HOMEWORK SET # $3$

ME$/$AE $6212$ Advanced Finite Element Analysis

Write a computer program $($MATLAB language or other programming languages like C$,$ FORTRAN, etc.$)$ to solve the following two$-$variable second order system problem.

$[M]\{u^{}\}+[C]\{u^{}\}+[K]\{u\}=\{F\}$;$\{u{\}}_{t_o}=\{u{\}}_{t_o}=0$

where

$[M]=\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]$;$[C]=[K]=\left[\begin{array}{cc}1& 1\\ 1& 3\end{array}\right]$;$\{F\}=\{[1],[2]\}$

Using Newmark's Integration Scheme, solve for $u_1,u_2,u_1^{},u_2^{},u_1^{}$ and $u_2^{}$ for $t=15$ sec with $t=0\mathrm{.}5sec.$

Need a summary of numerical results in both tabular and graphical form along with listing of code and sample output. The summary should follow the problem statement.

Note: This is a solved problem in the handout $($Example $5\mathrm{.}29,$ pp$.328-330,$ Dhatt and Touzot$).$