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Stiffness Matrix 
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#1
Oct607, 03:49 PM

P: 37

I spent almost 2 days to solve the following stiffness matrix
[tex]\left(\begin{array}{c}f1\\f2\\f3\\f4\\f5\end{arr ay}\right)=\left(\begin{array}{ccccc}20&20&0&0&0\\20&40&20&0&0\\0&20&40&20&0\\0&0&20&40&20\\0&0&0&20&20\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\\d4\\0\end{arr ay}\right)?[/tex] I have tried to partition the matrix like the following FIRST [tex]\left(\begin{array}{c}f1\\f2\\f3\end{array}\right)=\left(\begin{array}{ ccc}20&20&0\\20&40&20\\0&20&40\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\right )+\left(\begin{array}{cc}0&0\\0&0\\20&0\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)[/tex] SECOND [tex]\left(\begin{array}{c}f4\\f5\end{array}\right)=\left(\begin{array}{ccc} 0&0&20\\0&0&0\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\r ight)+\left(\begin{array}{cc}40&20\\20&20\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)[/tex] but still cannot solve for the equation. The partitioned matrix produced UNDETERMINED Multiplication and Addition of 2 matrices. Can anyone help me on this, please... 


#2
Oct607, 04:17 PM

HW Helper
P: 3,220

What exactly are you trying to obtain? Are you trying to find the ds?



#3
Oct607, 06:37 PM

P: 37

All of forces fx and displacements dx magnitude. Please look at my attached image for the system. Note that the magnitude of f3 = 10 kN/m and the displacement of node 1 and 5 is 0 also the magnitude of k1 is = k2 = k3 = k4 = 20 kN/m.



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