project 01 vinay anand fea p1

8/9/2019 Project 01 Vinay Anand Fea p1

1/19

ANALYSIS OF A CENTER LOADED SIMPLY

SUPPORTED BEAM

Prepared for:

AENG 551

FEM in Auto Structure Design

Prepared by:

VINAY ANAND BHASKARLA

UMID: 86549821


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Contents1. Introduction: ......................................................................................................................................... 3

2. Modeling: .............................................................................................................................................. 4

2.1. Model Geometry ................................................................................................................................ 4

2.1.1. The general steps involved in modeling and solving a problem using Finite Element Software:5

2.2 Types of Models ............................................................................................................................ 6

2.2.1. Analysis of Beam with 1D elements: ......................................................................................... 6

2.2.2. Analysis of Beam with 2D shell elements:................................................................................. 7

2.2.3. Analysis of Beam with 2D solid elements:................................................................................. 7

2.2.4. Analysis of Beam with 3D solid elements:................................................................................. 8

3. Results: ................................................................................................................................................ 10

3.1 Theoretical values ....................................................................................................................... 10

3.2 Practical Simulation Values:........................................................................................................ 11

3.2.1 1D Beam Element: ................................................................................................................... 11

4. Conclusions: ........................................................................................................................................ 19

1. Conclusions for 1D Element: ........................................................................................................... 19

2. Conclusions for 2D shell Elements:.................................................................................................. 19

3. Conclusions for 2D Solid Elements: ................................................................................................. 19

4. Conclusions for 3D solid Elements:.................................................................................................. 19


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1. Introduction:

Finite element analysis (FEA) is used for predicting how a component reacts to real-world

situations when it is subjected to loads under predefined boundary conditions. It helps in

knowing the stresses, strains and other factors that would generate at different points under

the loading conditions.

This project requires the user to simulate a physical problem which is essentially a center

loaded simply supported beam, and to analyze the behavior of the beam, using Finite Element

Analysis when it is subjected to a predefined load and other boundary conditions.

The analysis of the simply supported beam is done by using various element types with

different element sizes to find out the behavior of the beam.

There are usually three stages in the analysis:

1. Pre-processing or modeling: An input file is created, which contains the design data for a

finite-element analyzer (also called "solver").

2. Processing or finite element analysis: This stage produces an output visual file.

3. Post-processing: This stage is a visual rendering stage which involves generating

contours for comparison and analysis.

The following tools were used in the simulation and result generation process:

Pre-processor: HyperMesh

Processor/Solver: ABAQUSPost-processor: HyperView

HyperMesh which is the pre-processor uses a system of points called nodes which

makes a grid called a mesh. This mesh is programmed to contain the material and structural

properties which define how the structure will react to certain loading conditions. Nodes are

assigned at a certain density throughout the material. Points of interest may consist of

determining the deformation, stresses and strains.

ABAQUS which is the solver is designed to solve traditional implicit finite element analyses,

such as static, dynamics, and thermal. The mesh file that is generated in HyperMesh is solvedused ABAQUS.

HyperView is used to view the results. It is a complete post-processing and visualization

environment for finite element analysis (FEA). HyperView enables engineers to visualize data

interactively as well as capture, standardize, and automate post-processing activities.


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2.1.1. The general steps involved in modeling and solving a problem using Finite

Element Software:

1. Pre-Processor (Modeling in HyperMesh):

1. Selecting the Pre-Processor (HyperMesh)

2. Component Creation

Creating the geometry by using lines and surfaces.

3. Material Creation

Density

Elastic modulus

Poissons Ratio

4. Section Creation by HyperBeam (Applicable only for 1-D elements)

Assigning the length and width

5. Element Creation

Selecting the element type

Selecting the element configuration

Selecting the element size

Assigning the offsets

6. Property creation

7. Assigning the property to the elements

8. Applying the constraints and loads in the step manager( which can be found in the utility

menu)

Selecting the analysis procedure

Setting the Dataline

Creating the constrains

Application of Loads (Loads are to be distributed according to the number of

elements that are sharing the nodes)

Outputs are to be selected which consists of selecting the nodal outputs and

Elemental Outputs that need to be studied

9. Exporting the file that is readable in the Solver/Processor workbench

2. Processor/Solver (solving the file using ABAQUS):

1. Run the file that has been exported in the pre-processor (ABAQUS command)

2. Gather the ouput files in a folder


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3. Post-Processor (HyperView):

1. View the files in the Post-processor

2. Select the required contour plots for studying the behavior of the geometry and

compare different values such as deformation, stresses and strains and analyze the

results

2.2

Types of Models

2.2.1.Analysis of Beam with 1D elements:

The elements used in the 1D analysis are B31 and B32. These elements are found in the

element types in the standard 3d mode of the abaqus user profiles.

B31 Element:B31 is a first-order; three-dimensional beam element with two nodes and

this element use linear interpolation.

B32 Element: B32 is a second-order, three-dimensional beam element with three

nodes.

Both B31 and B32 elements are shear deformable and account for finite axial strains; therefore,

they are suitable for modeling both slender and stout beams.

Modeling:

The general process of modeling is followed as mentioned in 2.1.1, and the geometry is

created. Here the geometry is a line with the given length of the beam and the material and the

properties are defined according to the requirement. A beam section is generated using the

HyperBeam with the specified rectangular cross section (20*5), and a line mesh is made with

the element type namely B31 with the element size of 62.5mm. Now assign the properties and

define the loads and the boundary conditions in the step manager and also maintain the

analysis mode as static in the step manager. The outputs like displacement, stress and strain

are requested in the output block of the step manager. The file is exported in the Abaqus

readable form which is .inpfile. This file is now run in the Abaqus command prompt and an.odb file is generated which is used by HyperView to generate the results. The results are

read in the HyperView in the form of contour plots. A number of iterations are made with

different element sizes and the results are analyzed.

The above process is followed for the beam element B32 and the results are noted.


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2.2.2.

Analysis of Beam with 2D shell elements:

The elements used in the 2D analysis are the shell elements S4 and S4R. These elements are

found in the element types in the standard 3d mode of the abaqus user profiles.

S4 element: The S4 shell element uses a normal integration rule with four integration

points. This is a general purpose shell element.

S4R element:

This kind of element uses a reduced integration rule with one integration

point. This is also a general purpose shell element.

Modeling:

The general process of modeling is used as mentioned in2.1.1,and the geometry is created

using lines and surfaces with the required dimensions and the material and properties are

assigned according to the requirements. The card image is assigned as shell section and the

type is given as planar section and the required thickness is given in the properties. The mesh

type is given as S4 element type with 62.5mmas the element size. The loads and constraints

are given in the step manager and the required output consisting of displacements, stresses

and strains are requested. The analysis type is selected as static. The file is exported in the

abaqus readable form which is .inpfile. This file is now run in the abaqus command prompt

and an .odbfile is generated which is used by HyperView to generate the results. The results

are read in the HyperView in the form of contour plots. A number of iterations are made with

different element sizes and the results are analyzed.

The above process is followed with the shell element S4R and the results are noted.

2.2.3.

Analysis of Beam with 2D solid elements:

The elements used in the 2D solid analysis are the CPS4, CPE4, CPS4R, and CPE4R. These

elements are found in the element types in the standard2dmode of the abaqus user profiles.

CPS4: This is a continuum plane stress 4 node element. Four integration points form this

element.

CPS4R: This is a continuum plane stress 4 node reduced element. There will be only one

integration point for this type of element.

CPE4: This is a continuum plane strain 4 node element. There are four integration points

for this type of element.


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CPE4R: Continuum plane strain 4 node reduced element. This is similar to that of plane

strain 4 node element but with lesser number of integration points. This element is

defined by only one integration point.

Modeling:

The general process of modeling is used as mentioned in 2.1.1,and the geometry is created


assigned according to the requirements. The card image is assigned as solid section and the

type is given as solid section. Only the XY plane is available in the standard 2d mode of the solid

elements, so the surface with the dimensions 125mm*5mm is modeled and the width 20mm is

given as attribute. The element type is selected as CPS4 and the surface is meshed with a

3.125mm as the element size and the loads and constraints are applied. The file is exported in

the abaqus readable form which is .inp file. This file is now run in the abaqus command

prompt and an .odb file is generated which is used by HyperViewto generate the results. The

results are read in the HyperView in the form of contour plots. A number of iterations are made

with different element sizes and the results are analyzed.

The above process is followed for other 2D solid elements like CPS4R, CPE4, and CPE4R and the

results are tabulated.

2.2.4.Analysis of Beam with 3D solid elements:

The elements used in the 3D solid analysis are the C3D8, C3D8I and C3D8R. These elements are

found in the element types in the standard 3d mode of the Abaqus user profiles.

C3D8: The C3D8 element is a general purpose linear brick element, fully integrated (2x2x2

integration points).

Figure 2:8-node brick element

Due to the full integration, the element tends to be too stiff in bending.


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Figure 3:8-node brick element

To cause the angle A to change under the pure moment, an incorrect artificial shear stress hasbeen introduced. This also means that the strain energy of the element is generating shear

deformation instead of bending deformation. The overall effect is that the linear fully

integrated element becomes locked or overly stiff under the bending moment. Wrong

displacements, false stresses and spurious natural frequencies may be reported because of the

locking.

C3D8R:The C3D8R element is a general purpose linear brick element, with reduced integration.

Due to the reduced integration, the locking phenomenon observed in the C3D8 element isremoved.

Hourglass term comes into effect if reduced integration elements are used. Because of reduced

integration we might experience misleading results, which need to be avoided. To avoid these

false modes, hourglass effect is applied. The element tends to be not stiff enough in bending.

Stresses, strains are most accurate in the integration points. The integration point of the C3D8R

element is located in the middle of the element. Thus, small elements are required to capture a

stress concentration at the boundary of a structure.

C3D8I: C3D8I is first-order element that is improved by incompatible modes to improve the

bending behavior. The primary effect of these modes is to eliminate the shear stresses that

cause the regular first-order displacement elements to be too stiff in bending.


10/19

Modeling:

The general process of modeling is used as mentioned in 2.1.1 and the geometry is created


assigned according to the requirements. The card image is assigned as solid section and the

type is given as solid section. A rectangular surface of 125mmX20mm is created and the surface

is meshed with the element type as C3D8 with the required element size. From the 3D panel

the drag option is used to give the thickness as 5mm and the number of elements through

thickness is mentioned. The properties are assigned and the loads and the constraints are given

to the model using the step manager. The file is exported in the abaqus readable form which is

.inp file. This file is now run in the abaqus command prompt and an .odb file is generated

which is used by HyperView to generate the results. The results are read in the HyperView in

the form of contour plots. A number of iterations are made with different element sizes and the

results are analyzed.

The above process is followed with the 3D solid elements C3DR and C3D8I and the results are

noted.

3. Results:

The theoretical values are first calculated and then the simulation is done and the results are

evaluated. The simulated results are analyzed the best element is noted based on its

convergence to the theoretical values.

3.1

Theoretical values

Inputs for developing the equations for stress (S), strain (e) and the displacements (U) are

Youngs Modulus E

Distance from neutral axis Y

Load P

Moment of inertiaI

Bending MomentM

Fig.5 Beam section


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Outputs:

The Moment of Inertia I= BH3/12

Bending Moment M= PL/4

The displacement is given by U= (PL

3)/ (48EI)

The StressS= MY/I Straine= S/E

Using the data given, the values are calculated as:

Displacement U=0.93 mm

Stress S= 375 MPa

Strain e= 0.001786

3.2 Practical Simulation Values:

3.2.1

1D Beam Element:

The elements B31 and B32 are analyzed and the results are tabulated as below:

1D ELEMENTS

S.No ELEMENT TYPEELEMENT SIZE

(mm)DISPLACEMENT, U (mm) STRESS,S (Mpa) STRAIN E

1

B31

62.500 0.8771 187.5 0.0008929

2 6.250 0.934 356.3 0.001696

3 3.125 0.934 356.3 0.001696

1

B32

62.500 0.9345 187.5 0.0008929

2 6.250 0.9345 356.3 0.001696

3 3.125 0.9345 356.3 0.001696

Table2. B31 and B32


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Fig.6. Displacement vs Element size

Fig.7 Stress vs Element size

Fig.8 Strain vs Element size

From the graphs it can be concluded that the displacement for the Beam Element B31 varies

along with the element size, and as the size of the element decreases, the displacement

increases. But for the element size B32, there is no significant change in the displacement even

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.000 20.000 40.000 60.000 80.000

Displac

ement

Element Size

Element Size vs Displacement

B31 Displacement

B32 Displacement

0

100

200

300

400

0.000 20.000 40.000 60.000 80.000

Stress

Element Size

Element Size vs Stress

B31 Stress

B32 Stress

0

0.0005

0.001

0.0015

0.002

0.000 20.000 40.000 60.000 80.000

Strain

Element Size

Element Size vs Strain

B31 Strain

B32 Strain


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with the change in the element size. The element B32 gives more accurate results due to more

number of integration points.

3.2.2.

2D Shell Element:

2D Shell Element

Element Size

SIZE (mm)

Displacement

U (mm)

Stress S11

S (Mpa)Strain e11

S4

62.5 7.021E-01 1.875E+02 8.929E-04

6.25 9.349E-01 3.570E+02 1.686E-03

2.5 9.386E-01 3.683E+02 1.748E-03

S4R

62.5 7.021E-01 1.875E+02 8.929E-04

6.25 9.366E-01 3.572E+02 1.686E-03

2.5 9.386E-01 3.684E+02 1.748E-03

Table3. S4 and S4R elements


Fig.10. Stress vs Element size

0.000E+00

2.000E-01

4.000E-016.000E-01

8.000E-01

1.000E+00

0 20 40 60 80

Displacem

ent

Element Size

Displacement vs Element size

S4

S4R

0.000E+00

1.000E+02

2.000E+02

3.000E+02

4.000E+02

0 20 40 60 80

StressS11

Element Size

Stress vs Element Size

S4

S4R


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Fig.11. Strain vs Element size

From the plots, it can be noted that the displacement for the Shell Element S4 and S4R varies

along with the element size and as the size of the element decreases the displacement

increases.

3.2.3.2D Solid Element:

CPE4, CPE4R, CPS4, CPS4R are the 2D solid elements that are analyzed and the elements are

tabulated

2D Shell Element

Element SizeSIZE (mm)

DisplacementU (mm)

Stress S11S (Mpa)

Strain e11

CPE4

3.125 8.791E-01 1.867E+02 8.299E-04

2.5 9.269E-01 1.979E+02 8.724E-04

1.25 8.783E-01 2.820E+02 1.239E-03

CPE4R

3.125 1.148E+00 2.435E+02 1.074E-03

2.5 1.151E+00 2.448E+02 1.081E-03

1.25 9.214E-01 2.955E+02 1.300E-03

CPS43.125 7.972E-01 1.560E+02 7.453E-04

2.5 8.363E-01 1.645E+02 7.863E-04

1.25 9.091E-01 2.691E+02 1.283E-03

CPS4R

3.125 1.245E+00 2.434E+02 1.164E-03

2.5 1.248E+00 2.448E+02 1.171E-03

1.25 9.995E-01 2.955E+02 1.410E-03Table4.CPE4, CPE4R, CPS4 and CPS4R elements

0.000E+00

5.000E-04

1.000E-03

1.500E-03

2.000E-03

0 20 40 60 80

Strain

Element Size

Strain vs Element size

S4

S4R


15/19


Fig.13. Stress vs Element size

Fig.14. Strain vs Element size

From the result it can be concluded that the displacement for the 2D solid elements varies

along with the element size, and as the size of the element decreases the result converges to

the theoretical values.

0.000E+00

5.000E-01

1.000E+00

1.500E+00

0 1 2 3 4DISPL

ACEMENT

ELEMENT SIZE

DISPLACEMENT vs ELEMENT SIZE

CPE4

CPE4R

CPS4

CPS4R

0.000E+00

1.000E+02

2.000E+02

3.000E+02

4.000E+02

0 1 2 3 4

Stress

Element Size

Stress vs Element Size

CPE4

CPE4R

CPS4

CPS4R

0.000E+00

5.000E-04

1.000E-03

1.500E-03

0 1 2 3 4

Strain

ELEMENT SIZE

Strain vs Element Size

CPE4

CPE4R

CPS4

CPS4R


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3.2.4.

3D Solid Element:

C3D8, C3D8I, C3D8R are the 3D solid elements that are analyzed and the elements are

tabulated

3-D Displacements DRAG 1ELEMENT SIZE C3D8 C3D8I C3D8R

6.25 8.691E-01 9.366E-01 8.413E+01

2.5 1.829E+00 9.397E-01 8.431E+01

1.25 2.204E+00 9.406E-01 8.433E+01

3-D Displacements DRAG 4

ELEMENT SIZE C3D8 C3D8I C3D8R

6.25 5.799E-01 9.366E-01 9.987E-01

2.5 8.667E-01 9.399E-01 1.002E+00

1.25 9.337E-01 9.404E-01 1.003E+00

3-D Displacements DRAG 5


6.25 5.768E-01 9.367E-01 9.753E-01

2.5 8.610E-01 9.399E-01 9.792E-01

1.25 9.274E-01 9.405E-01 9.799E-01

Table5.C3D8, C3D8I, C3D8R elements

Fig.15. Displacement vs Element size for C3D8, C3D8I, C3D8R

0.000E+00

2.000E+01

4.000E+01

6.000E+01

8.000E+01

1.000E+02

0 2 4 6 8

DISPLACEMENT

ELEMENT SIZE

DISPLACEMENT FOR 1 ROW ELEMENT

C3D8

C3D8I

C3D8R


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Fig.16. Displacement vs Element size for C3D8, C3D8I, C3D8R for 4 row elements

Fig.17. Displacement vs Element size for C3D8, C3D8I, C3D8R for 4 row elements

3D element Stress DRAG 1


6.25 5.771E-01 1.040E+00 3.766E-01

2.5 5.361E+00 1.255E+00 5.948E-01

1.25 8.407E+00 1.255E+00 1.457E+00



6.25 1.717E+02 2.674E+02 2.674E+02

2.5 2.580E+02 2.757E+02 2.936E+02

1.25 2.790E+02 2.780E+02 2.964E+02



6.25 1.819E+02 1.819E+02 2.970E+02

2.5 2.727E+02 2.942E+02 3.060E+02

1.25 2.949E+02 2.967E+02 3.087E+02

0.000E+00

5.000E-01

1.000E+00

1.500E+00

0 2 4 6 8DISPLACEMENT

ELEMENT SIZE


C3D8

C3D8I

C3D8R

0.000E+00

5.000E-01

1.000E+00

1.500E+00

0 2 4 6 8

DISPLACEMENT

ELEMENT SIZE


C3D8

C3D8I

C3D8R


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Fig.18. Stress vs Element size for C3D8, C3D8I, C3D8R for 1 row elements



0.000E+00

2.000E+00

4.000E+00

6.000E+00

8.000E+00

1.000E+01

0 2 4 6 8

S

TRESS

ELEMENT SIZE

STRESS FOR 1 ROW ELEMENTS

C3D8

C3D8I

C3D8R

0.000E+00

1.000E+02

2.000E+02

3.000E+024.000E+02

0 2 4 6 8

STRESS

ELEMENT SIZE


C3D8

C3D8I

C3D8R

0.000E+00

1.000E+02

2.000E+02

3.000E+02

4.000E+02

0 2 4 6 8

STRESS

ELEMENT SIZE


C3D8

C3D8I

C3D8R


19/19

4. Conclusions:

1.

Conclusions for 1D Element:

o From the results obtained, it can be concluded that for the 1D elements, among

B31 and B32, for any given element size, the element B32 is giving constant

displacement values which are closer to the theoretical values due to more

number of integration points. So the element B32 is recommended for 1D

analysis.

2.

Conclusions for 2D shell Elements:

o From the results obtained in the analysis of 2D shell elements S4 and S4R, it can

be concluded that the shell elements S4 and S4R are giving similar values which

are closer to the theoretical values of displacement for different element sizes,so it is recommended to use S4R as it has reduced integration points which

would complete the job at a faster pace as the calculations are done at a single

integration point.

3.Conclusions for 2D Solid Elements:

o Among the 2D solid elements CPE4, CPE4R, CPS4, CPS4R, from the results, it is

recommended to use CPE4R, as all the other elements give stress values that are

deviating from the theoretical values but CPE4R is giving displacement and stress

values that are closer to the theoretical values.

4.

Conclusions for 3D solid Elements:

o From the 3D solid elements, C3D8I is concluded as the element that is most

suitable for the 3D analysis as it is observed that for any given element size and

any number of layers, it has values that are closer to the desired output, and this

is attributed to the improved bending behavior of the element.

project 01 vinay anand fea p1

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