Finite element analysis of bending in beams under loading using solidworks

You need to create the sketches shown below in solidworks:

Case 1:

Case 2:

Case 3:

(All Dimensions are in mm)

You need to extrude the sketches to a length of 400mm

Apply a load of 1500N on the smaller face(i.e. 45mm face for case 1, 40mm face for case 2 and 45 mm face for case 3)

and compare the results of stress, displacement and strain for all the three cases and suggest the best out of the three.

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Aim:

• To design different types of beam as per given dimensions using the solidworks.
• To create proper meshing and to perform the simulation.
• To discuss about the results obtained and to suggest the best beam out of three.

Introduction:

A cantilever beam is a beam that is only supported on one of its ends. The beam bears a specific weight on its open end as a result of the support on its enclosed end, in addition to its structural integrity. Cantilever construction is popular in many kinds of architectural design and in other kinds of engineering, where professionals use terms like end load, intermediate load, and end moment to identify how much a cantilever beam will hold. The term moment is related to torque and to a theoretical load on a beam.

Stress is nothing but force per unit area. Stress= Force/Area.

Strain, in physical sciences and engineering, number that describes relative deformation or change in shape and size of elastic, plastic, and fluid materials under applied forces.Strain = Change in length/original length

where stress is directly proportional to strain.

material Properties:

Name of the material Alloy steel

Elastic Modulus 2.1e+11 N/m^2
Poisson's Ratio 0.28 N/A
Shear Modulus 7.9e+10 N/m^2
Mass Density 7700 kg/m^3
Tensile Strength 723825600 N/m^2
Yield Strength 620422000 N/m^2
Thermal Expansion Coefficient 1.3e-05 /K
Thermal Conductivity 50 W/(m·K)
Specific Heat 460 J/(kg·K)

3d modelling and simulation:

case(i): Rectangular beam

One face of the beam is designed based on below dimensions and extruded to 400mm.

Mass properties of obtained 3d model:

Density = 0.01 grams per cubic millimeter

Mass = 11088.00 grams

Volume = 1440000.00 cubic millimeters

Surface area = 107200.00 square millimeters

Applied Mesh and load :

1. Very fine mesh is applied.
2. Beam is consider as a cantilever beam.
3. End having the green arrows is consider as fixed end and other end is set to free.
4. An external load of 1500N is applied at the face indicated by purple arrows.
5. Finally simulation is set to run.

Simulation results:

Minimum factor of saftey = 42

MAXIMUM RESULTANT DISPLACEMENT

NODE 65450

MAX. 9.42645E-05

MAXIMUM NODAL VON MISES STRESS

NODE 1727

MAX. 0.14664E+08

Obtained stress, strain and displacements plots are shown below

Animations obtained:

stress plot

strain plot:

displacement plot:

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Case(ii): I- shape beam

One of the face is designed based on the below dimensions and it is extruded to 400mm.

Mass properties:

Mass properties of the obtained 3d model

Density = 0.01 grams per cubic millimeter

Mass = 2329.54 grams

Volume = 302537.71 cubic millimeters

Surface area = 117312.36 square millimeters

Applied mesh and load:

• Very fine mesh is applied.
• Beam is consider as a cantilever beam.
• End having the green arrows is consider as fixed end and other end is set to free.
• An external load of 1500N is applied at the face indicated by purple arrows.
• Finally simulation is set to run.

End indicated by green arrows is the fixed end and the face indicataed by purple arrows is set to load of 1500N.

Simulations results:

Minimum factor of saftey: 22

MAXIMUM RESULTANT DISPLACEMENT

NODE 248

MAX. 8.76260E-05

MAXIMUM NODAL VON MISES STRESS

NODE 365

MAX. 0.28121E+08

Animations obtained:

stress plot:

Strain plot:

Displacement plot:

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Case(iii) C- shaped Beam

One of the face is designed based on the below dimensions and it is extruded to 400mm.

Mass properties:

mass properties of the obtained 3d model:

Density = 0.01 grams per cubic millimeter

Mass = 3062.23 grams

Volume = 397692.75 cubic millimeters

Surface area = 127862.38 square millimeters

Applied mesh and load:

• Very fine mesh is applied.
• Beam is consider as a cantilever beam.
• End having the green arrows is consider as fixed end and other end is set to free.
• An external load of 1500N is applied at the face indicated by purple arrows.
• Finally simulation is set to run.

End indicated by green arrows is the fixed end and the face indicataed by purple arrows is set to load of 1500N.

Simulations results:

MAXIMUM RESULTANT DISPLACEMENT

NODE 1

MAX. 3.47670E-04

MAXIMUM NODAL VON MISES STRESS

NODE 123

MAX. 0.47387E+08

Minimum factor of saftey: 13

Animations obtained:

stress:

strain:

displacement:

Results:

C shaped beam is consider to be the optimum beam design

• It withstands the load applied effectively and produces the most low displacement.
• Uniform distribution stress and strain occuring due to load acting in C-shaped beam is better than rectangular and I shaped beams.
• Twisting moment may tends to produce in the C shaped beam.

Conclusion:

1. 3d model is created for all the three beams and the mass properties is also tabulated.
2. Fine mesh and simulation is performed.
3. Results are displayed and C-shaped beam is suggested as optimum beam.