代写CS:Assignment 1: A Matlab program for a 3D structure Homework

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clc;

Clear command window.

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clear;

removes all variables from the workspace.

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close all;

closes all the open figure windows.

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N = textread('node.txt');

Read x and y coordinate for the node and assign

their values to N

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E = textread('elem.txt');

Read the near and far end for the beam and

assign

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NN = length(N);

Get the number of node

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NE = length(E);

Get the number of element

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E0 = 2.1e6;

Set Young’s modulus

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A0 = 22.8;

Set the area of cross section

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I0 = 935;

Set the second moment of inertia

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hold on;

holds the current plot and all axis properties so that subsequent graphing commands add to the

existing graph.

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for i=1:NE

Begin an iteration in which i begins from 1 to NE

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plot([N(E(i,1),1),N(E(i,2),1)],[N(E(i,1),2),N(

E(i,2),2)],'k','linewidth',2);

Plot a line starts from the near end to the far end of an element in black with the linewidth of

2.

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text((N(E(i,1),1)+N(E(i,2),1))/2,(N(E(i,1),2)+

N(E(i,2),2))/2,num2str(i),'color','b','fontsiz e',12);

Plot the element number at its middle in blue and 12 font size.

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end

End the iteration

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for i=1:NN

Begin an iteration in which i begins from 1 to NN

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if i<3

If i<3

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plot(N(i,1),N(i,2),'rs','markersize',12,'mark

erfacecolor','r');

Plot a red square marker at the node i with the

size of 12 and red marker face color.

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else

Else

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plot(N(i,1),N(i,2),'ko','markersize',8,'mark

erfacecolor','k');

Plot a black circle marker at the node i with the

size of 8 and black marker face color.

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end

End if

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text(N(i,1),N(i,2),num2str(i),'color','g','font

size',12);

Plot a green node number at the node i with the

size of 12.

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end

End the iteration

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F=zeros(3*NN,1);

Create the force vector and all members are

zero.

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FN = [11 12 17 18 23 24];

Set the node number at which a load is applied

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F(3*FN-2) = -20;

The x component of the load is -20

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F(3*FN-1) = -10;

The y component of the load is -10

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scale = 20;

Set the scaling factor

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for i=1:length(FN)

Begin an iteration in which i begins from 1 to the

number of loads

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plot( N(FN(i),1),N(FN(i),2),'b*','markersize'

,10,'markerfacecolor','b');

Plot a blue star with the size of 10 and blue

marker face color at the node where a load is applied.

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plot([N(FN(i),1),N(FN(i),1)-

100*sin(20/180*pi)],[N(FN(i),2),N(FN(i),2)

-100*cos(20/180*pi)],'-

>r','linewidth',2,'markerfacecolor','r');

Plot red “>” symbols to show the applied load in 20 degree angle with line width of 2 and red marker face color

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ang=-1.5*pi:0.5:-.5*pi;

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xp=scale*cos(ang);

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yp=scale*sin(ang);

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plot(N(FN(i),1)+xp,N(FN(i),2)+yp,'–

r>','linewidth',2,'markerfacecolor','r');

Plot 7 red “>” symbols to show the applied moment with line width of 2 and red marker

face color

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end

End the iteration

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title('A schematic of the power

tower','fontsize',12);

Plot the title of this figure with 12 font size

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set(gca,'fontsize',12);

Set the font size of current axis as 12

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axis equal tight

Set the axis property as “equal” and “tight”

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print('-dtiff','-r400','frame.tif');

Print the figure in the name of “frame.tif” with

tiff format and 400 resolution

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K=zeros(3*NN,3*NN);

Determine the global stiffness matrix, its size is

3NN by 3NN and all members are zero.

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for n=1:NE

Begin an iteration in which i begins from 1 to NN

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L = sqrt((N(E(n,1),1)-N(E(n,2),1))^2 +

(N(E(n,1),2)-N(E(n,2),2))^2);

Calculate the length of element

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lx = (N(E(n,2),1) – N(E(n,1),1))/L;

Calculate cos(theta)

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ly = (N(E(n,2),2) – N(E(n,1),2))/L;

Calculate sin(theta)

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a=A0*E0/L;

Calculate some parameters for the local matrix

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b=6*E0*I0/L^2;

Calculate some parameters for the local matrix

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c=12*E0*I0/L^3;

Calculate some parameters for the local matrix

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d=E0*I0/L;

Calculate some parameters for the local matrix

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Ke = [ a  0 0   -a 0 0

Determine the local matrix at local coordinate

system

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0   c b   0   -c b

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0 b 4*d 0 -b 2*d

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-a  0 0 a   0 0

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0  -c -b   0   c -b

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0 b 2*d 0 -b 4*d];

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Determine the transformation matrix

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T = [ lx ly 0 0 0 0

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-ly lx 0 0 0 0

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0 0 1 0 0 0

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0 0 0 -ly lx 0

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0 0 0 0 0 1];

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Ke = T'*Ke*T;

Determine the local matrix at global coordinate

system

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i = E(n,1);

Get the near end number of an element

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j = E(n,2);

Get the far end number of an element

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dof = [3*i-2:3*i 3*j-2:3*j];

6 degrees of the element

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K(dof,dof) = K(dof,dof) + Ke;

Assemble the global matrix from the local matrix

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end

End the iteration

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fixeddofs = [1 2 3 4 5 6];

Fixed degrees

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alldofs = [1:3*NN];

All degrees

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freedofs = setdiff(alldofs,fixeddofs);

Get the active degrees

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U(freedofs,:) =

K(freedofs,freedofs)\F(freedofs,:);

Calculate the equation Ax=b to get the

deformations for all active degrees.

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U(fixeddofs,:)= 0;

Make the fixed degrees equal zero

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figure;

Plot a new figure

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hold on;

holds the current plot and all axis properties so

that subsequent graphing commands add to the existing graph.

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ND = N + scale*[U(1:3:end) U(2:3:end)];

Plot the node after the deformation. Noted the

deformation is multiplied by the scaling factor.

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for i=1:NE

Begin an iteration in which i begins from 1 to NN

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plot([N(E(i,1),1),N(E(i,2),1)],[N(E(i,1),2),N(

E(i,2),2)],'linewidth',2,'color','k');

Plot a line starts from the near end (before deformation) to the far end (before deformation) of an element in black with the

line width of 2.

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plot([ND(E(i,1),1),ND(E(i,2),1)],[ND(E(i,1),2

),ND(E(i,2),2)],'–b','linewidth',2);

Plot a line starts from the near end (after deformation)to the far end (after deformation) of an element in blue with the dashed line width

of 2.

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end

End the iteration

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title(['The deformation magnified '

int2str(scale) ' times'],'fontsize',12);

Plot the title of this figure with 12 font size

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axis equal tight off

Set the font size of current axis as 12

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set(gca,'fontsize',12);

Set the axis property as “equal” and “tight”

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print('-dtiff','-r400','U_frame.tif');

Print the figure in the name of “U_frame.tif”

with tiff format and 400 resolution

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