University of Florida/Eml4507/s13.team4ever.Wulterkens.R3

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Problem 3.7 Verify Stiffness matrix

Given Equations[edit]

Given the two following equations, verify that they simplify to the bar element stiffness matrix .

Solution 1[edit]

Original Equation[edit]

Given Equations[edit]

Plugging into original Equation[edit]


Multiple the first two equations.

Pull out the K term.

Multiple the last two matrices to get the following equation:

This shows that the original equation can be simplified down to the bar element stiffness matrix.

Solution 2[edit]

Original Equation[edit]

Provided equations[edit]

Plugging into Original Equation[edit]


Begin by multiplying the first two matrices together.

Next, multiply the last two together.

This verifies our original expectation that the equation would simplify down to the bar element stiffness matrix.