Applications of FEM in Structural and

Durability AnalysisSoham Ghormade

MS Mechanical Engineering

FEM:Definition

Finite DOFs Approximate solution Interpolated betweennodes

Finite Element Method

Numerical method

Node Element

3-D Element Types

2-D Element Types

Classification by property

Classification based on number of nodes

Discretization/meshing solvable

Shape Function N = a + bx

DOF=Degree of Freedom

Durability

NVH:Noise Vibration and Harshness

• Customers expect a robust design.• provides early results and insight into the design • Types• load prediction• stress analysis • fatigue prediction

FEA-Process

Pre-processors:ANSA,HyperMesh

Solver:ABAQUS/Standard,NASTRANOptiStruct

Post-Processors:HyperView

Post-processingPre-processing Analysis

CAD:Unigraphics,SolidWorks,Inventor,

Pro/E,AutoCAD

E

Core Math

Example :Deflection of Cantilever Beam• Given a 250 mm long steel beam (.)with 20x 5mm cross section

compute its end deflection when subjected to 35 N force.• Analytical Solution:

𝛿=𝐹×𝐿3

3𝐸𝐼 =35×0.253

3×2.1×1011× 0.02×0.0053

12

=4.167𝑚𝑚

F=35N

250

20

5

PreprocessingMaterial Cross Section(mm) Force(N)

Steel 20 x 5 35

Element Type CBEAM

# of nodes 2

# of elements 1

Element Type PSHELL

# of nodes 78

# of elements 50

Element Type TETRA

# of nodes 4,317

# of elements 15,120

Constraint/BC

Load/BC

1-D

2-D

3-D

Element Type

Displacement(mm)

Analytical 4.167

1-D 4.168

2-D 4.140

3-D 4.132

Post-Processing

Displacement plot

Displacement plot

Displacement plot

1-D

2-D

3-D

Project#1:2-D Frame Structure

• Compute the displacement and reaction forces for the following 2-D frame structure .

Frames

Frame = Beam + Truss

Axial forcesVertical deflection and slopeBending Moment,Shear Force,Axial Force

{𝐹 }= [𝐾 ] {𝑑 }

4 DOFs 4 DOFs

u=horizontal deflectionv=vertical deflection Simply supported beam

𝑢1→,𝑣1↑,𝜙1↺

Stiffness Matrix equation for 2-D frame 6 DOFs

1: MATLAB Result

2:Hypermesh/Optistruct

Element Type CBEAM# of nodes 8

# of elements 14

6 7

8 Stress

Displacement X

Displacement YRecommendation:No change in matl. or c/s.current structure and material can withstand existing loading

Project#2:2-D Solid Simulation

• obtain the displacement and stresses plots of a thin plate

Element Type

Q4

# of Nodes 45

# of elements

62

1:MATLAB Result

Recommendation:

2:Hypermesh/OptiStruct

Material Steel

Element Type

PSHELL

# of Nodes 233

# of elements

200

Stress

Displacement

Meshed Model

Ford Taurus 2000 BIW Model

Material Steels(300MPa-800MPa)

Element Type

PSHELL

# of Nodes 344,072

# of elements

332,562

Meshed Model,after Quality Check ,#of elements failed:0%

Modelled as a plate For analysis

Project#3:Static Analysis• LH and RH Front Shock Towers• Rear Spring Seats-> 4 Constraints• Load/Passenger = 65kg = 637.5 N(as per OEM )

OEM = Original Equipment Manufacturer

Rear Spring Seat

RH Shock Tower

Seat And Door Modelling• CBUSH: Soft Mounts• RBE2:no deformation at nodes RBE3:deformation at nodes

W

CG

W

S S

S=Spring/Bush

RBE2(Bolted)

RBE3

RBE2Bolted

RBE2(Bolted)

RBE2(Hinge)

RBE2RBE2(Hinge)

RBE3≡

≡

RBE2(Bolted)

S Front Seat(LH/RH)

RearDoor Seat(RH)

CG = Centre of gravity of passenger specified by OEM

Static Analysis-2 Front Passengers

Element Stress(MPa)

Element Strain Energy(N-m)

Displacement(mm)

front

Max Min

Displacement(mm)

28.251 0

Stress(MPa)

297.5 0

Elastic Strain Energy(Nmm)

143.8 0

Static Analysis-four Passengers

Elastic Strain Energy

Element Stress

Displacement

center

Stress concentrationMax Min

Displacement(mm)

28.251 0

Stress(MPa)

297.5 0

Elastic Strain Energy(Nmm)

143.8 0

Twisting

Twisting Moment = 1200N-m(specified by OEM ) applied to front shock towersForce F= Twisting Moment/distance between front shock towers

Car moving over pot holes /cobbled road is subject to twisting load

Twisting

Displacement

Element Stress

Elastic Strain Energy

Max Min

Displacement(mm)

245.8 0

Stress(MPa)

254.4 0

Elastic Strain Energy(Nmm)

116.7 0

Modal Analysis𝑓 =√ 𝑘

𝑚

• used to calculate the vibration shapes and associated frequencies.• frequency: check resonance condition • shapes: prevent application of load at points causing resonance condition.

[𝑀 ] {�̈� }+ [𝐶 ] {�̇� }+ [𝐾 ] {𝑥 }=𝐹

F K=stiffness

For free vibration,

𝑓 =√𝜆2𝜋

Modal Analysis of a car using OptiStruct

0 0

Lanczos method Automated Multi-Level Sub-Structuring

Eigenvalue Solution Method (AMSES)

Eigenvalue calculation eigenvalues and associated mode shapes are calculated exactly.

portion of the eigenvector need be calculated.i.e

calculations are not exact

Number of modes required

small and the full shape of each mode is required

large

Run time Long short

Modal Analysis

Modal Analysis

1

2

3

4

5

6

#1

#2

# of modes = 10(1-6 -> Rigid Body Modes)

Modal Analysis

3#3#

#3

#4

Contacts ProblemNode to Surface Surface to Surface

Nodes on one surface ( slave ) contact thesegments on the other surface ( master )

Each contact constraint is formulated based on an integral over theregion surrounding a slave node

Contact enforced at discrete points (slave nodes)

Contact enforced in an average sense over a region surrounding each slave node

Benefits of surface-to-surface approach• Reduced likelihood of large localized penetrations• Reduced sensitivity of results to master and slave roles• More accurate contact stresses (without ―matching meshes‖)• Inherent smoothing (better convergence)

Claim:refined surface->slave

1:Coarse Slave

Contact Force

Reaction Force

StressF=1000N

Material aluminum steel

Element Type

TETRA TETRA

# of Nodes 73 534

# of elements

219 2,121

Fine Master(Steel)

Coarse Slave(Aluminum)

2:Fine Slave Surface

Reaction Force

Contact Force

Stress

Material aluminum steel

Element Type

TETRA TETRA

# of Nodes 306 141

# of elements

1176 417

Fine Slave(Aluminum)

Coarse Master(Steel)

ComparisonCoarse Slave

Max Min

Stress(MPa)

498.7 32.72

Contact Force(N)

0 -89.84

Reaction Force(N)

15 0

Fine Slave Max Min

Stress(MPa)

5558 8.279

Contact Force(N)

1000 0

Reaction Force(N)

373.2 0

Conclusion:A refined surface should be taken as slave surface for contacts analysis

Advantages Of FEA

• Visualization• Design cycle time• No. of prototypes• Testing• Optimum design

THANK YOU !

References

• [1] D. L. Logan, A first course in finite element method (2011) • [2] J. N. Reddy, An Introduction to the Finite Element Method, (2006) • [3]M.Goelke, Practical Aspects of Finite Element Simulation (2014)