FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling:...

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Introduction to FEM 7 FEM Modeling: Introduction IFEM Ch 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich Thien

Transcript of FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling:...

Page 1: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

7FEM Modeling:

Introduction

IFEM Ch 7 – Slide 1

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 2: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

FEM Terminology

degrees of freedom (abbrv: DOF)

state (primary) variables: displacements in mechanics

conjugate variables: forces in mechanics

stiffness matrix

master stiffness equations

K u = f

K u = f + fIM

IFEM Ch 7 – Slide 2

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 3: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Application State (DOF) vectoru Forcing vectorfProblem represents 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 Electric potential Charge density

Magnetostatics Magnetic potential Magnetic intensity

Physical Significance of Vectors u and f in Miscellaneous FEM Applications

IFEM Ch 7 – Slide 3

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 4: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

The FEM Simulation Process

Physicalsystem

Modeling + discretization + solution error

Discretization + solution error

Solution error

Discrete model

Mathematicalmodel

CONTINUIFICATIONREALIZATION &IDENTIFICATION

IDEALIZATION DISCRETIZATION SOLUTION

FEM Discretesolution

IFEM Ch 7 – Slide 4

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 5: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Idealization

joint

Physical System

support

member

IDEALIZATION

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Mathematical Model

IFEM Ch 7 – Slide 5

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Mathematical Model Definition

A model is a symbolic device built to simulate and predict aspects of behavior of a system

Scaled fabricated version of a physical system(think of a car or train model)

Simulation oriented definition

Traditional definition

IFEM Ch 7 – Slide 6

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 7: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Implicit Modeling

FEM Library

of Black-Box

FEM Code Component

discrete

model

Component

equations

Physical

system

System

discrete

model

Complete

solution

Mathematical

model

SYSTEM

LEVEL

COMPONENT

LEVEL

IFEM Ch 7 – Slide 7

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 8: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Recall the "Breakdown" DSM Steps

DisconnectionLocalizationMember (Element) Formation

Breakdown

Let Stop Here and Study Generic Elements next

IFEM Ch 7 – Slide 8

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 9: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

... Because Most of the Remaining DSM Steps

GlobalizationMergeApplication of BCsSolutionRecovery of Node Forces

are Element Independent

IFEM Ch 7 – Slide 9

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 10: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Attributes of Mechanical Finite Elements

DimensionalityNodes serve two purposes geometric definition home for DOFs (connectors)

Degrees of freedom (DOFs) or "freedoms"Conjugate node forces

Material propertiesFabrication properties

IFEM Ch 7 – Slide 10

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 11: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Element Geometry Is Defined by Node Locations

1D

2D

2D

3D

IFEM Ch 7 – Slide 11

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Classification of Mechanical Finite Elements

Primitive Structural

Continuum

Special

Macroelements

Substructures

Superelements

IFEM Ch 7 – Slide 12

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 13: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEMPrimitive Structural Elements

(often built from MoM models) PhysicalStructural

Component

Finite ElementDiscretization

bar

beam

tube, pipe

spar (web)

shear panel(2D version of above)

MathematicalModel Name

IFEM Ch 7 – Slide 13

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Continuum Elements

plates 3D solids

PhysicalFinite elementidealization

Physical Finite elementidealization

IFEM Ch 7 – Slide 14

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 15: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Special Elements

Infinity

Infinite element

Crackelement

Honeycombpanel

double node

IFEM Ch 7 – Slide 15

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 16: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

MacroElements

IFEM Ch 7 – Slide 16

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Substructures

IFEM Ch 7 – Slide 17

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Substructures (cont'd)

S1

S2

S3

S4

S5

S6

IFEM Ch 7 – Slide 18

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Boundary Conditions (BCs)

The most difficult topic for FEM program users ("the devil hides onthe boundary")

Two types

Essential

Natural

IFEM Ch 7 – Slide 19

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 20: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Boundary Conditions Essential vs. Natural

1. If a BC involves one or more DOF in a direct way, it is essential and goes to the Left Hand Side (LHS) of Ku = f

2. Otherwise it is natural and goes to the Right Hand Side (RHS) of Ku = f

Recipe:

IFEM Ch 7 – Slide 20

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 21: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Examples of Structural Models:Machine Component (Mech. Engrg)

IFEM Ch 7 – Slide 21

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 22: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Examples of Structural Models:Dam under Ground Motion (Civil Engrg)

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Cavitating volume

Base rock

Saturated soilUnsaturated fill

Concrete

Base ground motion

Water

Sandstone

IFEM Ch 7 – Slide 22

Department of Engineering Mechanics PhD. TRUONG Tich Thien

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Introduction to FEM

Examples of Structural Models:Rocket Nozzle (Aerospace Engrg)

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GRAPHITE

GLASS FILAMENTGLASS FABRIC

STEEL SHELLASBESTOSINSULATOR

(a) Typical solid rocket nozzle (Aerojet Corp., 1963)

Rotational axis

(b) Finite element idealization

21.37"

IFEM Ch 7 – Slide 23

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 24: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Examples of Structural Models:SuperTanker (Marine Engrg)

A

B

Neutral Axis

Cross section of tanker

Typical internal structure of tanker

Centerline Girder Longitudinal

Web Frame

Stringer

Introduction to FEM

IFEM Ch 7 – Slide 24

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 25: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Introduction to FEM

Examples of Structural Models: F16 External View (Aero)

IFEM Ch 7 – Slide 25

Department of Engineering Mechanics PhD. TRUONG Tich Thien

Page 26: FEM Modeling: Introductiontttruong/IFEM.Ch07.Slides.pdfIntroduction to FEM 7 FEM Modeling: Introduction IFEM C h 7 – Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich

Examples of Structural Models: F16 Internal Structure (Aero)

Introduction to FEM

IFEM Ch 7 – Slide 26

Department of Engineering Mechanics PhD. TRUONG Tich Thien