issue) improve current solver (direct solver,

O(N3)) iterative solver (O(N2))

Caterpillar has looked into this before Does not always converge for large

problems

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Future WorkMultipole accelerated BEM (O(NlogN)

operations) significant performance gain has to use iterative solver convergence for large problem

questionable would involve significant work

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Future WorkContinue gap, contact work

capability to analyze assembliesimplement line integral for thinner

structures improve accuracy