Stiffness Matrices 3-Finite Element Method-Assignment Solution, Exercises of Mathematical Methods for Numerical Analysis and Optimization

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• ASSIGNMENT #
  • Title: Problem # 6.

PROBLEM # 6.

The stiffness matrix of a planar frame element in the local coordinate system is given by

E

Where E is the Young's modulus, A is the area of cross section, I is the moment of inertia, and L is the length. Using this. generate the stiffness matrices of the three elements shown in Figure 6.7 in the local coordinate system and indicate the respective local degrees of freedom.

SOLUTION:

As each node has 3 degree of freedoms, therefore each local stiffness matrix is of order 6×6. And as there are 3 elements thus the global stiffness matrix is of order 12×12.