Ansys Workbench-Chapter03

Chapter 3 2D Simulations 1

Chapter 32D Simulations3.1 Step-by-Step: Triangular Plate

3.2 Step-by-Step: Threaded Bolt-and-Nut

3.3 More Details

3.4 More Exercise: Spur Gears

3.5 More Exercise: Filleted Bar

3.6 Review

Chapter 3 2D Simulations Section 3.1 Triangular Plate 2

Section 3.1Triangular Plate

Problem Description

• The plate is made of steel and designed to

withstand a tensile force of 20,000 N on each

of its three side faces.

• We are concerned about the deformations

and the stresses.

Chapter 3 2D Simulations Section 3.1 Triangular Plate 3

Techniques/Concepts • Project Schematic

• Concepts>Surface From Sketches

• Analysis Type (2D)

• Plane Stress Problems

• Generate 2D Mesh

• 2D Solid Elements

• <Relevance Center> and

<Relevance>

• Loads>Pressure

• Weak Springs

• Solution>Total Deformation

• Solution>Equivalent Stress

• Tools>Symmetry

• Coordinate System

Chapter 3 2D Simulations Section 3.2 Threaded Bolt-and-Nut 4

Section 3.2Threaded Bolt-and-Nut

Problem Description

[1] Bolt. [2] Nut.

[3] Plates.[4] Section

view.


The plane of symmetry

The axis of sym

metry

17 mm

[1] The 2D simulation

model.

[6] Frictionless support.


Techniques/Concepts

• Hide/Show Sketches

• Display Model/Plane

• Add Material/Frozen

• Axisymmetric Problems

• Contact/Target

• Frictional Contacts

• Edge Sizing

• Loads>Force

• Supports>Frictionless Support

• Solution>Normal Stress

• Radial/Axial/Hoop Stresses

• Nonlinear Simulations

Chapter 3 2D Simulations Section 3.3 More Details 7

Section 3.3More Details

Plane-Stress Problems

• Plane stress condition:

σ

Z= 0, τ

ZY= 0, τ

ZX= 0

• The Hook's law becomes

εX=σ

X

E−ν

σY

E

εY=σ

Y

E−ν

σX

E

εZ= −ν

σX

E−ν

σY

E

γXY

=τ

XY

G, γ

YZ= 0, γ

ZX= 0

• A problem may assume the

plane-stress condition if its

thickness direction is not

restrained and thus free to

expand or contract.

σ

X σ

X

σ

Y

τ

XY

τ

XY

τ

XY

τ

XY

X

Y Z

σ

Y Stress state at a point of a zero thickness

plate, subject to in-plane forces.


Plane-Strain Problems

[2] Strain state at a point of a plane-strain structure.

X

Y

Z

ε

Y

ε

X

γ

XY

ε

X

ε

Y

γ

XY

• Plane strain condition:

ε

Z= 0, γ

ZX= 0, γ

ZY= 0

• The Hook's law becomes

σX= E

(1+ ν )(1− 2ν )(1−ν )ε

X+ νε

Y⎡⎣ ⎤⎦

σY= E

(1+ ν )(1− 2ν )(1−ν )ε

Y+ νε

X⎡⎣ ⎤⎦

σZ= E

(1+ ν )(1− 2ν )νε

X+ νε

Y⎡⎣ ⎤⎦

τXY

= GγXY

, τYZ

= 0, τZX

= 0

• A problem may assume the plane-strain

condition if its Z-direction is restrained

from expansion or contraction, all cross-

sections perpendicular to the Z-direction

have the same geometry, and all

environment conditions are in the XY plane.


ε

R

ε

R

ε

Z

ε

Z

εθ

εθ

γ

RZ γ

RZ

σ

R

σ

R

σ

Z

σ

Z

σθ

σθ

τ

RZ τ

RZ

[1] Strain state at a point of a

axisymmetric structure.

[2] Stress state at a point of a

axisymmetric structure.

Axisymmetric Problems

• If the geometry, supports, and

loading of a structure are

axisymmetric about the Z-axis,

then all response quantities are

independent of θ coordinate.

• In such a case,

γ θR

= 0, γ θZ= 0

τθR

= 0, τθZ= 0

• both σθ andεθ are generally not

zero. They are termed hoop

stress and hoop strain respectively.


Mechanical GUI

• Pull-down Menus

and Toolbars

• Outline of Project

Tree

• Details View

• Geometry

• Graph

• Tabular Data

• Status Bar

• Separators


Project Tree

• A project tree may contain one or more

simulation models.

• A simulation model may contain one or more

<Environment> branches, along with other

objects. Default name for the <Environment>

branch is the name of the analysis system.

• An <Environment> branch contains <Analysis

Settings>, environment conditions, and a

<Solution> branch.

• A <Solution> branch contains <Solution

Information> and several results objects.


Unit Systems[1] Built-in unit

systems.

[2] Unit system for current

project.

[3] Default project unit

system.

[4] Checked unit systems won't be

available in the pull-down menu.

[5] These, along with the SI, are consistent unit

systems.

• Consistent versus Inconsistent

Unit Systems.

• Built-in versus User-Defined Unit

Systems.

• Project Unit System.

• Length Unit in <DesignModeler>.

• Unit System in <Mechanical>.

• Internal Consistent Unit System.


Environment Conditions


Results Objects

View Results

[1] Click to turn on/off the label of

maximum/minimum.

[2] Click to turn on/off the probe.

[4] You may select the scale of deformation.

[5] You can control how the contour

displays.

[6] Some results can display with

vectors.

[3] Label.

Chapter 3 2D Simulations Section 3.4 Spur Gears 15

Section 3.4Spur Gears

Problem Description

[2] And the bending stress here.

[1] What we are concerned most is the contact stress

here.

Chapter 3 2D Simulations Section 3.4 Spur Gears 16

Techniques/Concepts

• Copy bodies (Translate)

• Contacts

• Frictionless

• Symmetric (Contact/Target)

• Adjust to Touch

• Loads>Moment

• True Scale

Chapter 3 2D Simulations Section 3.5 Filleted Bar 17

100 100

100

50

R15

50 kN 50 kN

Section 3.5Filleted Bar

Problem Description

[2] The bar has a thickness of

10 mm.

[1] The bar is made of steel.


Part A. Stress Discontinuity

Displacement field is continuous over the

entire body.


[2] Original calculated stresses

(unaveraged) are not continuous across

element boundaries, i.e., stress at boundary

has multiple values.

[4] By default, stresses are averaged on the nodes, and the stress field is recalculated. That

way, the stress field is continuous over the body.


Part B. Structural Error

• For an element, strain energies calculated using averaged stresses and unaveraged

stresses respectively are different. The difference between these two energy values is

called <Structural Error> of the element.

• The finer the mesh, the smaller the structural error. Thus, the structural error can be

used as an indicator of mesh adequacy.


0.0779

0.0780

0.0781

0.0782

0.0783

0.0784

0.0785

0.0786

0.0787

0 2000 4000 6000 8000 10000 12000 14000

Dis

plac

emen

t (m

m)

Number of Nodes

Part C. Finite Element Convergence

[1] Quadrilateral element.

[2] Triangular element.

[3] Increasing nodes.


Part D. Stress Concentration

[1] To accurately evaluate the

concentrated stress, finer mesh is needed,

particularly around the corner.

[2] Stress concentration.


Part E. Stress Sigularity

The stress in this zero-radius fillet is theoretically

infinite.

• Stress singularity is not limited

to sharp corners.

• Any locations that have stress

of infinity are called singular

points.

• Besides a concave fillet of zero

radius, a point of concentrated

forces is also a singular point.

Ansys Workbench-Chapter03

Engineering

Transcript of Ansys Workbench-Chapter03