Lol Eq

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Chapter 3 2D Simulations 1

Chapter 32D Simulations

3.1 Triangular Plate

3.2 Threaded Bolt-and-Nut

3.3 More Details

3.4 Spur Gears

3. Stru!tural "rror# $" Con%ergen!e# and Stress

Singularit&

3.' (e%ie)

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Chapter 3 2D Simulations Se!tion 3.1 Triangular Plate 2

Se!tion 3.1 Triangular Plate

Problem Description

The plate is made o* steel and designed

to )ithstand a tensile *or!e o* 2+#+++ N

on ea!h o* its three side *a!es.

,e are !on!erned aout the

de*ormations and the stresses.

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Chapter 3 2D Simulations Se!tion 3.1 Triangular Plate 3

Techniques/ConceptsProe!t S!hemati!

Con!epts/Sur*a!e $rom

S0et!hes

nal&sis T&pe 2D

Plane Stress Prolems

Generate 2D Mesh

2D Solid "lements

Relevance Center and

Relevance

oads/Pressure

Weak Springs

Solution/Total De*ormation

Solution/"5ui%alent Stress

Tools/S&mmetr&

Coordinate S&stem

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Chapter 3 2D Simulations Se!tion 3.2 Threaded Bolt-and-Nut 4

Se!tion 3.2 Threaded Bolt-and-Nut

Problem Description617 Bolt.

627 Nut.

637Plates. 647 Se!tion

%ie).

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Chapter 3 2D Simulations Se!tion 3.2 Threaded Bolt-and-Nut

The plane o* s&mmetr&

Thea8iso*s&mmetr&

19 mm

67 The 2D

simulationmodel.

6'7$ri!tionless

support.

Problem Description

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Chapter 3 2D Simulations Se!tion 3.2 Threaded Bolt-and-Nut '

Techniques/Concept

s :ide;Sho) S0et!hes

Displa& Model;Plane

dd Material;$ro<en

8is&mmetri! Prolems

Conta!t;Target$ri!tional Conta!ts

"dge Si<ing

oads/$or!e

Supports/$ri!tionless

SupportSolution/Normal Stress

(adial;8ial;:oop Stresses

Nonlinear Simulations

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Chapter 3 2D Simulations Se!tion 3.3 More Details 9

Se!tion 3.3More Details

Plane-Stress

Problems

Plane stress !ondition=

The :oo0>s la) e!omes

prolem ma& assume the

plane-stress !ondition i* its

thi!0ness dire!tion is not

restrained and thus *ree to

e8pand or !ontra!t.

σ Ξ

σ Ξ

σ Ψ

τ ΞΨ

τ ΞΨ

τ ΞΨ

τ ΞΨ

X

Y Z σ

Ψ

Stress state at apoint in plane stress

!ondition.

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Chapter 3 2D Simulations Se!tion 3.3 More Details ?

Plane-Strain

Problems

627 Strain stateat a point inplane strain!ondition.

Plane strain !ondition=

The :oo0>s la) e!omes

prolem ma& assume the plane-

strain !ondition i* its Z -dire!tion is

restrained *rom e8pansion or

!ontra!tion# all !ross-se!tions

perpendi!ular to the Z -dire!tion ha%e

the same geometr&# and all

en%ironment !onditions are in the XY

l

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Chapter 3 2D Simulations Se!tion 3.3 More Details @

ε Ρ

ε Ρ

ε Ζ

ε Ζ

ε θ

ε θ

γ ΡΖ

γ ΡΖ

σ Ρ

σ Ρ

σ Ζ

σ Ζ

σ θ

σ θ

τ ΡΖ

τ ΡΖ

617 Strainstate at apoint in

a8is&mmetri!

!ondition.

627 Stressstate at a

point ina8is&mmetri!

!ondition.

Ais!mmetric Problems

A* the geometr&# supports#

and loading o* a stru!ture are

a8is&mmetri! aout the Z -

a8is# then all response

5uantities are independent o*

!oordinate.

An su!h a !ase#

oth andare generall& not

<ero. The& are termed hoop

stress and hoop strain

respe!ti%el&.

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Chapter 3 2D Simulations Se!tion 3.3 More Details 1+

Pull-do)n Menus and

Toolars

utline o* Proe!t Tree

Details ie)

Geometr&

Graph

Taular Data

Status Bar

Separators

Mechanical "#$

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Pro%ect Tree

proe!t tree ma& !ontain one or more

simulation models.

simulation model ma& !ontain one or

more &nvironment ran!hes# along )ith

other oe!ts. De*ault name *or the

&nvironment ran!h is the name o* the

anal&sis s&stem.

n &nvironment ran!h !ontains

Anal!sis Settings# en%ironment

!onditions# and a Solution ran!h.

Solution ran!h !ontains Solution

$n'ormation and se%eral results oe!ts.

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#nit S!stems617 Built-in

units&stems.

627 nits&stem *or

!urrentproe!t.

637 De*aultproe!t

units&stem.

647 Che!0edunit s&stems

are nota%ailale in

the pull-do)n menu.

67 These# along )ith theSA# are !onsistent unit

s&stems.

Consistent %ersus An!onsistent

nit S&stems.

Built-in %ersus ser-DeEned

nit S&stems.

Proe!t nit S&stem.

ength nit in DesignModeler.

nit S&stem in Mechanical.

Anternal Consistent nit

S&stem.

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&nvironment

Con(itions

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Results

)b%ects

*ie+ Results

617 Cli!0 to turnon;oF the lael

o*ma8imum;mini

mum.

627 Cli!0 toturn on;oF the

proe.

647 ou ma&sele!t the s!ale o*

de*ormation.

67 ou !an !ontrolho) the !ontour

displa&s.

6'7 Some results!an displa& )ith

%e!tors.

637 ael.

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Chapter 3 2D Simulations Se!tion 3.4 Spur Gears 1

Se!tion 3.4Spur Gears

Problem Description

627 nd theending stress

here.

617 , are!on!erned )ith

the !onta!tstress here.

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Chapter 3 2D Simulations Se!tion 3.4 Spur Gears 1'

Techniques/Concept

s

Cop& odies Translate

Conta!ts

$ri!tionless

S&mmetri!

Conta!t;Target

dust to Tou!h

oads/Moment

True S!ale

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Chapter 3 2D Simulations Se!tion 3. $illeted Bar 19

Se!tion 3.Stru!tural "rror# $"Con%ergen!e# and StressSingularit&Problem Description

1++ 1++

1 + +

+

(1

+ 0N + 0N

627 The arhas a

thi!0ness o*1+ mm.

617 The aris made o*

steel.

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Chapter 3 2D Simulations Se!tion 3. $illeted Bar 1?

Part A, Stress Discontinuit!

617 Displa!ementEeld is

!ontinuous o%erthe entire od&.

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Chapter 3 2D Simulations Se!tion 3. $illeted Bar 1@

627 riginal!al!ulatedstresses

una%eragedare not

!ontinuousa!ross element

oundaries# i.e.#stress at

oundar& hasmultiple %alues.

637 B& de*ault#stresses area%eraged on

the nodes# andthe stress Eeldis re!al!ulated. That )a&# thestress Eeld is

!ontinuous o%erthe od&.

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Chapter 3 2D Simulations Se!tion 3. $illeted Bar 2+

Part , Structural &rror

$or an element# strain energies !al!ulated using a%eraged stresses and

una%eraged stresses respe!ti%el& are diFerent. The diFeren!e et)een

these t)o energ& %alues is !alled Structural &rror o* the element.

The Ener the mesh# the smaller the stru!tural error. Thus# the stru!tural

error !an e used as an indi!ator o* mesh ade5ua!&.

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Part C, .inite &lement

Convergence617 Huadrilateral

element.

627 Triangularelement.

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Part D, Stress Concentration

617 To a!!uratel&e%aluate the

!on!entrated stress# Ener

mesh is needed#parti!ularl& around the

!orner.

627 Stress!on!entration.

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Part &, Stress

Singularit!Stress singularit& is not

limited to sharp !orners.

n& lo!ations that ha%e

stress o* inEnit& are !alled

singular points.Besides a !on!a%e Ellet o*

<ero radius# a point o*

!on!entrated *or!es is also

a singular point.

The stress in asharp !on!a%e

!orner istheoreti!all&

inEnite.

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Lol Eq