Finite Element Methods (global stiffness matrix)

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SUMMARY

The global stiffness matrix K for a 2-D finite element problem is determined by the number of nodes and their degrees of freedom. In the discussed problem, with 12 nodes each having 2 degrees of freedom, the global stiffness matrix size is confirmed to be 24 x 24. For another problem with 15 nodes, the matrix size is correctly calculated as 30 x 30. The methodology for calculating the global stiffness matrix size is consistently based on the formula: size of the matrix = number of nodes x degrees of freedom per node.

PREREQUISITES
  • Understanding of finite element methods (FEM)
  • Knowledge of degrees of freedom in structural analysis
  • Familiarity with global stiffness matrix concepts
  • Basic proficiency in matrix operations
NEXT STEPS
  • Study the derivation of the global stiffness matrix in finite element analysis
  • Learn about the implications of degrees of freedom on matrix size in FEM
  • Explore practical examples of 2-D finite element problems
  • Investigate software tools for FEM analysis, such as ANSYS or Abaqus
USEFUL FOR

Students preparing for exams in structural engineering, researchers in finite element analysis, and engineers involved in computational mechanics.

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Homework Statement


I have the following practice problem which is presented as follows:

What is the size of the global stiffness matrix K (i.e., Kuu) for the 2-D problem?

http://imgur.com/KZec3 (Unsolved)

http://imgur.com/piv1J (Solved)

Homework Equations



The Attempt at a Solution


So in the solved problem which I think I did right I counted the total number of nodes which is 12, since each has 2 degrees of freedom the size of the matrix is 24 x 24? Does this sound correct?

If so now I attempt the other problem, where the ? I think should just be theta's but I believe there was a rendering problem. Anyways my attempt would be again count the number of nodes in which case there are 15 nodes. And again the nodes have a total of 2 degrees of freedom so this is a 30 x 30 size matrix?

Does this sound correct? (there are few problems with which to practice this one, so I'm trying to understand the methodology here for an exam, so any insight would be helpful)
 
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the size of Global stiffness matrix = nodesxnodes.
 

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