Using matlab code format as follows

clc %clear command

clear % clear workspace

disp ('Solution for Problem 1')

%---input Data---

DOF = 9; %9 nodes one degree of freedom

elementnodes = [1 2; 2 3; 3 4; 4 5; 5 6; 6 7; 7 8; 8 9];

elementnumber = size(elementnodes,1);

k = [200;200;200;200;400;400;400;400];

K=zeros(DOF);

F=zeros(DOF,1);

%---Global Stiffness---

for e=1:elementnumber

elementdof = elementnodes(e,:);

K(elementdof,elementdof)=K(elementdof,elementdof)+k(e)*[1 -1;-1 1];

end

%---Boundary Conditions---

Kred=K; %red = reduced

prescribeddof = [1;9]; %we know displacement at these points (two boundary conditions)

numberBC = size(prescribeddof,1);

for bc=1:numberBC

bcvector = zeros(1,DOF);

bcvector(prescribeddof(bc))=1;

Kred(prescribeddof(bc),:)=bcvector;

end

%---loads---

F(5,1) = 1500;

%---Solution---

disp('Global Displacement Vector')

D=KredF;

ii=1:DOF;

[ii' D]

%---Results---

disp('Global Force Vector')

F=K*D;

ii=1:DOF;

[ii' F]

%Reaction Force vector

disp('Reaction Force Vector is;')

[prescribeddof F(prescribeddof)]

%forces for Each Element

for e=1:elementnumber

elementdof=elementnodes(e,:);

d=D(elementdof);

disp(['Forces in Element ',num2str(e),' are:'])

f = k(e)*[1 -1;-1 1]*d

end

Problem 3 (60 points): A tapered elastic bar is subjected to an applied tensile load P at one end and attached to a fixed support at the other end, as shown in the figure below. The cross-sectional area varies linearly from Ao at the free end (r-0) to 2Ao at r-L. Solve for the axial displacement and stress distribution in the bar. For the finite element discretization use 1, 2, 4 elements. Evaluate the cross- sectional area at the center of each element length and use that area for each element A(x) = Ao (1 + Let =4in, L-40 in, E-106 psi and P-2 kip. (a) (30 points): Plot the analytical solution for displacement and finite element solution for all cases (1, 2, 4 elements) on one graph. Do the same for stress distribution. The graph should include: title, labels for the x and y-axis and legend. Use different colors for each line. In order to present your results, use non-dimensional quantities, i.e. normalize the length of the bar (divide by L), displacements with the analytical solution at x-0, and stresses with Analytical solution for displacement is: ux-In What can you conclude for the displacement and stress plot? Problem 3 (60 points): A tapered elastic bar is subjected to an applied tensile load P at one end and attached to a fixed support at the other end, as shown in the figure below. The cross-sectional area varies linearly from Ao at the free end (r-0) to 2Ao at r-L. Solve for the axial displacement and stress distribution in the bar. For the finite element discretization use 1, 2, 4 elements. Evaluate the cross- sectional area at the center of each element length and use that area for each element A(x) = Ao (1 + Let =4in, L-40 in, E-106 psi and P-2 kip. (a) (30 points): Plot the analytical solution for displacement and finite element solution for all cases (1, 2, 4 elements) on one graph. Do the same for stress distribution. The graph should include: title, labels for the x and y-axis and legend. Use different colors for each line. In order to present your results, use non-dimensional quantities, i.e. normalize the length of the bar (divide by L), displacements with the analytical solution at x-0, and stresses with Analytical solution for displacement is: ux-In What can you conclude for the displacement and stress plot