Purpose of the Course 1

Lecturer:

Lars Andersen, MSc, PhD, Associate Professor

Department of Civil Engineering, Division of Structural MechanicsA lb U i it S h d h l j 57 DK 9000 A lbAalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg

Phone: 9940 8455 | E-mail: la@civil.aau.dk

Homepage of the course:

www.wind.civil.aau.dk → Teaching Activities → Finite Element Design

After the course, the student must be able to:

Understand the basic concepts in Finite Element Analysis (FEA)Understand the basic concepts in Finite Element Analysis (FEA)

Use a FEA program (STAAD.Pro 2007)

K th b i t d l ith b hi d th l iKnow the basic terms and algorithms behind the analysis

Be able to analyse large complex structures

Come up with realistic dimensions of structural elements.

Contents of the lecture 2

Introduction to the Finite-Element Method (FEM)

ه What is Finite-Element Analysis (FEA)?

ه Historic overview

ه Why use FEA?

ه Input and output from an FEAp p

ه How does FEM work?

ه Example in STAAD.ProExample in STAAD.Pro

ه Exercise: Learn to use STAAD.Pro (plane-frame problem)

Short Historic Overview of FEM 3

FEM is tied with the development of computer technology

Approximately 40 years old

NASA developed NASTRAN in the 1960s

First College Course in FEM was offered in 1970

In the 1970s, FEM was limited to large corporations with expensive mainframe computers

In the 1980s, “powerful” desktop computers made FEM an indispensable engineering toolindispensable engineering tool

In the 1990s, more complex elements are introduced, optimization capabilities are integrated and CAD programs areoptimization capabilities are integrated, and CAD programs are used for modelling complex structures

Originally, the method was developed for the analysis of g y p ystresses in structures – but today FEM is used to analyse heat transfer, fluid flow, electric and magnetic fields etc.

Why use FEA? Simple Statically Determinate System 4

Freeway-crossing north of Aalborg ...

i t d b t ti ll d t i t t... approximated by statically determinate system

5 reaction forces determined by 5 equilibrium equations

Why use FEA? Simple Statically Indeterminate System 5

Freeway-crossing north of Aalborg ...

i t d b t ti ll i d t i t t... approximated by statically indeterminate system

6 reaction forces but only 3 equilibrium equations

Why use FEA? Complex Structure 6

David Fay Custom Chair

Golden Gate Bridge, San Francisco

Antwerp Railway Station, Belgium Kandahar Airport, Afghanistan

Why use FEA? Load combinations 7

Discrete Versus Continuous System 8

Prototype = reality

Continuous system Discrete system = FE model

Input and Output from an FEA 9

Di i f hInput:

ه Dimensions of the structure

ه Cross-section types (circular, rectangular, I-profile, ...)

ه Material properties (wood, steel, concrete, glass, ...)

ه Supports (fixed, free, moving, ...)

ه Loads (concentrated, line, surface, combinations)

ه Deformation components (translation, rotation)Output:

ه Section force curves, reactions (shear, normal, moment)

ه Strains and stresses (shear, normal)

ه Fulfilment of design criteria (Eurocode, ...)

ه Eigenmodes (dynamic resonance risk, ...)

Eigenmodes/Eigenfrequencies 10

Tacoma Narrows Bridge, 1940

Eigenmodes/Eigenfrequencies 11

Millenium Bridge London, 2000/2002

Eigenmodes/Eigenfrequencies 12

FEA Programs 13

Commercial Finite-Element Programs:

ه ABAQUS (www.simulia.com)

ه COSMOSWorks (SolidWorks) (www.cosmosm.com)

ه FEMLAB (www.comsol.dk)

ه STAAD.Pro (www.bentley.com)STAAD.Pro (www.bentley.com)

ه ANSYS Structural (www.ansys.com)

ه etcه etc.

How Does FEA work? Dividing the structure into elements 14

ه From the user input, a given structure is divided into small elements (finite elements) (done partly by user and partly by program)(done partly by user and partly by program)

ه Each element is assigned material properties (done by user)

ه Each element’s mechanical behaviour is defined by a set of differential equationsه Each element s mechanical behaviour is defined by a set of differential equations from the choice of element type and material properties (done by program)

How Does FEA work? Matrix Equations for the Elements are Found 15

ه The differential equations for each element are solved and d i t t i f l ti it bl f tarranged into a matrix formulation suitable for computer-

aided solutions (done by program)

How Does FEA work? Matrix Equation for the Global System is Assembled 16

ه The element matrices are combined into a global system of ti d fi d f th l t f th tiequations defined from the placement of the respective

elements (done by program)

ه From this the global structural equation is obtainedه From this the global structural equation is obtained(done by program)

How Does FEA work? Load and Boundary Conditions are Applied 17

ه The boundary conditions (loads and supports) are specified(d b )(done by user)

ه The boundary conditions are incorporated into the system of differential equations (done by program)differential equations (done by program)

How Does FEA work? The Structural Matrix Equation is Solved 18

ه The displacement (and rotations) of all nodes are found from solving th t f ti (d b )the system of equations (done by program)

ه Displacements at intermediate points are found from interpolation of nodal values (done by program)nodal values (done by program)

How Does FEA work? Stresses and Strains are found 19

ه The strains are found from the displacements (done by program)

ه Stresses are found from a constitutive relation (done by program)

How Does FEA work? The design criteria are checked 20

ه The design criteria are checked (done by user/program)

ه The structure is modified to fulfil criteria and a new analysis is made (done by user)

Example – Analytical Solution 21

Structural system:

Analytical solution:Analytical solution:

STAAD.Pro – Overview

Editor22

Editor

Add beam

Mark beam

Hold down ctrl to move the starting point of a beam

Menu S dMenu Snap node

STAAD.Pro – Overview 23

General D t bGeneral, property, support, l d

Database

load

STAAD.Pro – Overview 24

Analyse/printAnalyse/print

All

STAAD.Pro – Script file 25

Node coordinates

Member definition

M t i l d fi itiMaterial definition

Section assignment

Material assignment

Support assignmentSupport assignment

Load assignment

Analysis definition

STAAD.Pro – Analysis Analyze Mode 26

STAAD.Pro – Results 27

Double-click givesDouble click gives section displacement

Node displacement

Reactions

Section forces

Example – Numerical Result from STAAD.Pro 28

Analytical solution:Analytical solution:

Today's Problem 29

Plane bridge

Determine the profile types from the deformation criteria (1/200 of span).ete e t e p o e types o t e de o at o c te a ( / 00 o spa )

Change the supports and determine the profile types in the same manner.

Get familiar with the program. (Use the menu Geometry/Split Beam to p g ( y pdivide the vertical beam into 3 for easy applying the load)

Today's Problem 30

Support types(F)ixed, (P)ined, (F)ixed (B)ut (direction)

Profile types Maximum deformation(Global deformation), local (x,y)-coordinates

FB P F IPE160 HE200B di di di

(F)ixed, (P)ined, (F)ixed (B)ut (direction) (Global deformation), local (x,y) coordinates

+FB(Fx,Mz)

P F IPE160 HE200B y-dir139.2 mmx=4.167

y-dir165.6 mmx=5.833

x-dir33.8 mmy=2.85+1.45

FB P F(Fx,Mz)

F F F

P P P

50 mm50 mm

50 mmMaximum allowed deformation 1/200 of span = 50 mm