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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)