Solving a 5×5 stiffness matrix with partitioned equations

[tomcenjerrym]

I spent almost 2 days to solve the following stiffness matrix

$$\left(\begin{array}{c}f1\\f2\\f3\\f4\\f5\end{arr ay}\right)=\left(\begin{array}{ccccc}20&-20&0&0&0\\-20&40&-20&0&0\\0&-20&40&-20&0\\0&0&-20&40&-20\\0&0&0&-20&20\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\\d4\\0\end{arr ay}\right)?$$

I have tried to partition the matrix like the following

FIRST

$$\left(\begin{array}{c}f1\\f2\\f3\end{array}\right)=\left(\begin{array}{ccc}20&-20&0\\-20&40&-20\\0&-20&40\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\right)+\left(\begin{array}{cc}0&0\\0&0\\-20&0\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)$$

SECOND

$$\left(\begin{array}{c}f4\\f5\end{array}\right)=\left(\begin{array}{ccc}0&0&-20\\0&0&0\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\right)+\left(\begin{array}{cc}40&-20\\-20&20\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)$$

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...

 

[radou]

What exactly are you trying to obtain? Are you trying to find the d-s?

 

[tomcenjerrym]

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.