Figure shows a cluster of four springs. Calculate the deflection of each spring when a force of 2000N is applieed. Model the springs as 1-D element.

Subject: Finite Element Analysis

Topic: One Dimensional Problems

Difficulty: Medium

a) Number of elements and nodes,

b) Element matrix Equation is given by,

$k\begin{bmatrix} 1&-1\\ -1&1 \end{bmatrix}\begin{Bmatrix} u_1^e\\ u_2^e \end{Bmatrix}\begin{Bmatrix} F_1^e \\ F_2^e \end{Bmatrix} $

For element 1, k=25
$25\begin{bmatrix} 1&-1\\ -1&1 \end{bmatrix}\begin{Bmatrix} u_1^1\\ u_2^1 \end{Bmatrix}\begin{Bmatrix} F_1^1 \\ F_2^2 \end{Bmatrix} $

For element 2, k=75
$75\begin{bmatrix} 1&-1\\ -1&1 \end{bmatrix}\begin{Bmatrix} u_1^2\\ …