Subject: Finite Element Analysis

Topic: One Dimensional Problems

Difficulty: Medium

a) Number of elements and nodes,

b) Element matrix Equation is given by,

$\begin{bmatrix} K \end{bmatrix}^e=\frac{AE}{h_e}\begin{bmatrix} 1&-1\\ -1&1 \end{bmatrix}$

$For\,\, element \,\,1,\,\,A=250mm^2 \,\,,\,\, h_e=300mm$
$\frac{AE}{h_e}=\frac{250*2*10^5}{300}=167.67*10^3$
$\begin{bmatrix} K \end{bmatrix}^1=10^3\begin{bmatrix} 167.67&-167.67\\ -167.67&167.67 \end{bmatrix}$

$For\,\, element \,\,2,\,\,A=400mm^2 \,\,,\,\, h_e=200mm$
$\frac{AE}{h_e}=\frac{400*2*10^5}{200}=400*10^3$
$\begin{bmatrix} K \end{bmatrix}^2=10^3\begin{bmatrix} 400&-400\\ -400&400 \end{bmatrix}$

$For\,\, element \,\,3,\,\,A=400mm^2 \,\,,\,\, h_e=200mm$
$\frac{AE}{h_e}=\frac{400*2*10^5}{200}=400*10^3$
$\begin{bmatrix} …