Download - FEM Modelling
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FEM Modelling
ME438
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Finite Element Analysis
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FEM Terminology
• Degrees of freedom (DOF)
• State (primary) variable: displacement in mechanics
•
Conjugate variable: force in mechanics
• Stiffness matrix
• Global stiffness equations
=
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Physical Significance of Vectors u and f in
Miscellaneous FEM Applications
Application
Problem
State (DOF) vector u
represents
Forcing vector f
represents
Structures and solid mechanics Displacement Mechanical force
Heat conduction Temperature Heat flux
Acoustic fluid Displacement potential Particle velocity
Potential flows Pressure Particle velocity
General flows Velocity Fluxes
Electrostatics Electrical potential Charge density
Magnetostatics Magnetic potential Magnetic intensity
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Mathematical Model
Traditionaldefinition
Scaled fabricated version of a physicalsystem e.g. a car or train model
Simulation
orienteddefinition
A model is a symbolic device built tosimulate and predict aspects of
behavior of a system
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ELEMENTS
Finite Element Method
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Attributes of Mechanical Finite Elements
• Dimensionality
• Nodes: serve two purposes
– Geometric definition
–Home for DOFs (connectors)
• Degrees of freedom (DOFs)
• Conjugate nodal forces
• Material properties
• Fabrication properties
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Element Geometry Defined by Node Locations
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Classification of Mechanical Finite Elements
Primitive Structural
Continuum
Special
Macro Elements
Substructures
Superelements
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Primitive Structural Elements
Often built from MoM models
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Continuum Elements
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Special Elements
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Macro Elements
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Substructures
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Substructures
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Early Use of Substructuring
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EXAMPLES OF STRUCTURAL MODELS
FEM
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Machined Component (Mechanical)
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Dam Underground Motion (Civil Engineering)
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Rocket Nozzle (Aerospace)
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Super Tanker (Marine)
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F-16 Internal Structure (Aerodynamics)
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General FEM Modelling Rules
• Use the simplest elements that will do the job
• Do not use complicated elements or special elements
unless sure of what is happening
• Use the coarsest mesh that will capture the
dominant behavior of the physical model,
particularly in design situations
• Simplest model is the best model
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Simplicity
• In production design situation
• Several FEM models of increasing refinement will be
set up as design evolves
• Do not overkill at the beginning
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MESH
Finite Element Method
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Where to Use a Finer Mesh?
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Avoid Elements of Bad Aspect Ratio
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Elements Must Not Cross Interfaces
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Element Geometry Preferences
• In 2D
–Quadrilaterals over Triangles
• In 3D
– Bricks over Wedges
– Wedges over Tetrahedra
Other things being equal, prefer
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LOADS
Finite Element Method
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Load Types
Wind / WaterPressure
Snow Weights onRoofs
Lift in Airplanes
Live Loads onBridges
SurfaceLoads Weight
Inertia
Centrifugal
Thermal
Prestress
Electromagnetic
VolumeLoads
Integration ofsurface loadsalong atransverse
direction
Integration ofvolume loadsalong twotransversedirections
LineLoads
Concentrated / Point Loads
Distributed Loads (more common in structural problems)
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BOUNDARY CONDITIONS
Finite Element Method
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Boundary Conditions
• The most difficult topic for FEM program users
“the devil hides in the boundary”
Natural
Essential
Two Types
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Minimum Support Conditions to Suppress
Rigid Body Motions in 2D
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Minimum Support Conditions to Suppress
Rigid Body Motions in 3D
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Visualizing Symmetry and Antisymmetry
Conditions in 2D
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Example of Application of Symmetry BCs
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Example of Application of Antisymmetry BCs
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Breaking Up Point Loads at Symmetry BCs
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Breaking Up Point Loads at Antisymmetry BCs