Finite Element Method Study
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Publicado: 14 de enero de 2013
MIFEM1 2012
Assignment 1
Finite Element Method.
Guillermo Rodriguez Martinez
21/11 2012
1. Set up the global stiffness matrix for the system using bar elements in 2D.
Globalstiffness matrix equation:
Where:
In our assembly we have 2 bars, 3 nodes and each node has 2 DOF, wich makes 6 DOF in total.
The rotation of the bar stiffness matrix can be written as:
Bar BCdoes not need to be rotates, then we can just expand it’s local stiffness matrix to the size of the global one.
Bar BA has to be rotates 45 degrees.
Adding up all stiffness matrices, totalbecomes:
The total equation set is:
Apply fixtures and loads and solve analytically for the displacement of point B.
Resulting the displacements in B:
3. In SolidWorks, calculate thedisplacements using truss elements.
First at all we defined the two beams and we draw it in solid works like in an assembly.
In Y direction we have these values of displacement.
As we can see in thegraphic, the displacement in the two bar are increasing as we are close to the force applied in point B, this forces made that the two beams has a displacement of 2.316e-0,002 mm in Y direction.
In Zdirection we have the following values of displacement.
As we can see in the graphic, the displacement in the two bar are increasing as we are close to the force applied in point B, this forces madethat the two beams has a displacement of 6.063e-0,003 mm in Z direction.
The displacement in Z direction in point B, are smaller than in Y direction, one grade bellow.
4. In SolidWorks, calculatethe displacements using beam elements.
When we treated like a beam the results are quite different in relation of the displacement.
The displacement in Y direction is -2,292e-0,002 mm
Thedisplacement in Z direction is 6,001e-0,003 mm
The displacement in X direction is 9,856 e-10 mm
5. In SolidWorks, calculate the displacements using solid elements and argue for your choice of model...
Assignment 1
Finite Element Method.
Guillermo Rodriguez Martinez
21/11 2012
1. Set up the global stiffness matrix for the system using bar elements in 2D.
Globalstiffness matrix equation:
Where:
In our assembly we have 2 bars, 3 nodes and each node has 2 DOF, wich makes 6 DOF in total.
The rotation of the bar stiffness matrix can be written as:
Bar BCdoes not need to be rotates, then we can just expand it’s local stiffness matrix to the size of the global one.
Bar BA has to be rotates 45 degrees.
Adding up all stiffness matrices, totalbecomes:
The total equation set is:
Apply fixtures and loads and solve analytically for the displacement of point B.
Resulting the displacements in B:
3. In SolidWorks, calculate thedisplacements using truss elements.
First at all we defined the two beams and we draw it in solid works like in an assembly.
In Y direction we have these values of displacement.
As we can see in thegraphic, the displacement in the two bar are increasing as we are close to the force applied in point B, this forces made that the two beams has a displacement of 2.316e-0,002 mm in Y direction.
In Zdirection we have the following values of displacement.
As we can see in the graphic, the displacement in the two bar are increasing as we are close to the force applied in point B, this forces madethat the two beams has a displacement of 6.063e-0,003 mm in Z direction.
The displacement in Z direction in point B, are smaller than in Y direction, one grade bellow.
4. In SolidWorks, calculatethe displacements using beam elements.
When we treated like a beam the results are quite different in relation of the displacement.
The displacement in Y direction is -2,292e-0,002 mm
Thedisplacement in Z direction is 6,001e-0,003 mm
The displacement in X direction is 9,856 e-10 mm
5. In SolidWorks, calculate the displacements using solid elements and argue for your choice of model...
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