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Acoustic Simulation Seminar

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Title: Acoustic Simulation Seminar


1
Acoustic Simulation Seminar
2
BEASY Home Ashurst Lodge
3
Administrative Issues
  • Fire Exits
  • Assembly point by flagpoles
  • Toilets
  • Messages
  • Reception

4
Computational Mechanics
  • Group formed in 1978
  • Headquarters -
  • Southampton England
  • Billerica Massachusetts USA
  • Main Activities -
  • Software
  • Publishing
  • Training
  • Research Development

5
Group Activities
6
Computational Mechanics Worldwide
  • Clients in over forty countries
  • Head office in Southampton,UK
  • North American office in Billerica Massachusetts
  • Software and services partners worldwide

7
BEASY
  • Development of BEASY Software
  • Sales and Marketing of BEASY products
  • Support services
  • Customisation services
  • Training
  • Consultancy
  • Software development and R D

8
BEASY support service
  • www site for news and updates
  • email support
  • ftp for updates and support
  • Hot line support service
  • Training courses and seminars
  • In company training service
  • Newsletter
  • User Group meetings
  • Maintenance
  • Consultancy

9
Mathematical Modelling and Numerical Methods
  • Our team of engineers offers
  • extensive expertise and experience of modelling
    problems in many different application areas
  • a thorough understanding of computer and
    numerical methods and their associated
    limitations
  • customised simulation tools and software
    development
  • intelligent application of modelling tools and
    analysis of results
  • the development of new techniques

10
Project Management
  • Partial list of clients
  • Rolls-Royce (UK)
  • GKN Westland Helicopters (UK)
  • Shell (Netherlands)
  • General Electric (USA)
  • Conoco (Norway)
  • United States Navy (USA)
  • European Space Agency (Netherlands)
  • Ford (USA)
  • Honda (Japan)
  • Hamilton Standard United Technologies (USA)

11
Our Clients
  • A selected list of our clients is given below
  • BAESystems (UK)
  • Alstom Power (Switzerland)
  • Ford (USA)
  • Ansto (Australia)
  • Clay Technology (Sweden)
  • Rolls-Royce (UK)
  • Volkswagen (Germany)
  • Agusta Westland (UK)
  • Alfa Avio (Italy)
  • Boeing (USA)
  • KOGAS (Korea)
  • Suzuki (Japan)
  • NPL (UK)
  • Hamilton Sundstrand United Technologies (USA)
  • NASA (USA)
  • Kockums (Sweden)
  • Chevron (USA)
  • US Navy (USA)
  • Defence Evaluation Research Agency (UK)
  • Engage (UK)
  • Mobil (USA)
  • Bombardier (Canada)
  • Cyfronet (Poland)
  • DSTO (Australia)

12
BEASY Applications Areas
13
BEASY Products
  • BEASY Mechanical Design
  • Stress, thermal and contact simulation
  • BEASY Fatigue and Crack Growth
  • Crack growth simulation and multi site damage
  • BEASY Corrosion and CP
  • Corrosion control simulation and interference
    prediction
  • BEASY CRM
  • Corrosion simulation,ICCP and related electric
    and magnetic fields
  • BEASY ECOAT
  • Simulation of electrochemical coating processes
  • BEASY Acoustic Design
  • Acoustic simulation

14
BEM Technology
  • BEASY solutions are for the most part based on
    Boundary Element Method Technology (BEM)
  • BEM is a technique similar to the Finite Element
    Method (FEM)
  • However it is based on an Integral Equations
    methodology which provides substantial benefits
    for many applications
  • Simplified Modelling
  • Accurate modelling of small features and details
  • Simplified modelling of large regions and
    infinite boundaries
  • Accurate representation of surface phenomena

15
How BEM can help
  • Ease of use and faster data preparation gives
    substantial reduction in analysis costs
  • Boundary-only model integrates well with CAD
    models
  • Small details and features can be easily
    incorporated
  • High Accuracy gives increased confidence in the
    product quality and reliability

16
BEM Basics
  • With BEASY you only need to define elements on
    the BOUNDARY or SURFACE
  • BOUNDARY ELEMENTS

17
Model only the Surface or Boundary
The BEASY Model describes only the Surface
18
BEASY Results
Deformed Shape
Stress Distribution
19
Brief Overview of Technology
  • Mechanical Design
  • Stress, thermal analysis to predict performance
    and durability
  • Contact Simulation
  • Predict load transfer characteristics and wear
  • Fatigue and Crack Growth
  • Predict integrity and life
  • Corrosion and CP
  • Predict effectiveness of corrosion control
    measures
  • Electrocoating
  • Optimise coating processes

20
Brake Caliper
Bolt Hole Fixed in 3 Coord. Directions
Symmetry Plane
13.8 MPa Pressure Applied as Normal Traction in
Bore (including Pockets)
two zone model with 1520 elements
21
Von Mises Stress
446 MPa (avg. mesh point value)
359 MPa (avg. mesh point value)
22
BEASY-Non-conforming Contact
  • Fixities

All displacement components set to zero
All displacement components set to zero
All displacement components set to zero
This position is Corner A
23
BEASY-Non-conforming Contact
24
BEASY-Non-conforming Contact
  • Principal stress

Two regions where contact pressure is high
Two regions where contact pressure is high
This position is Corner A
25
Structural Integrity Assessment
  • All structures contain flaws to some extent, E.G.
    As a result of
  • The manufacturing process
  • The fabrication
  • Localised in-service damage
  • Numerical fracture mechanics answers the
    following questions
  • Will the crack grow ?
  • Will it grow in an unstable fast or slow manner ?
  • If growth is stable, at what rate will it grow ?
  • To what size can the crack grow before becoming
    unstable ?

26
Initial Boundary Element Mesh
27
Crack Growth Results After Applying Loading Cycles
28
Detailed View Of Crack Growth From Bolt Holes
ADVANCING CRACKS
29
Actual Crack Growth Pattern During Experimental
Testing
30
Electrochemical Coating
  • BEASY can be used to predict the performance of
    coating processes
  • In this model there is
  • a single plate anode
  • Two plates close together to be coated
  • Results include
  • Coating thickness distribution
  • Potential and current fields

31
Coating Performance With Time
T.03
T17
T.15
32
Corrosion Control
33
Modelling Is Simple As Only the Wetted Area of
the Ship is Modelled
BEASY can predict the effectiveness of corrosion
control measures.
For defence applications it can also predict the
corrosion related electric and magnetic fields
34
BEASY Modelling Products
  • BEASY
  • Includes its own modelling and visualisation
    tools
  • BEASY PATRAN
  • Create and visualise BEASY models in PATRAN
  • BEASY IDEAS
  • Create and visualise BEASY models in IDEAS
  • BEASY NASTRAN
  • Convert NASTRAN bulk data files to BEASY models

35
BEASY Acoustic Design
36
BEASY Acoustic Design
  • What can BEASY Acoustic Design Do ?

Architectural Acoustics
Sound Radiation
Vibro Acoustics
Wheel Noise
37
BEASY Acoustic Design
  • Prediction of Interior Exterior Noise Fields
  • Noise Control and Reduction
  • Structural Acoustic Scattering and Radiation
  • Vibro Acoustics
  • Panel Contribution Analysis
  • Architectural and Environmental Acoustic Design

38
BEASY Acoustic Design
  • Vehicle Acoustic Design
  • Modelling of Reflective, Absorbing Open
    Boundaries
  • Multi Region Analysis
  • Acoustic Diagnostic sensitivity Analysis
  • Prediction of Sound Power, Pressure and Intensity

39
BEASY Acoustic Design
  • Sound Propagation through Absorbing Material
  • Noise Analysis of Soft and Rigid Half Space
  • Multi Frequency Analysis
  • Prediction of Acoustic Efficiency
  • Allowing for Complex Frequency, Density and Speed
    of Sound
  • NASTRAN Interface

40
Vehicle Sound Reduction
  • Predicted sound pressure level in vehicle. Note
    cut away elements to reveal the internal details
    of the seat models

41
Acoustic Problem Types
  • BEASY can Solve
  • Interior Acoustic Problems
  • Exterior Acoustic Problems
  • Coupled Exterior and Interior Acoustic Problems

42
Applications
  • The Acoustic Domain is Surrounded by the Boundary
  • Muffler
  • Passenger Compartment Acoustics
  • Room Acoustics
  • Acoustic Cavities

43
Exterior Problems
  • Boundary of the problem surrounded by the
    acoustic domain
  • Radiation problems
  • Scattering problems

44
Acoustic Zones
  • BEASY can model multiple acoustic regions e.g.
  • Vehicles
  • Engine Compartment
  • Passenger's Cabin
  • Interior/exterior coupled

45
Acoustic Zones
  • You may use Multi Zone Facility for
  • Coupling Regions with Different Acoustic
    Properties
  • Coupling Regions of Different Types E.g. Interior
    Exterior
  • Reducing the Computer Resources Requirement

46
Surface Conditions
  • BEASY can Model different Surface Conditions

Baffles
47
BEASY Acoustic Boundary Conditions
  • Complex Pressure
  • Complex Velocity
  • Complex Surface Velocity
  • Complex Velocity Potential
  • Complex Acceleration
  • Complex Impedance
  • Complex Admittance

48
Sound Absorbent Boundaries
Panels can be sound absorbent
Impedance or Admittance
User specifies the structure velocity and
impedance or Admittance
49
Open Fully Absorbent Boundaries
Sound is free to leak from the interior
50
Fully Reflecting Boundaries
Velocity set to Zero
Sound is Reflected Back to the Domain
51
Features of BEASY Acoustic
  • Employs Advanced BE methods to Solve Acoustic
    Problems
  • Comprehensive BE Element Library
  • Comprehensive Boundary Conditions Type
  • Error Analysis to evaluate the Accuracy of the
    Results
  • Comprehensive Data Check
  • Step_Wise Analysis Options and Restart

52
Advantages of BEASY for Acoustics
  • Describe only the surface of structure
  • Easy to model geometrical complexity
  • with reduced cost
  • Easy to Interface with CAD Systems
  • Exterior problems with Infinite boundaries
  • Reduced number of degrees of freedom
  • particularly for high frequencies
  • Accurate solution

53
Theoretical Introduction and Verification Example
54
Theoretical Foundations
  • Acoustic Wave propagation
  • Where u(x,t) Velocity Potential
  • c Speed of Sound
  • b(x,t) Noise Source
  • x and t Position and Time variable

55
Theoretical Foundations
  • Acoustic pressure
  • Where mass density of the acoustic media
  • Velocity

56
Theoretical Foundations
  • Assuming time harmonic
  • Transform from the time to frequency domain
  • Where k w/c the wave number
  • w angular frequency

57
Theoretical Foundations
  • The resulting BEM Equations at the specified
    frequency w are
  • Where
  • u Velocity Potential
  • q Normal Velocity
  • Note all values are complex

58
Diagnostic Analysis
  • From BE Internal Point equation
  • Where
  • v velocity on the boundary
  • p pressure on the boundary
  • g and h are the influence coefficients

59
Diagnostic Analysis
  • Contribution to the pressure at a point due to
    the pressure on one element
  • Pressure h p
  • Similarly the contribution due to the velocity of
    one surface element
  • Pressure g v

60
Sensitivity
  • The influence terms g and h enable us to compute
    the sensitivity
  • The change in the pressure due to a unit change
    in the surface velocity
  • Eg How much do I have to reduce the velocity on
    element n to reduce the sound level at this point
    by 10

61
Verification Examples
  • Multi zone Piston with complex materials
  • Features
  • High Accuracy
  • Multiple Acoustic Regions
  • Sound Absorbing Materials

62
Multi Zone Piston
  • Multi Zone problem with different materials
  • Acoustic propagation through porous
  • material with complex properties

63
Multi Zone Piston
64
Sound Pressure Level
65
Acoustic Pressure at Surface of Piston
66
Acoustic Pressure at Surface of Piston
67
Transmission Loss Assessment
C. Calì1, R. Citarella1, A.Galasso2 2Elasis
S.C.p.A. (FIAT GROUP), Pomigliano (NA),
ITALY 1Dept. of Mechanical Engineering,
University of Salerno, ITALY
68
Transmission Loss Assessment
  • One of the most valuable criteria for vehicle
    quality assessment is based on acoustic emission
    levels
  • A car is judged comfortable depending upon the
    noise level transmitted inside
  • Consequently there is a general attention to
    design criteria aimed to improve the
    structural-acoustic behaviour
  • Such design approach, based on experimental and
    numerical procedures, enables the
  • prediction of noise emissions
  • correlation with the structural vibration sources

69
Experimental Set Up
  • A rectangular panel is placed as a separation
    between
  • A reverberant room, where a uniform acoustic
    field is artificially generated
  • An anechoic room where it is possible to measure
    the transmitted (by the panel vibrations)
    acoustic field
  • In the reverberant room a rotating microphone
    provides the pressure level frequency spectrum

70
FEM Model of Panel

.

Loaded side by a spatially uniform pressure, as
provided by the frequency spectrum
71
BEM Model of the Cavity
Vibrating Panel
72
First Vibration Mode
73
Dynamic Analysis
  • The procedure starts with the dynamic assessment
    of the component behaviour by an FEM modal
    analysis
  • The results are compared with the experimental
    measurements in order to validate the model.

74
FEM Panel Model
  • The FEM panel model is fully constrained on 32
    uniformly spaced points along the borders,
    consistent with the welding points applied to the
    real panel
  • The following input data were used
  • Panel dimensions 1760x1020x2 mm
  • Material steel
  • Density 7850 kg/m3
  • Damping 0.005
  • Young modulus 2.1E05 N/mm2
  • Poisson ratio 0.3
  • ANSYS element type Shell 63

75
BEM Acoustic Analysis
  • For the acoustic analysis, the BEM mesh has to be
    sufficiently refined depending on the higher
    frequency of interest (at least four quadratic
    elements per wavelength)
  • For the acoustic analysis, the modelled fluid
    properties are the following
  • density 1.22 kg/m3
  • sound speed 344 m/s
  • reference pressure 2E-0.5 N/m2

76
Transmission Loss
Predicted
Experimental
77
Difference Between Numerical and Experimental
Transmission Loss
78
Summary
  • Satisfactory agreement is obtained between the
    numerical procedure and with the experimental
    data.
  • The FEM-BEM coupled approach can be easily
    applied to solve vibration acoustic problems
  • A more refined FEM and BEM mesh is required if
    higher frequencies are to be studied
  • The same procedure can be applied to complex
    components such as car bodies.

79
Panel Contribution Analysis
80
Acoustic Simulation
  • First Generation
  • Analysis Tool to predict acoustic fields
  • Second Generation
  • Design Tool to Evaluate Diagnostic and Solution
    Sensitivities
  • Panel Contributions

81
Diagnostic Analysis What does it tell us ?
  • Acoustic analysis predicts the sound field
  • Diagnostics/Panel Contributions predict
  • How much sound each part of the structure is
    Directly and Indirectly generating at a given
    position ?
  • What are the major contributors to the sound
    level at any position ?
  • What is the sensitivity of the sound level to
    changes in surface Conditions ?
  • What is the contribution from each structural
    panel ?

82
Panel Contributions
83
Direct and Indirect Contributions
  • In most cases the sound from a vibrating
    structural panel travels Directly and Indirectly
    to the diagnostic point (Eg Drivers ear)
  • It reflects from other surfaces
  • BEASY can compute both the Direct and Indirect
    Contribution by a powerful analytic technique

84
True Contribution
Includes both direct and indirect contributions
85
Acoustic Diagnostic Application
  • Sound Signature of an Under Water Vehicle

86
Diagnostic Analysis Under Water Vehicle
  • Underwater Vehicle near a sound source
  • The objective is to
  • determine the quantity of sound entering the
    vehicle
  • determine the sound level at an observation point
    outside the vehicle
  • determine how much of the sound level at the
    observation point is contributed by the
    structural surfaces inside the vehicle
  • ie How much sound enters the vehicle and is
    reflected back

87
BEM Model
External surface of vessel
Sea
Open Compartment
88
Sound Pressure Level Surrounding The Vessel
89
Panel Contributions
  • Contribution of each element on the inside
    surface of the vessel to the sound level at the
    observation point

The element colour indicates how much sound each
element contributes
90
Acoustic Pressure Contribution
  • The contributions of the two end panels to the
    sound level at the observation point. Each panel
    contributes over 3 to the sound level.

91
Acoustic Diagnostic Application
  • Acoustic Design of a Vehicle Interior

92
Acoustic Design of an automobile
  • In this application the vibration of the vehicle
    structure is driving the acoustic field
  • The structure vibration can be obtained from
  • A FEM model of the vehicle structure
  • A user specified velocity
  • A measurement system
  • The objective is to predict the sound levels and
    determine the parts of the structure which must
    be modified to reduce the sound level

93
Sound Pressure Level in Vehicle
94
Diagnostic Analysis
  • Objective
  • To determine the contributions to the sound
    perceived by the driver

95
Panel Contributions
96
Redistributed Velocity Contribution
97
Sensitivity Analysis of a Car's Cabin
  • The influence coefficients can also be displayed
  • They provide information on the sensitivity of
    the sound level at the observation point to the
    velocity of individual elements or panels

98
Redistributed Velocity Influence
  • Contour display of the influence (sensitivity) of
    sound level at the drivers ear to the velocity of
    each element

99
Redistributed Velocity Contribution
  • Contour display of the true contribution of each
    element to the sound level at the drivers ear

SPL
100
Automobile Diagnostic Analysis
  • Objective To determine the contributions to the
    sound perceived by rear seat passenger

Passenger position
101
Redistributed Velocity Contribution
  • Contour display of the influence (sensitivity) of
    sound level at the passengers ear to the velocity
    of each element

102
Redistributed Velocity Contribution
103
Diagnostic Analysis
  • Acoustic analysis predicts the sound field
  • Diagnostics predict
  • How much sound each part of the structure is
    Directly and Indirectly generating at a given
    position ?
  • What are the major contributors to the sound
    level at any position ?
  • What is the sensitivity of the sound level to
    changes in surface Conditions ?

104
Applications
105
Architectural Acoustics
  • Objective
  • Predict the sound propagation through a building
  • Procedure
  • The BEM model describes the surfaces of the
    building.
  • Each surface can have its own properties. eg
  • Impedance
  • Each room can be described as an acoustic zone
    which can have its own acoustic properties. eg
  • Speed of sound
  • Density
  • The noise source can be defined as
  • Point source or line source
  • Vibrating structure

106
BEM Model of the Building
Zone Interfaces
Room 3
Room 1
Room 2
107
Sound Pressure Level on Structure
Noise source inside room 1
108
Sound Pressure Level on Structure
109
Acoustic Surfaces Impedance
  • Objective
  • Determine the impact of acoustic impedance
    conditions of the surface of the structure on the
    acoustic performance
  • Procedure
  • Define the surface of the structure with elements
  • Specify the surface conditions using the
    impedance values
  • Define the noise sources

110
Predicting Acoustic Performance
BEM Model
111
Predicted Sound Pressure
112
Predicted Sound Pressure
113
Sound Sources
  • Objective
  • Determine the sound field in a room with multiple
    speakers
  • Procedure
  • Define the BEM mesh of the surface
  • Define impedance values of the surfaces
  • Define any number of acoustic sources
  • Define the display plane

114
Sound Sources
Speakers
BEM Mesh of the Room
Display Plane
115
Sound Pressure Levels on the Display Plane
116
Noise Radiated From a Wheel
  • Objectives
  • Determine the noise radiated from a wheel due to
    its vibration
  • Procedure
  • Define the BEM surface elements
  • Input the structural velocities from the FEM
    model
  • Define the display planes

117
BEM Model of a Wheel
118
Predicted Sound Level on Wheel
119
Sound Level on Display Surfaces
120
Vibro Acoustics
  • Objective
  • To compute the acoustic response in the air
    surrounding the structure
  • Procedure
  • Develop the BEM model of the surface of the
    structure
  • Import the surface velocities from the structural
    FEM analysis or measurement system
  • Select the range of frequencies to be studied
  • Define how the results are to be viewed

121
BEM Mesh on the Structure
122
Cylindrical Display Surface
123
Sound Pressure at 300 Hz
124
Acoustic Radiation
  • Results can be displayed on the display planes or
    on the structure
  • Results can include
  • Sound Pressure Level
  • Velocities
  • Energy
  • etc
  • Displays can include
  • Contours
  • Graphs
  • Tables

125
Sound Pressure Level at 250 Hz
126
Sound Pressure Level at 150 Hz
127
Acoustic Radiation
  • Results from different frequencies can be
    displayed

128
Sound Pressure Level at250 Hz
129
Sound Pressure Level at 150 Hz
130
Sound Pressure Level at 50 Hz
131
Underwater Acoustic Study
  • In this application the acoustic fields
    surrounding a boat are predicted
  • The noise source is part of the structure
    vibrating

132
BEM Model
BEM Mesh
133
Sound Pressure Level Near The Boat
134
Surrounding Acoustic Fields
Sound Pressure Level
Z Velocity
X Velocity
135
Pump NoiseStudy
136
BEM Mesh on the Pump
Structural Vibration data is used to predict the
radiated noise
137
Predicted SPL Near the Pump
138
Predicted Radiated Noise
SPL contour in the air near the pump
Pump
139
Fan NoiseStudy
140
Industrial Fan
  • The objective was to predict
  • The noise generated by a fan
  • The root cause of the noise

141
Modelling Methodology
  • FEM model used to predict the vibration of the
    fan
  • NASTRAN bulk data including GRIDs and CQUAD4s
  • NASTRAN punch file with structural velocity
    information
  • BEASY computes the vibro acoustic solution

142
Model Data
  • Distances in M
  • Speeds in M/second
  • Air Density1.25 Kg/m3
  • Sound Speed600m/second
  • Reference Pressure 1.E-8 Pa

143
BEASY- Modelling 1
  • Bulk data file read into the BEASY User Interface

Each CQUAD4 converted into a quadrilateral surface
144
BEASY- Modelling 2
  • Some parts removed for this evaluation
  • Surfaces reversed as necessary

Openings in fan casing
Openings in fan casing
145
BEASY- Modelling 3
  • Fan casing has internal partitions

Surfaces cut-away to show internal partition
146
BEASY- Modelling 5
  • Zones defined

Fan interior part 1
Fan exterior (infinite)
Fan interior part 2
147
BEASY- Modelling 4
  • Extra surfaces created as necessary

Surfaces created to close the openings
Surfaces created to close the openings
Surfaces created to close the openings
148
BEASY- Modelling 6
  • The CQUAD4 elements from the bulk data file were
    meshed with QUAD9 elements
  • Materials properties defined

149
BEASY- Modelling 7
  • Group created containing elements for which
    structural velocity Boundary Conditions are
    required from the NASTRAN result file
  • Element geometry file written containing
    details of the elements

Elements on which structural velocities are NOT
required
Elements on which structural velocities are NOT
required
Elements on which structural velocities are NOT
required
Elements on which structural velocities are NOT
required
150
BEASY- Modelling 8
  • BEASY automatically applies NASTRAN structural
    velocities to the element geometry file.
  • Selected frequency75 Hz

Arrows show velocity components
151
BEASY- Results 1
  • Sound pressure level outside the fan

152
BEASY- Results 2
Sound pressure level inside the fan
153
BEASY- Results 3
  • Sound pressure level inside the fan

154
BEASY- Results 4
SPL radiating away from the fan
155
BEASY- Simplified Model
  • Part of the fan removed
  • New (bigger) surfaces created
  • Model of only the outside of the fan

Mesh of 290 elements
22 surfaces
156
BEASY- Results 5
  • Simplified model Sound pressure level

157
BEASY- Panel Contribution 1
Panel Contribution Analysis activated
Array of internal points at which contribution is
required
Array of internal points at which contribution is
required
Array of points at which contribution is required
158
BEASY- Results 6
Panel Contribution analysis predicts Contribution
to SPL at one of the target points
Target point
Target point
159
BEASY- Summary
  • Easy translation of geometry from bulk data file
    into BEASY
  • Structural velocities automatically extracted
    from NASTRAN results files
  • Clear visualisation of the acoustics field allows
    identification of source of the noise
  • Panel Contribution analysis
  • gives precise information on
  • which parts of structure
  • contribute most noise
  • to selected target locations

160
Summary
  • BEASY employs Boundary Element Method to Solve
    Wide Range of Industrial and Environmental
    Acoustic Problems
  • BEASY allows Multiple Acoustic Zones
  • BEASY supports wide range of Acoustic Boundary
    Conditions
  • BEASY provides a Comprehensive Element Library

161
Summary
  • BEASY provides Powerful Diagnostic Analysis
  • BEASY Provides Acoustic Sensitivity Analysis
  • The advantages of the BEASY approach is clear
  • Simple modeling
  • Reduced problem size
  • Flexible modeling
  • High accuracy

162
Next Step
  • As you can see from this short overview BEASY
    provides effective solutions to an important
    range of problems
  • Benefits include
  • Improved quality of predictions
  • Reduced cost
  • BEASY provides an effective solution to many
    problems which could not be solved in a cost
    effective way with other technologies
  • To find out more contact your nearest BEASY
    representative

163
Contact Information
Email info_at_beasy.com Web www.beasy.com Europe C
omputational Mechanics BEASY Ashurst Lodge
Ashurst, Southampton, SO40 7AA, UK Tel 44 (0) 238
029 3223 Fax 44 (0) 238 029 2853 North
America Computational Mechanics Inc 25 Bridge
Street, Billerica, Ma 01821 Tel (1) 978 667
5841 Fax (1) 978 667 7582
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