fem modelling

8/18/2019 FEM Modelling

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FEM Modelling

ME438

–

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



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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



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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



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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

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