analysis of beam

7/28/2019 Analysis of beam

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Problem Description

Given

Here, cantilevers beam with a point load at the end is analyzed with two dimensional elements in

ANSYS Mechanical APDL.

Preferences

1. Go to Main Menu -> Preferences

2. Check the box that says Structural

3. ClickOK

PreprocessorElement Type

1. Go to Main Menu -> Preprocessor ->

Element Type -> Add/Edit/Delete

2. ClickAdd


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3. ClickShell -> 4node 181 the elements

that we will be using are four node elements with six degrees of freedom.

4. ClickOK

SHELL181 is suitable for analyzing thin to moderately-thick shell structures. It is a 4-node

element with six degrees of freedom at each node: translations in the x, y, and z directions, and

rotations about the x, y, and z-axes. (If the membrane option is used, the element has

translational degrees of freedom only). The degenerate triangular option should only be used asfiller elements in mesh generation.

SHELL181 is well-suited for linear, large rotation, and/or large strain nonlinear applications.

Change in shell thickness is accounted for in nonlinear analyses. In the element domain, both full

and reduced integration schemes are supported. SHELL181 accounts for follower (load stiffness)

effects of distributed pressures.

Real Constantsadd the thickness to beam.


Real Constants -> Add/Edit/Delete

2. ClickAdd


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3. ClickOK

4. UnderReal Constants for SHELL181 ->

Shell thickness at node I TK(I) enter 10 (assumed Value)

for the thickness

5. ClickOK

6. ClickClose

Material properties


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1. Main Menu -> Material Props -> Material Models

2. Material Model Number 1 -> Structural -> Linear -> Elastic -> Isotropic

3. Enter210E6for Youngs Modulus (EX) and .3 for Poissons Ratio (PRXY)

4. ClickOK

Keypoints

Since we will be using 2D Elements, our goal is to model the length and width of the beam.

1. Go to Main Menu -> Preprocessor -> Modeling -> Create ->

Keypoints -> In Active CS

In the dialog box key in the following Key points

No X Y

1 0 0

2 100 0

3 100 10

4 50 20

5 50 10

6 0 20


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Areas

1. Go to Main Menu -> Preprocessor -> Modeling -> Create ->

Areas -> Arbitrary -> Through KPs

2. Select Pick

3. Connect all Key points

4. OK


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Meshing


Meshing -> Mesh Tool

2. Go to Size Controls: -> Global -> Set

3. UnderSIZE Element edge lengthput 2.


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This will create a mesh of square elements

with width 2 meters.

4. ClickOK

5. ClickMesh

6. ClickPick All

7. ClickClose


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Loads

Main Menu -> Preprocessor -> Loads -> Define Loads ->

Apply -> Structural -> Displacement-> On Lines

Pick the Line on the left corner

ClickOK

8. ClickAll DOF to secure all degrees of freedom

9. UnderValue Displacement valueput 0. The left

face is now afixed end

10. ClickOK


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Point Load

1. Go to Main Menu -> Preprocessor -> Loads -> Define Loads ->

Apply -> Structural ->Force/Moment -> On Nodes

2. Select Pick -> Single -> List of Items

3. UnderLab Direction of Force/mom select FY

5. UnderValue Force/moment value type -460


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6. Press OK

Solution

1. Go to Main Menu -> Solution ->Solve -> Current LS (solve). LS stands for Load Step. This

step may take some time depending on mesh size and the speed of your computer (generally a

minute or less).


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General Postprocessor

We will now extract the Preliminary Displacement and Von-Mises Stress within our model.

Displacement

1. Go to Main Menu -> General Postprocessor -> Plot Results -> Contour Plot -> Nodal

Solution

2. Go to DOF Solution -> Displacement Vector Sum

3. ClickOK


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Equivalent (Von-Mises) Stress

1. Go to Main Menu -> General Postprocessor -> Plot Results -> Contour Plot -> Nodal

Solution

2. Go to Nodal Solution -> Stress -> von Mises stress

3. ClickOK


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Compute Equivalent stress of the beam analytically and compare the result with the simulationresult

Von Mises Stress

Assuming plane stress, the Von Mises Equivalent Stress can be expressed as:

-------- 1

we are analyzing the set of nodes through the top center of the cross section of the beam:

Due to symmetric loading about the yz cross sections, analyzing the nodes through the top center

will give us deflections that approximate beam theory. Additionally, since the nodes of choice

are located at the top surface of the beam, the shear stress at this location is zero.


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Using these simplifications, the Von Mises Equivelent Stress from equation 1 reduces to:

Bending Stress (is given by:

Where and . From statics, we know that

So

With Maximum Stress at

Here

P= 460 N

(x-L)= 50

B= 10

H= 10


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Simulated Result Analytical result

Von Mises stress 117.925 138

Percentage error

The percent error (%E) in the model Von Mises Stress can be defined as:

[ ]

[ ]

We derive that our model has 14.54 % error in the max equivalent stress. Thus, it is reasonable

that our choice of two elements through the width of the beam is not Fine a mesh. Since the 2D

Elements we are using linearly interpolatebetween nodes, we can expect a degree oftruncation

errorin our model.

analysis of beam

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