Institute of Structural Engineering Page 1

Method of Finite Elements I

Part 1 : Modelling

Practical application of the MFE

Method of Finite Elements I

Institute of Structural Engineering Page 2

Method of Finite Elements I

Goals of this Lecture

• Demonstrating the importance of modelling

when applying the MFE

• Closing the gap between

structural analysis theory and

application of FE software

Note: In this lecture the focus is on structural engineering

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Method of Finite Elements I

Structural Engineering=

Mission impossible

"Structural engineering is the art of molding materials we

don't wholly understand, into shapes we can't fully analyze,

so as to withstand forces we can't really assess, in such a

way that the community at large has no reason to suspect

the extent of our ignorance."

Always keep this in mind when doing

advanced FE calculations!

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Method of Finite Elements I

Structural Engineering

X

Y

Physical

PROBLEM

Analytical

SYSTEM

Finite Element

MODELFinite Element

RESULT

Detailed

CONSTRUCTION

Computational Structural Analysis

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Method of Finite Elements I

X

Y

Physical

PROBLEM

Analytical

SYSTEM

Finite Element

MODELFinite Element

RESULT

Detailed

CONSTRUCTION

Modelling Calculation Detailing

engineer computer engineer

Note: The computer is playing a minor role!

Structural Engineering

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Method of Finite Elements I

FE Modelling

X

Y

Physical

PROBLEM

Analytical

SYSTEM

Finite Element

MODEL

• Structure type e.g. 2D/3D, frame, shell

• Analysis type linear statics, nonlinear dynamics

• Analytical system nodes, elements, boundary conditions

• Actions moving load, earthquake

Modelling = defining…

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Method of Finite Elements I

World

Object Airplane Building

Problem Vibrations

Cracking

Deformations

Collapse

(FE) Model

Analysis Linear dynamics

Stresses

Linear statics/dynamics

Ultimate load

Structure 3D shell 2.5D slabs

3D frame

Mechanical Eng Civil Eng

FE Modelling

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Method of Finite Elements I

Example: Modelling a Girder

Model B

Model A

Model C

?

?

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Method of Finite Elements I

Modelling

• Building an appropriate, consistent analytical system

• Making assumptions based on engineering judgement

• The (one and only) correct model does not exit

Modelling is hard, but the most important step!

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Method of Finite Elements I

Example: Slab on ColumnsFE Model

2D slab

3 dof/node, bending element

linear elastic analysis

point support

=> Stress concentrations at support node !

Best FE model = ?

FE Model A

slab

column

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Method of Finite Elements I

1. Find reactions from point support

FE Model B

Example: Slab on Columns

=> No clamped support possible !

FE Model C

elastic element support

=> Best results !

2. Add correcting loads:

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Method of Finite Elements I

Example: Modelling a Building

Physical Problem FE Models

Incr

ease

d c

om

ple

xit

y

?

3D shell

3D frame

2.5D slabs + 3D frame /

system of beams

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Method of Finite Elements I

Example: Modelling a Building

1.

2.

Storey i

Storey i-1

3.

2.5 D Model for vertical loads: "Stack of slabs"

1. Upper story: 2D slab analysis

=> reactions

2. Walls/columns: reaction transfer

+ dead load => foot reactions

3. Lower story: import reactions

as slab loads

Start with top story:

Continue to next story and

repeat the 3 steps

all the way to the foundation.

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Method of Finite Elements I

Example: Modelling a Building

3D frame /

system of beams3D shell

Equivalent

cantilever

beam

??

EarthquakeAnalysis

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Method of Finite Elements I

Model: 3D Shell

• Good

– Suitable for any geometry (curved shells..)

– Nicest result pictures (marketing..)

• Bad

– Most detailed model (big input => big output)

– Verifying the results is extremely demanding

– Not fully covered by codes

– Long computing times (=> no sensitivity analysis possible..)

– No direct results for construction (reinforcement of walls..)

• Verdict

– Not suited for engineering practice

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Method of Finite Elements I

Model: 3D Frame

• Good

– Based on beam theory (=> result interpretation..)

– Directly supported by codes

– Very well covered by literature

– Suitable for all types of analysis

– Short computing times (=> sensitivity analysis..)

– Direct results for construction

• Bad

– Cannot model 3D curved shell structures

• Verdict

– Best model for engineering practice

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Method of Finite Elements I

The 4 Golden Rulesof FE-Modelling

1. Understand the problem before

starting the FE software

2. Model the (structural) system not the geometry

3. Unverifiable FE results are generally false

4. Follow the basic system assumptions

all the way to the construction

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Method of Finite Elements I