fea basic introduction training by praveen
DESCRIPTION
FEA Basic Introduction Training By Praveen conducted in 2008TRANSCRIPT
Finite Element Analysis
Praveen Patil
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Contents
• Introduction to the Finite Element Method
(FEM)
••• Future Future Future TrendsTrendsTrends
FEM Applied to Solid Mechanics Problems
Create elementsof the beam
dxi 1 dxi 2
dyi 1 dyi 21 2
4 3
Nodal displacement and forces
• A FEM model in solid mechanicscan be thought of as a system ofassembled springs. When a loadis applied, all elements deformuntil all forces balance.
• F = Kd
• K is dependant upon Young’s modulus and Poisson’s ratio, as well as the geometry.
• Equations from discrete elements are assembled together to form the global stiffness matrix.
• Deflections are obtained by solving the assembled set of linear equations.
• Stresses and strains are calculated from the deflections.
Classification of Solid-Mechanics Problems
Analysis of solids
Static Dynamics
Behavior of Solids
Linear Nonlinear
Material
Fracture
GeometricLarge Displacement
Instability
Plasticity
ViscoplasticityGeometric
Classification of solids
Skeletal Systems1D Elements
Plates and Shells2D Elements
Solid Blocks3D Elements
TrussesCablesPipes
Plane StressPlane StrainAxisymmetricPlate BendingShells with flat elementsShells with curved elements
Brick ElementsTetrahedral ElementsGeneral Elements
Elementary Advanced
Stress Stiffening
Governing Equation for Solid Mechanics Problems
[K] {u} = {Fapp} + {Fth} + {Fpr} + {Fma} + {Fpl} + {Fcr} + {Fsw}
+ {Fld}
[K] = total stiffness matrix
{u} = nodal displacement
{Fapp} = applied nodal force load vector
{Fth} = applied element thermal load vector
{Fpr} = applied element pressure load vector
{Fma} = applied element body force vector
{Fpl} = element plastic strain load vector
{Fcr} = element creep strain load vector
{Fsw} = element swelling strain load vector
{Fld} = element large deflection load vector
• Basic equation for a static analysis is as follows:
Six Steps in the Finite Element Method
• Step 1 - Discretization: The problem domain is discretized into a collection of simple shapes, or elements.
• Step 2 - Develop Element Equations: Developed using the physics of the problem, and typically Galerkin’s Method or variational principles.
• Step 3 - Assembly: The element equations for each element in the FEM mesh are assembled into a set of global equations that model the properties of the entire system.
• Step 4 - Application of Boundary Conditions: Solution cannot be obtained unless boundary conditions are applied. They reflect the known values for certain primary unknowns. Imposing the boundary conditions modifies the global equations.
• Step 5 - Solve for Primary Unknowns: The modified global equations are solved for the primary unknowns at the nodes.
• Step 6 - Calculate Derived Variables: Calculated using the nodal values of the primary variables.
Process Flow in a Typical FEM Analysis
StartProblemDefinition
Pre-processor
• Reads or generates nodes and elements (e.g. MD-Patran)
• Reads or generates material property data.
• Reads or generates boundary conditions (loads and constraints.)
Processor/Solver
• Generates element shape functions
• Calculates master element equations
• Calculates transformation matrices
• Maps element equations into global system
• Assembles element equations
• Introduces boundary conditions
• Performs solution procedures
Post-processor
• Prints or plots contours of stress components.
• Prints or plots contours of displacements.
• Evaluates and prints error bounds.
Analysis anddesign decisions
Stop
Step 1, Step 4
Step 6
Steps 2, 3, 5
Step 1: Discretization - Mesh Generation
airfoil geometry(from CAD program e.g CATIA)
e.g. MD-Patran
surface model
ET,1,SOLID45N, 1, 183.894081 , -.770218637 , 5.30522740N, 2, 183.893935 , -.838009645 , 5.29452965..TYPE, 1E, 1, 2, 80, 79, 4, 5, 83, 82E, 2, 3, 81, 80, 5, 6, 84, 83...
meshed model
Step 4: Boundary Conditions for a Solid Mechanics Problem
• Displacements ⇒ DOF constraints usually
specified at model boundaries to define rigid
supports.
• Forces and Moments ⇒ Concentrated loads on
nodes usually specified on the model exterior.
• Pressures ⇒ Surface loads usually specified on
the model exterior.
• Temperatures ⇒ Input at nodes to study the
effect of thermal expansion or contraction.
• Inertia Loads ⇒ Loads that affect the entire
structure (ex: acceleration, rotation).
Step 4: Applying Boundary Conditions (Thermal Loads)
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150175
Tempmapper
Nodes fromFE Modeler
Thermal Soln Files
bf, 1,temp, 149.77bf, 2,temp, 149.78...bf, 1637,temp, 303.64bf, 1638,temp, 303.63
Step 4: Applying Boundary Conditions (Other Loads)
• Speed, temperature and hub fixity applied to sample
problem.
• FE Modeler used to apply speed and hub constraint.
XY
Z
antype,staticomega,10400*3.1416/30d,1,all,0,0,57,1
Information Available from Various Types of FEM Analysis
• Static analysis
» Deflection
» Stresses
» Strains
» Forces
» Energies
• Dynamic analysis
» Frequencies
» Deflection (mode shape)
» Stresses
» Strains
» Forces
» Energies
• Heat transfer analysis
»Temperature
» Heat fluxes
» Thermal gradients
» Heat flow from convection faces
• Fluid analysis
» Pressures
» Gas temperatures
» Convection coefficients
» Velocities
Example FEM Application Areas
• Automotive industry
» Static analyses
» Modal analyses
» Transient dynamics
» Heat transfer
» Mechanisms
» Fracture mechanics
» Metal forming
» Crashworthiness
• Aerospace industry
» Static analyses
» Modal analyses
» Aerodynamics
» Transient dynamics
» Heat transfer
» Fracture mechanics
» Creep and plasticity analyses
» Composite materials
» Aeroelasticity
» Metal forming
» Crashworthiness
• Architectural
» Soil mechanics
» Rock mechanics
» Hydraulics
» Fracture mechanics
» Hydroelasticity
Variety of FEM Solutions is Wide and Growing Wider
• The FEM has been applied to a richly diverse array of scientific and technological problems.
• FEM is increasingly applied to a variety of real-world design and analysis problems.
Technologies That Compete With the FEM
• Other numerical solution methods:
– Finite differences
» Approximates the derivatives in the differential equation using
difference equations.
» Useful for solving heat transfer and fluid mechanics problems.
» Works well for two-dimensional regions with boundaries parallel
to the coordinate axes.
» Cumbersome when regions have curved boundaries.
– Weighted residual methods (not confined to a small subdomain):
» Collocation
» Subdomain
» Least squares*
» Galerkin’s method*
– Variational Methods* (not confined to a small subdomain)
* Denotes a method that has been used to formulate finite element
solutions.
Technologies that Compete With the FEM (cont.)
• Prototype Testing
» Reliable. Well-understood.
» Trusted by regulatory agencies (FAA, DOT, etc.)
» Results are essential for calibration of simulation software.
» Results are essential to verify modeled results from simulation.
» Non destructive testing (NDT) is lowering costs of testing in
general.
» Expensive, compared to simulation.
» Time consuming.
» Development programs that rely too much on testing are
increasingly less competitive in today’s market.
» Faster product development schedules are pressuring the quality of
development test efforts.
» Data integrity is more difficult to maintain, compared to
simulation.
Contents
••• Introduction to the Finite Element Method Introduction to the Finite Element Method Introduction to the Finite Element Method
(FEM)(FEM)(FEM)
• Future Trends
Future Trends in the FEM and Simulation
• The FEM in particular, and simulation in general, are becoming
integrated with the entire product development process (rather than just
another task in the product development process):
– FEM cannot become the bottleneck.
• A broader range of people are using the FEM:
– Not just hard-core analysts. Future (?? Word excel??)
• Increased data sharing between analysis data sources (CAD, testing,
FEM software, ERM software.)
• FEM software is becoming easier to use:
– Improved GUIs, automeshers.
– Increased use of sophisticated shellscripts and “wizards.(??)”
Achieved overnightBIP optimization on SGI 2800/256, with
equivalent yield of 9 months CPU time
NVH & Crash Optimization of Vehicle Body Overnight
• Ford body-in-prime (BIP) model of 390K DOF
• MSC.Nastran for NVH, 30 design variables
• RADIOSS for crash, 20 design variables
• 10 design variables in common
• Sensitivity based Taylor approx. for NVH
• Polynomial response surface for crash
Conflicting Variables . . .with Reducing time
Future Trends in the FEM and Simulation (cont.)
• Enhanced multiphysics capabilities are coming:
– Coupling between numerous physical phenomena.
» Ex: Fluid-structural interaction is the most common example.
» Ex: Semiconductor circuits, EMI and thermal buildup vary with current
densities.
• Improved life predictors, improved service estimations.
• Increasing use of non-deterministic analysis and design methods:
– Statistical modeling of material properties, tolerances, and anticipated loads.
– Sensitivity analyses.
• Faster and more powerful computer hardware. Massively parallel processing.
• FEM and simulation software available via Internet subscription.
• Decreasing reliance on testing. But (??)
Workstationsand Servers
Mainframes
Economics: Physical prototyping costs continue IncreasingEngineer more expensive than simulation tools
1960 2006Years
Cost of CAESimulation
Cost of PhysicalPrototyping
Cost of CAEEngineer
MSC/NASTRANSimulation Costs
(Source: General Motors)
MSC/NASTRANSimulation Costs
(Source: General Motors)
CAE Engineervs. System Costs(Source: Detroit Big3)
CAE Engineervs. System Costs(Source: Detroit Big3)
1960$30,000
1960$30,000
Engineer$36/hr
Engineer$36/hr
2006$0.022006$0.02
System$1.5/hrSystem$1.5/hr
Thanks.