Sammelmappe1 ansys

Chapter 1 Introduction 1

Chapter 1Introduction1.1 Case Study: Pneumatically Actuated PDMS Fingers

1.2 Structural Mechanics: A Quick Review

1.3 Finite Element Methods: A Conceptual Introduction

1.4 Failure Criteria of Materials

1.5 Review

Chapter 1 Introduction Section 1.1 Case Study: Pneumatically Actuated PDMS Fingers 2

Section 1.1Case Study: Pneumatically Actuated PDMS Fingers

[1] The pneumatic fingers are part of a

surgical parallel robot system remotely

controlled by a surgeon through the Internet.

[2] A single finger is studied in

this case.

Problem Description


[6] Undeformed shape.

[5] As air pressure applies, the finger bends

downward.

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1.0

Stre

ss (

MPa

)

Strain (Dimensionless)

[4] The strain-stress curve of the PDMS elastomer used in

this case.

[3] Geometric

model.


Static Structural Simulations

[1] Prepare material

properties.

[2] Create geometric model.

[3] Generate finite element mesh.

[4] Set up loads and supports.

[5] Solve the model.

[6] View the results.


[7] Displacements.

[8] Strains.


Buckling and Stress-Stiffening

[2] The upper surface would undergo compressive stress.

It in turn reduces the bending stiffness.

[1] If we apply an upward

force here...

• Stress-stiffening: bending stiffness increases with increasing axial tensile stress, e.g., guitar string.

• The opposite also holds: bending stiffness decreases with increasing axial compressive stress.

• Buckling: phenomenon when bending stiffness reduces to zero, i.e., the structure is unstable.

Usually occurs in slender columns, thin walls, etc.

• Purpose of a buckling analysis is to find buckling loads and buckling modes.


Dynamic Simulations

• When the bodies move and

deform very fast, inertia effect

and damping effect must be

considered.

• When including these

dynamic effects, it is called a

dynamic simulation.


Modal Analysis

• A special case of dynamic

simulations is the simulation of free

vibrations, the vibrations of a

structure without any loading.

• It is called a modal analysis.

• Purpose of a modal analysis is to

find natural frequencies and mode

shapes.


Structural Nonlinearities

-30

-25

-20

-15

-10

-5

0

0 40 80 120 160 200

Def

lect

ion

(mm

)

Pressure (kPa)

[1] Solution of the nonlinear simulation of the PDMS finger.

[2] Solution of the linear simulation pf the PDMS finger.

• Linear simulations assume that

the response is linearly

proportional to the loading.

• When the solution deviates from

the reality, a nonlinear simulation

is needed.

• Structural nonlinearities come

from large deformation, topology

changes, nonlinear stress-strain

relationship, etc.

Chapter 1 Introduction Section 1.2 Structural Mechanics: A Quick Review 10

Section 1.2Structural Mechanics: A Quick Review

• Engineering simulation: finding the responses of a problem domain subject to

environmental conditions.

• Structural simulation: finding the responses of bodies subject to

environmental conditions.

• The bodies are described by geometries and materials.

• Environment conditions include support and loading conditions.

• Responses can be described by displacements, strains, and stresses.


Displacements

X

Y

[1] The body before deformation.

[2] The body after deformation.

[4] After the deformation, the

particle moves to a new position.

[5] The displacement vector {u} of the particle is formed by connecting the positions before and after

the deformation.

[3] An arbitrary particle of position (X, Y, Z), before

the deformation.

u{ } = uX

uY

uZ{ }


Stresses

X Y

Z

σ

Y

τ

YX

τ

YZ σ

X

τ

XY

τ

XZ

σ

Z

τ

ZX

τ

ZY

[1] The reference frame XYZ.

[2] This face is called X-face, since the X-direction is normal

to this face.

[4] The X-component of the stress on X-face.

[3] This face is called negative X-face.

[5] The Y-component of the stress on X-face.

[6] The Z-component of the stress on X-face.

σ{ } =σ

Xτ

XYτ

XZ

τYX

σY

τYZ

τZX

τZY

σZ

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪

τ

XY= τ

YX, τ

YZ= τ

ZY, τ

XZ= τ

ZX

σ{ } = σ

Xσ

Yσ

Zτ

XYτ

YZτ

ZX{ }


Strains

X

Y

′A ′B

′C

′′B

′′C

A B

C

′′′C

′′′B

D

[2] Original configuration ABC.

[3] After deformation, ABC moves to

′A ′B ′C .[4] To compare with original configuration, rotate ′A ′B ′C to a new configuration ′A ′′B ′′C .

[5] Translate ′A ′′B ′′C so

that ′A coincides with A. The new configuration is

A ′′′B ′′′C . Now C ′′′C is the amount of stretch of ABC in

Y-face.

[6] The vector BD describes the stretch of

ABC in X-face.

[7] And the vector D ′′′B describes the twist

of ABC in X-face.

[1] The reference frame.

Strain on X-face =

B ′′′BAB

ε

X= BD

AB, γ

XY= D ′′′B

AB


ε{ } =ε

Xγ

XYγ

XZ

γYX

εY

γYZ

γZX

γZY

εZ

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪

γ

XY= γ

YX, γ

YZ= γ

ZY, γ

XZ= γ

ZX

ε{ } = ε

Xε

Yε

Zγ

XYγ

YZγ

ZX{ }

• Physical meaning of strains:

• The normal strain εX is the

percentage of stretch of a fiber which

lies along X-direction.

• The shear strain γ XY is the angle

change (in radian) of two fibers lying

on XY-plane and originally forming a

right angle.

• We can define other strain components

in a similar way.


Governing Equations

u{ } = u

Xu

Yu

Z{ }

σ{ } = σ

Xσ

Yσ

Zτ

XYτ

YZτ

ZX{ }

ε{ } = ε

Xε

Yε

Zγ

XYγ

YZγ

ZX{ }Totally 15 quantities

• Equilibrium Equations (3 Equations)

• Strain-Displacement Relations (6 Equations)

• Stress-Strain Relations (6 Equations)


Stress-Strain Relations: Hooke's Law

εX=σ

X

E−ν

σY

E−ν

σZ

E

εY=σ

Y

E−ν

σZ

E−ν

σX

E

εZ=σ

Z

E−ν

σX

E−ν

σY

E

γXY

=τ

XY

G, γ

YZ=τ

YZ

G, γ

ZX=τ

ZX

G

G = E

2(1+ ν )

• For isotropic, linearly elastic materials,

Young's modulus (E) and Poisson's ratio (ν )

can be used to fully describe the stress-

strain relations.

• The Hooke's law is called a material

model.

• The Young's modulus and the Poisson's

ratio are called the material parameters

of the material model.


εX=σ

X

E−ν

σY

E−ν

σZ

E+αΔT

εY=σ

Y

E−ν

σZ

E−ν

σX

E+αΔT

εZ=σ

Z

E−ν

σX

E−ν

σY

E+αΔT

γXY

=τ

XY

G, γ

YZ=τ

YZ

G, γ

ZX=τ

ZX

G

• If temperature changes (thermal loads)

are involved, the coefficient of thermal

expansion, (CTE, α ) must be included.

• If inertia forces (e.g., dynamic

simulations) are involved, the mass

density must be included.

Chapter 1 Introduction Section 1.3 Finite Element Methods: A Conceptual Introduction 18

Section 1.3Finite Element Methods: A Conceptual Introduction

• A basic idea of finite element methods is to divide the structural body into small and

geometrically simple bodies, called elements, so that equilibrium equations of each

element can be written, and all the equilibrium equations are solved simultaneously

• The elements are assumed to be connected by nodes located on the elements' edges

and vertices.

Basic Ideas


In case of the pneumatic finger, the structural body is divided into 3122

elements. The elements are connected by 17142 nodes. There are 3x17142 unknown

displacement values to be solved.

• Another idea is to solve unknown

discrete values (displacements at the

nodes) rather than to solve unknown

functions (displacement fields).

• Since the displacement on each node

is a vector and has three components

(in 3D cases), the number of total

unknown quantities to be solved is

three times the number of nodes.

• The nodal displacement components

are called the degrees of freedom

(DOF's) of the structure.


• In static cases, the system of equilibrium equations has following form:

K⎡⎣ ⎤⎦ D{ } = F{ }

• The displacement vector {D} contains displacements of all degrees of

freedom.

• The force vector {F} contains forces acting on all degrees of freedom.

• The matrix [K] is called the stiffness matrix of the structure. In a special

case when the structure is a spring, {F} as external force, and {D} as the

deformation of the spring, then [K] is the spring constant.


Basic Procedure of Finite Element Method

1. Given the bodies' geometries, material properties, support conditions, and loading

conditions.

2. Divide the bodies into elements.

3. Establish the equilibrium equation: [K] {D} = {F}

3.1 Construct the [K] matrix, according to the elements' geometries and the material

properties.

3.2 Most of components in {F} can be calculated, according to the loading conditions.

3.3 Most of components in {D} are unknown. Some component, however, are known,

according to the support conditions.

3.4 The total number of unknowns in {D} and {F} should be equal to the total number

of degrees of freedom of the structure.


4. Solve the equilibrium equation. Now, the nodal displacements {d} of each element are

known.

5. For each element:

5.1 Calculate displacement fields {u}, using an interpolating method, {u} = [N] {d}. The

interpolating functions in [N] are called the shape functions.

5.2 Calculate strain fields according to the strain-displacement relations.

5.3 Calculate stress fields according to the stress-strain relations (Hooke's law).


Shape Functions

d

1

d

2

d

3

d

4

d

5

d

6

d

7

d

8

X

Y

[1] A 2D 4-node quadrilateral element

[2] This element's nodes locate at

vertices.

• Shape functions serve as interpolating

functions, allowing the calculation of

displacement fields (functions of X, Y,

Z) from nodal displacements (discrete

values).

u{ } = N⎡⎣ ⎤⎦ d{ }

• For elements with nodes at vertices,

the interpolation must be linear and

thus the shape functions are linear (of

X, Y, Z).


• For elements with nodes at vertices as well as at middles of edges, the interpolation

must be quadratic and thus the shape functions are quadratic (of X, Y, Z).

• Elements with linear shape functions are called linear elements, first-order elements, or

lower-order elements.

• Elements with quadratic shape functions are called quadratic elements, second-order

elements, or higher-order elements.

• ANSYS Workbench supports only first-order and second-order elements.


Workbench Elements

[1] 3D 20-node structural solid. Each node has 3

translational degrees of

freedom: DX, DY, and DZ.

[2] Triangle-based prism.

[3] Quadrilateral-based pyramid.

[4] Tetrahedron.3D Solid Bodies


2D Solid Bodies

[5] 2D 8-node structural solid. Each node has 2

translational degrees of

freedom: DX and DY.

[6] Degenerated Triangle.


3D Surface Bodies

[7] 3D 4-node structural shell. Each node has 3

translational and 3 rotational degrees of freedom: DX, DY, DZ, RX, RY, and RZ.

[8] Degenerated Triangle

3D Line Bodies

[9] 3D 2-Node beam. Each node has 3 translational and 3 rotational degrees of freedom: DX, DY, DZ,

RX, RY, RZ.

Chapter 1 Introduction Section 1.4 Failure Criteria of Materials 28

Section 1.4Failure Criteria of Materials

Ductile versus Brittle Materials

• A Ductile material exhibits a large amount of strain before it

fractures.

• The fracture strain of a brittle material is relatively small.

• Fracture strain is a measure of ductility.


σ

y

Stre

ss

Strain

[3] Yield point.

[2] Fracture point.

[1] Stress-strain curve for a ductile material.

• Mild steel is a typical ductile material.

• For ductile materials, there often exists an

obvious yield point, beyond which the

deformation would be too large so that the

material is no longer reliable or functional;

the failure is accompanied by excess

deformation.

• Therefore, for these materials, we are most

concerned about whether the material

reaches the yield point σ y .

Failure Points for Ductile Materials


Failure Points for Brittle Materials

• Cast iron and ceramics are two examples

of brittle materials.

• For brittle materials, there usually doesn't

exist obvious yield point, and we are

concerned about their fracture point σ f .

Stre

ss

Strain

[2] Fracture point.

[1] Stress-strain curve for a

brittle material.

σ

f


Failure Modes

• The fracture of brittle materials is mostly due to

tensile failure.

• The yielding of ductile materials is mostly due to shear

failure


Principal Stresses

σ

X σ

X

σ

Y

σ

Y

τ

XY

τ

XY

τ

XY

τ

XY

X

Y

[1] Stress state.

τ

(σ

X,τ

XY)

(σ

Y,τ

XY)

σ

[2] Stress in the base direction.

[3] Stress in the direction that forms 90o with

the base direction.

[4] Other stress pairs could be

drawn.

[6] Point of maximum normal stress.

[7] Point of minimum normal stress.

[8] Point of maximum

shear stress.

[9] Another Point of

maximum shear stress.

[5] Mohr's circle.

• A direction in which the shear

stress vanishes is called a

principal direction.

• The corresponding normal stress

is called a principle stress.


• At any point of a 3D solid, there are three principal directions and

three principal stresses.

• The maximum normal stress is called the maximum principal stress

and denoted by σ1 .

• The minimum normal stress is called the minimum principal stress and

denoted by σ3 .

• The medium principal stress is denoted by σ2 .

• The maximum principal stress is usually a positive value, a tension;

the minimum principal stress is often a negative value, a

compression.


Failure Criterion for Brittle Materials

• The failure of brittle materials is a tensile failure. In other words, a

brittle material fractures because its tensile stress reaches the

fracture strength σ f .

• We may state a failure criterion for brittle materials as follows: At a

certain point of a body, if the maximum principal stress reaches the

fracture strength of the material, it will fail.

• In short, a point of material fails if

σ1 ≥σ f


Tresca Criterion for Ductile Materials

• The failure of ductile materials is a shear

failure. In other words, a ductile material yields

because its shear stress reaches the shear

strength τ y of the material.

• We may state a failure criterion for ductile

materials as follows: At a certain point of a

body, if the maximum shear stress reaches the

shear strength of the material, it will fail.

• In short, a point of material fails if

τmax ≥τ y

• It is easy to show (using

Mohr's circle) that

τmax =

σ1−σ3

2

τ y =

σ y

2

• Thus, the material yields if

σ1−σ3 ≥σ y

• (σ1−σ3) is called the stress

intensity.


Von Mises Criterion for Ductile Materials

• In 1913, Richard von Mises proposed a theory for predicting the yielding of ductile

materials. The theory states that the yielding occurs when the deviatoric strain energy

density reaches a critical value, i.e.,

wd ≥wyd

• It can be shown that the yielding deviatoric energy in uniaxial test is

wyd =

(1+ν )σ y2

3E

• And the deviatoric energy in general 3D cases is

wd =1+ν

6Eσ1−σ2( )2 + σ2 −σ3( )2 + σ3 −σ1( )2⎡

⎣⎢⎤⎦⎥


• After substitution and simplification, the criterion reduces to that the yielding

occurs when

12

σ1−σ2( )2 + σ2 −σ3( )2 + σ3 −σ1( )2⎡⎣⎢

⎤⎦⎥≥ σ y

• The quantity on the left-hand-side is termed von Mises stress or effective stress, and

denoted by σe ; in ANSYS, it is also referred to as equivalent stress,

σe =

12

σ1−σ2( )2 + σ2 −σ3( )2 + σ3 −σ1( )2⎡⎣⎢

⎤⎦⎥

Chapter 2 Sketching 1

Chapter 2Sketching2.1 Step-by-Step: W16x50 Beam

2.2 Step-by-Step: Triangular Plate

2.3 More Details

2.4 More Exercise: M20x2.5 Threaded Bolt

2.5 More Exercise: Spur Gears

2.6 More Exercise: Microgripper

2.7 Review

Chapter 2 Sketching Section 2.1 W16x50 Beam 2

Section 2.1W16x50 Beam

16.2

5"

.628 "

.380"

7.07 "

R.375"

W16x50

[1] Wide-flange I-shape section.

[2] Nominal depth 16 in.

[3] Weight 50 lb/ft.

Problem Description


• Start up <DesignModeler>

• Sketching/Modeling modes

• Draw>Rectangle

• Draw>Polyline

• Dimensions>General

• Dimension>Horizontal

• Dimensions>Display

• Dimensions>Move

• Modify>Copy/Paste

• Modify>Trim

• Modify>Fillet

• Constraints>Symmetry

• Auto Constraints

• Constraint Status

• Extrude

Techniques/Concepts


[1] Click: single selection

[2] Control-click: add/remove selection

[3] Click-sweep: continuous selection.

[4] Right-click: open context menu.

[5] Right-click-drag: box zoom.

[6] Scroll-wheel: zoom in/out.

[7] Middle-click-drag: rotation.

Basic Mouse Operations

Chapter 2 Sketching Section 2.2 Triangular Plate 5

Section 2.2Triangular Plate

40

mm

30 mm

300 mm

[1] The plate has three planes of

symmetry.

[2] Radii of the fillets

are 10 mm.

Problem Description


Techniques/Concepts

• Draw>Arc by Center

• Dimensions> Radius

• Modify>Replicate

• Modify>Offset

• Constraints>Equal Length

• Weak/Strong Dimensions

• Weak/Strong Constraints

• Selection Filter

• Single/Box Selection


2D Graphics Controls

[8] <Undo>.

[9] <Redo>.

[2] <Zoom to Fit>.

[4] <Box Zoom>.[5] <Zoom>.

[1] <Look At Face/Plane/Sketch>.

[6] <Previous View>.

[7] <Next View>. [3] <Pan>.

Chapter 2 Sketching Section 2.3 More Details 8

• Pull-down Menus

and Toolbars

• Mode Tabs

• Tree Outline

• Sketching

Toolboxes

• Graphics area

• Details View

• Status Bar

• Separators

Section 2.3 More Details


[1] Currently active plane.

[2] To create a new plane, click <New

Plane>.

[3] There are many ways of creating new planes.

Sketching Planes

• A sketch must be created on a

sketching plane; each plane may

contain multiple sketches.

• In the very beginning of a

<DesignModeler> session, three

planes are automatically created:

<XYPlane>, <YZPlane>, and

<ZXPlane>.


Sketches

• A sketch consists of points and edges; edges may be straight lines or curves.

• Multiple sketches may be created on a plane.

[1] To create a new sketch on the active sketching plane,

click <New Sketch>.

[2] Currently active sketch.


Auto Constraints

• C - The cursor is coincident with a line.

• P - The cursor is coincident with another point.

• T - The cursor is a tangent point.

• ⊥ - The cursor is a perpendicular foot.

• H - The line is horizontal.

• V - The line is vertical.

• // - The line is parallel to another line.

• R - The radius is equal to another radius.

[1] You can turn on/off <Auto Constraints>.


Sketching Toolboxes

Chapter 2 Sketching Section 2.4 M20x2.5 Threaded Bolt 13

Section 2.4M20x2.5 Threaded Bolt

Problem Description

M20x2.5

[1] Metric system.

[2] Nominal diameter

d = 20 mm.

[3] Pitchp = 2.5 mm.


32

11×

p=

27.5

d

1

d

Externalthreads(bolt)

Internalthreads(nut)

H

H4

H8

p

Minor diameter of internal thread d

1

Nominal diameter d

H = ( 3 2)p = 2.165 mm

d1= d − (5 8)H × 2 =17.294 mm

p


• Dimensions>Angle


• Revolve

Techniques/Concepts

Chapter 2 Sketching Section 2.5 Spur Gears 16

Section 2.5Spur Gears

Problem Description

• To satisfy the fundamental law

of gearing, the gear profiles

are cut to an involute curve.


[7] Common tangent of the pitch circles.

[6] Contact point (pitch

point).

[8] Line of action (common normal of contacting gears). The pressure angle is 20o.

[3] Pitch circlerp = 2.5 in.

[9] Addendumra = 2.75 in.

[10] Dedendumrd = 2.2 in.

[1] The driving gear rotates clockwise.

[2] The driven gear rotates

counter-clockwise.

[4] Pitch circle of the driving gear.

[5] Line of centers.

[12] The fillet has a radius of

0.1 in.

[11] The shaft has a radius of 1.25 in.


Techniques/Concepts

• Draw>Construction Point

• Draw>Spline


• Constraints>Perpendicular

Chapter 2 Sketching Section 2.6 Microgripper 19

Section 2.6Microgripper

Problem Description

[2] Actuation direction.

[1] Gripping direction.

[3] SMA actuator.

[4] Glass bead.


480

144

176

280

400

140

212

77

47

87

20

R25 R45

32

92

D30

Unit: µm

Thickness: 300 µm


Techniques/Concepts

• Constraints>Equal Radius

• Copy bodies (Mirror)

• Create new sketch

• Constraints>Tangent

• Multiple parts

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.

Chapter 4 3D Solid Modeling 1

Chapter 43D Solid Modeling4.1 Step-by-Step: Beam Bracket

4.2 Step-by-Step: Cover of Pressure Cylinder

4.3 Step-by-Step: Lifting Fork

4.4 More Details

4.5 More Exercise: LCD Display Support

4.6 Review

Chapter 4 3D Solid Modeling Section 4.1 Beam Bracket 2

Section 4.1Beam Bracket

Problem Description

The beam bracket is made of WT8x25 steel.

X

Y

Z

Chapter 4 3D Solid Modeling Section 4.1 Beam Bracket 3

• Local coordinate systems

• Sketching with plane view

versus in 3D view

• Use of Triad

• Add Material

• Rounds/Fillets

• Turn on/off edges display

Techniques/Concepts

Chapter 4 3D Solid Modeling Section 4.2 Cover of Pressure Cylinder 4

Section 4.2Cover of Pressure Cylinder

Problem Description

[1] Pressure cylinder.

[2] Cylinder Cover.

[3] Back view of the cover.


30.3

25.3

21.0 1.3

31.

0

3.0 10.0

R8.5 R7.5

R19.0

Unit: mm. 62.0

2.3 1.6 7.4

R4.9 R3.2

R9.0 R14.5 R18.1

R25.4

R27.8

7.4

62.

0

R3.4


Techniques/Concepts

• Create new planes

• Set up local coordinate systems

• Plane with boundary

• Modify>Duplicate

• Cut Material

Chapter 4 3D Solid Modeling Section 4.3 Lifting Fork 7

Section 4.3Lifting Fork

Problem Description[1] Fork (steel).

[2] Glass panel (1.0 mm).


Unit: mm.

220

0

2500

2400

200

200

1600

[1] The cross section here is 160x40 mm.




Techniques/Concepts

• Skin/Loft

• Lofting guide line

• Add Frozen

• Copy bodies (Pattern)

• Boolean

• Create 3D surface bodies

Chapter 4 3D Solid Modeling Section 4.4 More Details 10

• Triad

• Isometric View

• Rotation

• Selection Filters

• Extend Selection

• Selection Panes

• Edge Display

• Tools for 3D

features

Section 4.4 More Details


Triad

[1] Click an arrow will orient the

view normal to that arrow.

[2] A black arrow represents

a negative direction.

[4] Click the cyan sphere to return to the

isometric view.

[3] If the cyan sphere coincides with the origin, that means the view is an

isometric view.


Rotations

[1] Hold the middle mouse button down while moving around the graphic

area, you can rotate the model.

[2] Free rotation.

[3] Roll, rotation about screen Z-axis.

[4] Yaw, rotation about

screenY-axis.

[5] Pitch, rotation about screen X-axis.

[6] The type of rotation depends on the location of the cursor.


Selection Aides

• Selection Filters

• Extend Selectin

• Selection Panes


Bodies and Parts

• A body is entirely made of one kind of material and is the basic building blocks of a model.

• A 3D body is either a solid body, a surface body, or a line body.

• A part is a collection of same type of bodies. All bodies in a part are assumed to be bonded together with one another.

• In <Mechanical>, parts are meshed independently

• A model may consist of one or more parts.

• In <Mechanical>, connections (contacts, joints) among parts must be established to complete a model.

This is the only geometric

entities that will be attached to

<Mechanical> for simulations.


FeaturesFeatures• Based Features

• Extrude• Revolve• Sweep• Skin/Loft• Surface• Lines• Point• etc.

• Placed Features• Thin/Surface• Blend• Chamfer• etc.

• Planes• Operations• etc.

Chapter 4 3D Solid Modeling Section 4.5 LCD Display Support 16

Section 4.5LCD Display Support

Problem Description


200

80

60

10 5

0 4

2

17

Unit: mm


• Revolve

• Skin/loft

• Thin/Surface

Techniques/Concepts

Documents

Sammelmappe1 ansys