ME 450: Computer-Aided Engineering
Applications of the Finite
Element Method
K. Nema
&
H. Akay
Spring 2004
Engineering Analysis and Design
Engineers need to analyze various
components/designs for a variety of
loading, material, manufacturing
conditions
Come up with a best design without
extensive experiments and prototype
building
FEA is a computational (numerical)
modeling method
Types of Computer-Based Simulations
Solution of Algebraic equations
– Set of algebraic equations
– Geometric equations
– Kinematics, synthesis
Solution of Ordinary Differential
Equations
– One dimensional
– Control systems
– 1D field problems
Solution of Partial Differential Equations
– Multi-dimensional
– Mechanics, heat transfer, fluid flow, electro-
Why FEA is Needed?
Reduces the amount of prototype testing

Computer simulation allows multiple “what-if”
scenarios to be tested quickly and effectively
Models designs that are not suitable for
prototype testing

Example: Surgical implants, such as an artificial
knee
The bottom line



Cost savings
Time savings… reduces time to market!
Create more reliable, better-quality designs
What is FEA?
Finite Element Analysis is a way to
simulate various conditions (loading,
material, etc.) on a design and determine
the Design’s response
Finite Element Method (FEM) divides a
design model into smaller “elements” and
solves the resulting system of equations
FEA is used in many industries to conduct
modal, structural, harmonic, thermal and
other analysis
Historical Note
• The finite element method of structural
analysis was created by academic and
industrial researchers during the 1950s
and 1960s
• The underlying theory is over 100 years
old, and was the basis for pen-and-paper
calculations in the evaluation of
suspension bridges and steam boilers
Three Phases of the Finite
Element Method
Preprocessing
Solution
Postprocessing
Preprocessing Phase
Discretizing the solution domain into
finite elements
Assuming a solution that approximates
the behavior of an element
Developing equations for an element
Assembling the elements to present the
entire problem
Solution Phase
Solving a system of algebraic equations
simultaneously to obtain nodal values of
primary variables, e.g., displacements
Postprocessing Phase
Obtaining information on elemental
values of secondary variables, e.g.,
strains, stresses and forces
About ANSYS

ANSYS is a complete FEA software package used
by engineers worldwide in virtually all fields of
engineering:

Structural

Thermal

Fluid, including CFD (Computational Fluid
Dynamics)

Electrical / Electrostatics

Electromagnetics

Coupled field analysis:

Fluid-Structure interactions

Acoustics and vibration

Thermal-stress analysis (heat transfer and stress analysis)
FEA Definitions
• Node
• Degree of Freedom (DOF)
• Element
• Boundary Conditions
Steps of FEA with ANSYS
Preprocessing
Specify element types to be used
Specify options for element behavior
Specify real constants
Specify material model
Specify material properties
Create geometry (primitives, hierarchical – points, lines,
areas, volumes, direct generation)
Specify meshing options
Mesh model
Apply boundary conditions
Solve problem
Postprocessing (reviewing results)
Structural Analysis: Statics


Structural analysis is used to determine
deformations, strains, stresses, and
reaction forces
Static analysis



Used for static loading conditions
Linear behavior under small deflections and
strains
Nonlinear behavior under large deflections
and strains, plasticity, hyperelasticity, and
creep can be simulated
Structural Analysis:
Dynamics
• Dynamic analysis – Includes mass and damping
effects
• Modal analysis calculates natural frequencies
and mode shapes
• Harmonic analysis determines a structure’s
response to sinusoidal loads of known amplitude
and frequency.
• Transient dynamic analysis determines a
structure’s response to time-varying loads and
can include nonlinear behavior
• Other structural capabilities
l Spectrum analysis, random vibrations
l Substructuring, submodeling
Various Applications
 Stress analysis of structures
 Static and dynamic
 Linear nonlinear
 Buckling





Heat transfer analysis
Fluid dynamics
Biomechanics
Solid-fluid interactions
Materials processing
Stress Analysis of Geer Tooth
IUPUI Electric Race Car Components
Structural Analysis
Trailer Hitch
Design Constraints
2,950 lbf
0.35 sq
in
8,450 psi
Trailer Hitch (con’t)
ANSYS Modeling
Proposed Trailer Design
Car Crash Simulations
-- Ford Taurus --
Car Crash Simulations
Electronic Package Reliability
Thermal Fatigue of a Surface Mount Assembly
Low-cycle thermal fatigue of solder joints connecting electronic
chips to the printed circuit board due to solder creep is of concern.
Different types of interconnection methods
in electronic packages
chip carrier
lead
solder
copper pad
PWB
Schematic of a LDCC type (gull-wing)
Different types of interconnection methods
in electronic packages
chip carrier
solder
copper pad
PWB
Schematic of a LLCC type
Typical 2D LLCC and LDCC cases used for
curve fitting
Y
X
Finite element mesh for 20-pin LLCC
Typical 2D LLCC and LDCC cases used for
curve fitting
Y
X
Finite element mesh for 28-pin LDCC-TSOP (gull-wing)
Biomedical Application -- Hip Implant
-- Interaction of a hip implant with the femur
-- Computed stresses
Mesh for Flow Around an Oscillating Missile
Mach Number Contours Around an Oscillating Missile
(Unsteady Flow)
Biomedical Application -Prosthetic Cardiac Valve Simulations
Patient Specific Three-Dimensional Finite
Element Models of Defibrillation
•Ventricular fibrillation characterized by
unsynchronized contraction of heart - deadly if
not reversed
•Defibrillate by delivering an electrical shock to
reset heart
•Implantable cardioverter defibrillator (ICD) for
patients who are at high risk
Lungs
Rib Cage
Heart
HVAC/Climate control in a passenger car,
showing transient ice melting on the windscreen
Aerodynamics of Jeff Gordon’s
NASCAR Race Car
Aerodynamic Simulations with
ANSYS FLOTRAN
Velocity by 30 m/s
Velocity by 100 m/s
Static Pressures with ANSYS at
100 m/s
Parallel Computing
• A computational mesh is
generated for the domain
• The mesh is partitioned into
blocks
• The blocks are distributed to
processors on the network
and solved concurrently
• Processors communicate
data through interfaces
between blocks using a
message passing library,
such as MPI and PVM
Aerodynamics, Aeroelasticity, and Structural
Integrity of an Aircraft Using Computer Simulations
Unsteady Aerodynamics
Deformed mesh at maximum and minimum angle of
attack positions (16-block partition)
Unsteady Aerodynamics
Mach Contours
Unsteady Lift Coefficient Variation
Coarse Grid 16 Blocks
Fine Grid 16 Blocks
Coarse Grid Single Block
0.50
0.40
0.30
Lift Coefficient
0.20
0.10
0.00
-0.10
-0.20
-0.30
-0.40
-0.50
0
30
60
90
120
150
180
210
wt(deg)
240
270
300
330
360
Steady State Solution
(200 Time Steps, One Block per Processor)
36
32
28
Speedup
24
Coarse Grid
Fine Grid
Ideal Speedup
20
16
12
8
4
0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Number of Blocks
Unsteady Solution
(200 Time Steps, One Block per Processor)
36
32
28
Speedup
24
Coarse Grid
20
Fine Grid
Ideal Speedup
16
12
8
4
0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Number of Blocks
Metacomputing with I-Light at CFDL
Metacomputing is an efficient approach to utilize the resources of geographically
distant computers that are connected by a network.
CFDL uses I-light, a high speed optical fiber network connecting IU, IUPUI, and PU
and to Internet2, for that purpose.
I-Light has presently increased the access speed to 30 times than before (1 Gb/s)
and is expandable to 100 Gb/s in the future.
CFDL, IUPUI, Indianapolis
5 CPU PIII/Linux
14 CPU PII/W2K
6 CPU RS6K/AIX
NASA/Glenn, Cleveland, OH
128 CPU PIII/Linux
I-light
Univ of Lyon, Lyon, France
10 CPU PIII/Linux
IU Bloomington
500 CPU IBM SP2/AIX
32 CPU PIII/Linux
Aeroelastic Coupling Algorithm
Obtains solution of:



Aerodynamic pressures using a CFD
(Computational Fluid Dynamics) code
Deformation of structures using a CSD
(Computational Solid Dynamics) code
Movements of the flow mesh using an
elastic spring network
Uses separate computational meshes
for flow and structure (CFD and CSD
meshes)
The CFD and CSD meshes are
loosely coupled using a code coupling
approach across multiple processors
CFD mesh is subdivided into multiple
blocks for parallel and metacomputing
on distributed systems
Test Case
Transient solid-fluid interactions of an
aircraft wing is solved using two codes:


CFD code: USER3DP
CSD code: MODAL
The CFD domain is solved via
partitioned flow meshes for parallel
computing
The codes and their meshes are
coupled via MpCCI
Transient solutions of 500,000 flow and
2,000 structural equations are obtained
in a coupled fashion
Objectives:


To demonstrate the feasibility of I-light for
metacomputing
To test the speed of I-light
Aeroelastic Flutter – A Solid-Fluid Interaction Problem
Results of Test Case with I-Light
Parallel Speedup:
Sp =T1 Tp
Speedup
Speedup (Sp)
10
8
Ideal
6
CFDL
4
IUB
2
I-Light
0
2
4
6
Number of Blocks, p
8
Escape System Analysis
•
Surface Pressures
Mach Contours
Canopy Trajectory Simulation in Flight Emergency
Plastics Manufacturing
Injection Molding of Curved File Cabinet
(Polymer Processing)
Metal Manufacturing -- Casting
of a 4-Cylinder Engine Block
Engine Block Cavity Filling Simulations
Life After ME 450
Good Design
and Analysis
Jobs
in
Industry