# Adding more rows to the existing matrix(more element)Think of how to get the connectivity matrix in a general case to the existing matlab code.clc;clear all;close all;E=2e11; %(N/m^2) Young's...

Adding more rows to the existing matrix(more element)
Think of how to get the connectivity matrix in a general case to the existing matlab code.

clc;

clear
all;

close
all;

E=2e11;
%(N/m^2) Young's Modulus

v=1/6;
%Poisson Ratio

rho=7850;%(kg/m^2) Density

a=1;
%(m)Length of one side

b=2;
%(m)Length of the other side

h=0.02;%(m)

Nnodes=9;
%number of nodes

Connectivity= 1;

alpha=a/b;

beta=b/a;

%coordinates=[...

% ];

%Coefficients of the Mass Matrix

m11_p=[...

3454 922*b -922*a 1226 398*b 548*a

922*b 320*b*b -252*a*b 398*b 160*b*b 168*a*b

-922*a -252*a*b 320*a*a -548*a -168*a*b -240*a*a

1226 398*b -548*a 3454 922*b 922*a

398*b 160*b*b -168*a*b 922*b 320*b*b 252*a*b

548*a 168*a*b -240*a*a 922*a 252*a*b 320*a*a];

m22_p=[...

3454 -922*b 922*a 1226 -398*b -548*a

-922*b 320*b*b -252*a*b -398*b 160*b*b 168*a*b

922*a -252*a*b 320*a*a 548*a -168*a*b -240*a*a

1226 -398*b 548*a 3454 -922*b -922*a

-398*b 160*b*b -168*a*b -922*b 320*b*b 252*a*b

-548*a 168*a*b -240*a*a -922*a 252*a*b 320*a*a];

m21_p=[...

394 232*b -232*a 1226 548*b 398*a

-232*b -120*b*b 112*a*b -548*b -240*b*b -168*a*b

232*a 112*a*b -120*a*a 398*a 168*a*b 160*a*a

1226 548*b -398*a 394 232*b 232*a

-548*b -240*b*b 168*a*b -232*b -120*b*b -112*a*b

-398*a -168*a*b 160*a*a -232*b -112*a*b -120*a*a];

% me=(rho*h*a*b/6300)*[...

% m11 m21'

% m21 m22];

m11=m11_p(1:3,1:3);

m21=m11_p(4:6,1:3);

m22=m11_p(4:6,4:6);

m12=m21';

m31=m21_p(1:3,1:3);

m41=m21_p(4:6,1:3);

m13=m31';

m14=m41';

m32=m21_p(1:3,4:6);

m42=m21_p(4:6,4:6);

m23=m32';

m24=m42';

m33=m22_p(1:3,1:3);

m43=m22_p(4:6,1:3);

m34=m43';

m44=m22_p(4:6,4:6);

%Elemental Mass Matrix;

me=[...

m11 m12 m13 m14

m21 m22 m23 m24

m31 m32 m33 m34

m41 m42 m43 m44];

% T3=[...

% lx mx nx

% ly my ny

% lz mz nz];

%

% T=diag(T3);

%

% M=T'*me*T;

% Coefficients of the stiffness matrix

k11_11=4*(beta^2+alpha^2)+2*(7-2*v)/5;

k11_21=2*b*(2*(alpha^2)+((1+4*v)/5));

k11_31=2*a*((-2*(beta^2))-((1+4*v)/5));

k11_22=4*(b^2)*((4*(alpha^2)/3)+(4*(1-v)/15));

k11_32=-4*v*a*b;

k11_33=4*(a^2)*((4*(beta^2)/3)+(4*(1-v)/15));

k11=[...

k11_11 k11_21 k11_31;

k11_21 k11_22 k11_32;

k11_31 k11_32 k11_33];

k21_11=-2*(2*beta^2-alpha^2)+2*(7-2*v)/5;

k21_12=2*b*((alpha^2)-((1+4*v)/5));

k21_13=2*a*((2*(beta^2))+((1-v)/5));

k21_21=k21_12;

k21_31=-k21_13;

k21_22=4*(b^2)*((2*(alpha^2)/3)-(4*(1-v)/15));

k21_33=4*(a^2)*((2*(beta^2)/3)-(1*(1-v)/15));

k21=[...

k21_11 k21_12 k21_13

k21_21 k21_22 0

k21_31 0 k21_33];

k31_11=-2*(beta^2+alpha^2)-2*(7-2*v)/5;

k31_12=2*b*(-(alpha^2)+((1-v)/5));

k31_13=2*a*((beta^2)-(1-v)/5);

k31_21=2*b*((alpha^2)-((1-v)/5));

k31_22=4*(b^2)*(((alpha^2)/3)+(1*(1-v)/15));

k31_31=2*a*(-(beta^2)+(1-v)/5);

k31_33=4*(a^2)*(((beta^2)/3)+(1*(1-v)/15));

k31=[...

k31_11 k31_12 k31_13

k31_21 k31_22 0

k31_31 0 k31_33];

k41_11=2*((beta^2)-2*(alpha^2))-2*(7-2*v)/5;

k41_12=2*b*(-2*(alpha^2)-(1-v)/5);

k41_13=2*a*(-(beta^2)+(1+4*v)/5);

k41_21=2*b*(2*(alpha^2)+(1-v)/5);

k41_22=4*(b^2)*((2*(alpha^2)/3)-(1*(1-v)/15));

k41_31=2*a*(-(beta^2)+(1+4*v)/5);

k41_33=4*(a^2)*((2*(beta^2)/3)-(4*(1-v)/15));

k41=[...

k41_11 k41_12 k41_13

k41_21 k41_22 0

k41_31 0 k41_33];

I1=[...

-1 0 0

0 1 0

0 0 1];

I2=[...

1 0 0

0 -1 0

0 0 1];

I3=[...

1 0 0

0 1 0

0 0 -1];

k22=I3'*k11*I3;

k32=I3'*k41*I3;

k42=I3'*k31*I3;

k33=I1'*k11*I1;

k43=I1'*k21*I1;

k44=I2'*k11*I2;

% exp_k=1;

kn=E*(h^3)/(48*(1-(v^2))*a*b);

k=kn*[...

k11 k21' k31' k41'

k21 k22 k32' k42'

k31 k32 k33 k43'

k41 k42 k43 k44];

% eqn1=k-(omega^2)*me;

% solve(det(k-(omega^2).*me==0),omega)

% solu=solve(eqn1=0,omega);

z=zeros(3,3);

% Node coordinates and connectivity matrix

% GNodeCoords = [0 0; Lx 0; Lx Ly; 0 Ly];

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

%K_global=assemble(K_local,B)

%K_global is global stiffness matrix

%k is local stiffness matrices of all elements

% B = connectivity matrix

% when B=ElConnMatrix 1

[NE,j] = size(B);
%number of elements and number of nodes per element

Nnodes = max(max(B));

K_global = zeros(3*Nnodes,3*Nnodes);

M_global = zeros(3*Nnodes,3*Nnodes);

for
i=1:NE

aux=[3*B(i,:)-2;3*B(i,:)-1;3*B(i,:)];

aux=aux(:);

K_global(aux,aux)=K_global(aux,aux)+k;

M_global(aux,aux)=M_global(aux,aux)+me;

end

%Global Stiffness Matrix

K=kn*[...

k11 k21' z k41' k31' z z z z

k21 k22+k11 k21' k42' k32'+k41' k31' z z z

z k21 k22 z k42' k32' z z z

k41 k42 z k44+k33 k43+k43' z k32 k31 z

k31 k32+k41 k42 k43'+k43 k33+3*k44 k43+k41 k42 k43+k41 k42

z k31 k32 z k43'+k41' k33+k11 z k31' k21'

z z z k32' k42' z k22 k21 z

z z z k31' k43'+k41' k31 k21' k33+k11 k32

z z z z k42' k21 z k32' k22];

%Global Mass Matrix

% M=(rho*h*a*b/6300)*[...

M=[...

m11 m21' z m41' m31' z z z z

m21 m22+m11 m21' m42' m32'+m41' m31' z z z

z m21 m22 z m42' m32' z z z

m41 m42 z m44+m33 m43+m43' z m32 m31 z

m31 m32+m41 m42 m43'+m43 m33+3*m44 m43+m41 m42 m43+m41 m42

z m31 m32 z m43'+m41' m33+m11 z m31' m21'

z z z m32' m42' z m22 m21 z

z z z m31' m43'+m41' m31 m21' m33+m11 m32

z z z z m42' m21 z m32' m22];

[vecfreq,freq]=eig(K,M);

% freq = diag(freq) ;

% freq=sqrt(freq); % UNITS :rad per sec

% freqHz = abs(freq/(2*pi)) ; % UNITS : Hertz

% freqs=sort(freqHz);

[freq_sorted, ind] = sort(diag(freq),'ascend');

V_sorted = vecfreq(:,ind);

req_freq=sqrt(freq_sorted(1:10));
%Top 10 natural frequencies

freqHz = abs(req_freq/(2*pi));
% UNITS : Hertz

for
jj=1:10

V = zeros(size(V_sorted,2),size(V_sorted,2)) ;

x_a=linspace(0,a*2,27);

y_b=linspace(0,b*2,27);

[s,t] = meshgrid(x_a,y_b);

for
ii = 1:size(V_sorted,2)

V(:,ii) = V_sorted(:,jj);

% figure(ii)

% plot(V(:,ii));

end

% figure(jj)

% surf (s,t,abs(V));

end

% N1 = 1/4*(1-t).*(1-s);

% subplot(2,2,1);

% surf(s,t,abs(vecfreq));

% xlabel('a');

% ylabel('b');

%

% N2 = @(s,t)1/4*(1-t).*(1+s);

% subplot(2,2,2);

% surf(s,t,N2(s,t));

% xlabel('a');

% ylabel('b');

%

% N3 = @(s,t)1/4*(1+t).*(1+s);

% subplot(2,2,3);

% surf(s,t,N3(s,t));

% xlabel('a');

% ylabel('b');

%

% N4 = @(s,t)1/4*(1+t).*(1-s);

% subplot(2,2,4);

% surf(s,t,N4(s,t));

% xlabel('a');

% ylabel('b');

SymmetryM=(M-M.');

SymmetryK=(K-K.');

SymmetryMe=(me-me.');

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M=[... m11 m21' z m41' m31' z z z z m21 m22+m11 m21' m42' m32'+m41' m31' z z z z m21 m22 z m42' m32' z z z m41 m42 z m44+m33 m43+m43' z m32 m31 z m31 m32+m41 m42 m43'+m43 m33+3*m44 m43+m41 m42 m43+m41 m42 z m31 m32 z m43'+m41' m33+m11 z m31' m21' z z z m32' m42' z m22 m21 z z z z m31' m43'+m41' m31 m21' m33+m11 m32 z z z z m42' m21 z m32' m22]; [vecfreq,freq]=eig(K,M); % freq = diag(freq) ; % freq=sqrt(freq); % UNITS :rad per sec % freqHz = abs(freq/(2*pi)) ; % UNITS : Hertz % freqs=sort(freqHz); [freq_sorted, ind] = sort(diag(freq),'ascend'); V_sorted = vecfreq(:,ind); req_freq=sqrt(freq_sorted(1:10)); %Top 10 natural frequencies freqHz = abs(req_freq/(2*pi)); % UNITS : Hertz for jj=1:10 V = zeros(size(V_sorted,2),size(V_sorted,2)) ; x_a=linspace(0,a*2,27); y_b=linspace(0,b*2,27); [s,t] = meshgrid(x_a,y_b); for ii = 1:size(V_sorted,2) V(:,ii) = V_sorted(:,jj); % figure(ii) % plot(V(:,ii)); end % figure(jj) % surf (s,t,abs(V)); end % N1 = 1/4*(1-t).*(1-s); % subplot(2,2,1); % surf(s,t,abs(vecfreq)); % xlabel('a'); % ylabel('b'); % % N2 = @(s,t)1/4*(1-t).*(1+s); % subplot(2,2,2); % surf(s,t,N2(s,t)); % xlabel('a'); % ylabel('b'); % % N3 = @(s,t)1/4*(1+t).*(1+s); % subplot(2,2,3); % surf(s,t,N3(s,t)); % xlabel('a'); % ylabel('b'); % % N4 = @(s,t)1/4*(1+t).*(1-s); % subplot(2,2,4); % surf(s,t,N4(s,t)); % xlabel('a'); % ylabel('b'); SymmetryM=(M-M.'); SymmetryK=(K-K.'); SymmetryMe=(me-me.');
Answered 12 days AfterJun 06, 2023

## Answer To: Adding more rows to the existing matrix(more element)Think of how to get the connectivity matrix in...

Kshitij answered on Jun 13 2023
SOLUTION.PDF