6 FEM Modeling: Introduction IFEM Ch 6 Slide 1 Introduction to - - PDF document

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6 FEM Modeling: Introduction IFEM Ch 6 Slide 1 Introduction to - - PDF document

Oct 19, 2022 575 likes •855 views

Introduction to FEM 6 FEM Modeling: Introduction IFEM Ch 6 Slide 1 Introduction to FEM FEM Terminology degrees of freedom (abbrv: DOF) state (primary) variables: displacements in mechanics conjugate variables: forces in mechanics

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SLIDE 1

Introduction to FEM

6

FEM Modeling: Introduction

IFEM Ch 6 – Slide 1

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SLIDE 2

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 + fI

M

IFEM Ch 6 – Slide 2

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SLIDE 3

Introduction to FEM

Application State (DOF) vector u Forcing vector f Problem 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 6 – Slide 3

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SLIDE 4

Introduction to FEM

Where FEM Fits (from Chapter 1)

Physical system Modeling + discretization + solution error Discretization + solution error Solution error Discrete model Mathematical model CONTINUIFICATION REALIZATION & IDENTIFICATION IDEALIZATION DISCRETIZATION SOLUTION

FEM

Discrete solution

IFEM Ch 6 – Slide 4

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SLIDE 5

Introduction to FEM

Idealization Process (from Chapter 2)

joint

Physical System

support member IDEALIZATION

  • Mathematical Model

IFEM Ch 6 – Slide 5

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SLIDE 6

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 6 – Slide 6

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SLIDE 7

Introduction to FEM

Implicit Modeling

FEM Library

  • f Black-Box

FEM Code Component

discrete model Component equations Physical system System discrete model Complete solution Mathematical model

SYSTEM LEVEL COMPONENT LEVEL IFEM Ch 6 – Slide 7

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SLIDE 8

Introduction to FEM

Recall the "Breakdown" DSM Steps

Disconnection Localization Member (Element) Formation

  • > generic elements

Breakdown

  

Let Stop Here and Study Generic Elements next

IFEM Ch 6 – Slide 8

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SLIDE 9

Introduction to FEM

... Because Most of the Remaining DSM Steps

Globalization Merge Application of BCs Solution Recovery of Node Forces are Element Independent

IFEM Ch 6 – Slide 9

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SLIDE 10

Introduction to FEM

Attributes of Mechanical Finite Elements

Dimensionality Nodes serve two purposes: geometric definition home for DOFs (connectors) Degrees of freedom (DOFs) or "freedoms" Conjugate node forces Material properties Fabrication properties

IFEM Ch 6 – Slide 10

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SLIDE 11

Introduction to FEM

Element Geometry Is Defined by Node Locations

1D 2D 2D 3D

IFEM Ch 6 – Slide 11

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SLIDE 12

Introduction to FEM

Classification of Mechanical Finite Elements

Primitive Structural Continuum Special Macroelements Substructures

  

Superelements

IFEM Ch 6 – Slide 12

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SLIDE 13

Introduction to FEM

Primitive Structural Elements

(often built from MoM models)

Physical Structural Component Finite Element Discretization bar beam tube, pipe spar (web) shear panel (2D version of above) Mathematical Model Name

IFEM Ch 6 – Slide 13

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SLIDE 14

Introduction to FEM

Continuum Elements

plates 3D solids Physical Finite element idealization Physical Finite element idealization

IFEM Ch 6 – Slide 14

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SLIDE 15

Introduction to FEM

Special Elements

Infinity

Infinite element Crack element Honeycomb panel

double node

IFEM Ch 6 – Slide 15

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SLIDE 16

Introduction to FEM

MacroElements

IFEM Ch 6 – Slide 16

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SLIDE 17

Introduction to FEM

Substructures

IFEM Ch 6 – Slide 17

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SLIDE 18

Introduction to FEM

Substructures (cont'd)

S1 S2 S3 S4 S5 S6

IFEM Ch 6 – Slide 18

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SLIDE 19

Introduction to FEM

Boundary Conditions (BCs)

The most difficult topic for FEM program users ("the devil hides in the boundary") Two types

Essential Natural   

IFEM Ch 6 – Slide 19

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SLIDE 20

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 6 – Slide 20

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SLIDE 21

Introduction to FEM

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

IFEM Ch 6 – Slide 21

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SLIDE 22

Introduction to FEM

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

  • Cavitating volume

Base rock Saturated soil Unsaturated fill Concrete Base ground motion Water Sandstone

IFEM Ch 6 – Slide 22

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SLIDE 23

Introduction to FEM

Examples of Structural Models: Rocket Nozzle (Aerospace Engrg)

  • GRAPHITE

GLASS FILAMENT GLASS FABRIC STEEL SHELL ASBESTOS INSULATOR

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

Rotational axis

(b) Finite element idealization

21.37"

IFEM Ch 6 – Slide 23

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SLIDE 24

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 6 – Slide 24

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SLIDE 25

Introduction to FEM

Examples of Structural Models: F16 External View (Aero)

IFEM Ch 6 – Slide 25

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SLIDE 26

Examples of Structural Models: F16 Internal Structure (Aero)

Introduction to FEM

IFEM Ch 6 – Slide 26