Write a MATLAB function which solves the two$-$dimensional linear elasticity problem for a singlepatch geometry. The body is assumed to be homogeneous and isotropic. Your function should take

the form:

function $[$d$]=$ Linear$\_$Elasticity$($p$\_1,$p$\_2,$n$\_1,$n$\_2,$Xi$\_1,$Xi$\_2,$P$,$w$,$n$\_$q$,$problem$)$

where d is an array storing the control variables for the discrete displacement field, p$\_1$ and p$\_2$

are the polynomial degrees in directions $\backslash$xi $1$ and $\backslash$xi $2$ respectively, n$\_1$ and n$\_2$ are the number of

basis functions in directions $\backslash$xi $1$ and $\backslash$xi $2,$ Xi$\_1$ and Xi$\_2$ are the univariate knot vectors in directions

$\backslash$xi $1$ and $\backslash$xi $2,$ P is an array storing the control points for the NURBS surface, w is an array storing

the weights for the NURBS surface, n$\_$q is the number of quadrature points in each direction, and

problem is an integer corresponding to a problem specification. The Young$$s modulus E$,$ Poisson

ratio

u $,$ prescribed body force f$,$ prescribed boundary displacements g$1$ and g$2,$ prescribed boundary

tractions h$1$ and h$2,$ Dirichlet boundaries $\backslash$Gamma D$1$ and $\backslash$Gamma D$2,$ and Neumann boundaries $\backslash$Gamma N$1$ and $\backslash$Gamma N$2$

should all be determined by the integer problem. Moreover, the integer problem should determine

whether the body is subject to plane strain or plane stress. For this homework, you should have

three possible values for the integer problem, namely:

problem $=$

$8<$:

$1$ for Problem $3$

$2$ for Problem $4,$ Part $1$

$3$ for Problem $4,$ Part $2$