MECH $6351/4$v$95$: Homework $3$

$($Due by $2$:$00$ pm online on $\backslash (10/08\backslash ))$

The one dimensional FEM code in MATLAB called fem$1$d$.$m can be downloaded from e$-$learning website.

$1.$ Modify the program to implement boundary conditions using the $\backslash (1-0\backslash )$ method discussed in the class. Solve the $2-$element problem below first by hand and obtain the nodal displacement and reactions forces. For Matlab implementation, please partition the whole domain with $15$ elements with equal lengths. Parameters for bar $1$ and $2$ are $\backslash (\backslash$mathrm$\{$L$\}\_\{1\}=1\mathrm{.}0\backslash$mathrm$\{$~m$\},\backslash$mathrm$\{$~L$\}\_\{2\}=0\mathrm{.}5\backslash$mathrm$\{$~m$\},\backslash$mathrm$\{$~A$\}\_\{1\}=10\backslash$mathrm$\{$~cm$\}^\{2\},\backslash$mathrm$\{$~A$\}\_\{2\}=5\backslash$mathrm$\{$~cm$\}^\{2\},\backslash$mathrm$\{$E$\}\_\{1\}=10\backslash$mathrm$\{$GPa$\}\backslash ),\backslash (\backslash$mathrm$\{$E$\}\_\{2\}=50\backslash$mathrm$\{$GPa$\}\backslash ).$ Submit the code and results. $($you are recommended to revise the code so that it reads information from an input file that contains all the necessary information such as the element number, length, etc.$)$

$2.$ Modify the above version of the code to allow for arbitrary prescribed displacement. Solve in matlab with $15$ elements of equal length, but replace the force at node $3($in the figure above$)$ by a displacement value of $0\mathrm{.}1$ mm and keep $\backslash ($ F$\_\{2\}\backslash )$ unchanged. Solve the same problem by hand first as a $2-$element problem for validation purpose, then solve it using Matlab. Provide the nodal displacements and reaction forces.

A typed report is required for this homework. You need to describe your implementations. In addition, you need to submit the codes and provide simple instructions on how to run these codes and get the output.

Please submit your files in a single zip file through e$-$learning by the deadline. The name of the file shall be lastname$\_$firstname.zip

ANY SUBMISSSION NOT FOLLOWING THE INSTRUCTION ABOVE WILL NOT BE GRADED.