% Title of the problem: Project_Title='Test for Linear Elastic Plane Stress Case Using Q4-elements';

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Lampiran 1 : Kode MATLAB untuk Data Input

% INPUT DATA FORMAT

% Title of the problem:

Project_Title='Test for Linear Elastic Plane Stress Case Using Q4-elements';

% Control Data

% Ndofn: Number of degrees of freedom per nodal point

% Ngaus: The order of Gaussian numerical integration rule to be employed

% Ntype: Problem type parameter 1-Plane stress, 2-Plane strain Control_cards=[ 3 3 1 1 ];

% Nodal Coordinate

% Ipoin: Nodal point number

% Coord: Coordinate of the node Node_cards=[ % m

1 1 1 2 -1 1 3 -1 -1 4 1 -1];

% Element Connectivity

% Numel: Element number

% Matno: Material property number

% Lnods: Element node numbers listed per each element Element_cards=[

1 1 1 2 3 4];

% Nodal Boundary Condition

% Nofix: Restrained node number

% Ifpre: Condition of restraint

% Presc: Prescribed value of nodal displacements Restrained_cards=[

2 1 0 0 0 0 0 3 1 1 0 0 0 0];

% Material Properties

% Numat: Material identification number

% Props: Elastic modulus, Poisson's ratio, material thickness Material_cards=[ % KN/m2

1 210e06 0.3 0.1 ];

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Lampiran 1 : Kode MATLAB untuk Data Input (sambungan)

% Nodal Force

% Lodpt: Node number

% Point: Applied nodal point forces Applied_load_cards=[ % KN

1 4 0 0 4 4 0 0];

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Lampiran 2 : Kode MATLAB untuk Mengolah Data Input

function [Project_Title, Ndofn, NgausK , NgausP, Ntype , Npoin, Nelem, Nnode, Nsvab, ...

Lnods, Coord, Matno, Props, Ifpre, Fixed, Point] = ...

Echo_data (Input_file_name)

% Giving general information of the input data file and feeding

% the necessary input for subsequent calculation processes

%

% Input

% Input_file_name

%

% Output

% All of variables needed for subsequent calculation processes

eval(Input_file_name);

Project_Title

%

Ndofn= Control_cards(1,1);

fprintf('Number of degrees of freedom per nodal point: %d \n', Ndofn);

NgausK= Control_cards(1,2);

fprintf('The order of Gaussian numerical integration rule for K matrix: %d \n', NgausK);

NgausP= Control_cards(1,3);

fprintf('The order of Gaussian numerical integration rule for P matrix: %d \n', NgausP);

Ntype= Control_cards(1,4);

if Ntype==1

fprintf('Linear-elastic plane stress problem. \n') elseif Ntype==2

fprintf('Linear-elastic plane strain problem. \n') else

error('Wrong problem type parameter! \n');

end

%

Npoin=size(Node_cards,1); Ndime=size(Node_cards,2)-1;

fprintf('\nTotal number of nodal points in the structure: %d \n', Npoin);

fprintf('Number of coordinate components required to ');

fprintf('define each nodal points: %d \n', Ndime);

%

Nelem=size(Element_cards,1); Nnode=size(Element_cards,2)-2;

fprintf('\nTotal number of elements in the structure: %d \n', Nelem);

fprintf('Number of nodes per element: %d \n', Nnode);

%

Nmats=size(Material_cards,1);

fprintf('\nTotal number of different materials in the structure: %d \n', Nmats)

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Lampiran 2 : Kode MATLAB untuk Mengolah Data Input (sambungan)

%

Nsvab=Npoin*Ndofn;

fprintf('\nNumber of global structural variables (DOF): %d \n', Nsvab)

%

Matno=Element_cards(:,2);

Lnods=Element_cards;

Lnods(:,[1 2])=[];

%

Coord=Node_cards;

Coord(:,1)=[];

%

Props=Material_cards(:,2:end);

%

Ifpre1=Restrained_cards(:,1: (1+Ndofn));

Fixed1=Restrained_cards(:, [ 1 (Ndofn+2):end ] );

Ifpre= Node2eqns(Ifpre1, Nsvab);

Fixed= Node2eqns(Fixed1, Nsvab);

%

Point= Node2eqns(Applied_load_cards, Nsvab);

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Lampiran 3 : Kode MATLAB untuk Matriks Kekakuan untuk D-Type

function Estiff = StifpsQ4( Coord , Lnods , Ielem , Props , NgausK , NgausP , Ndofn , Matno , Ntype )

%Stifness Matriks for Membran Elements using D-Type

h = Props(Matno(Ielem),3);

Elcod=Coord(Lnods(Ielem,:),:);

[l,n] = lnmatx( Elcod );

%

[PosgpK, WeigpK] = GaussqK (NgausK);

K=zeros(12,12);

for Igaus = 1:NgausK for Jgaus = 1: NgausK

r=PosgpK(Igaus); s=PosgpK(Jgaus);

W1=WeigpK(Igaus); W2=WeigpK(Jgaus);

[Deriv, Shape , SShape, SDeriv, NB9] = SfrQ4(r,s);

[Djacb, Xjabi , Cartd] = Jacob(Ielem, Deriv, Elcod);

B = Bmatps(Cartd, Ndofn);

G = Gmatps(Xjabi , l , n , SDeriv);

Dmatx = Modps(Matno, Props, Ntype, Ielem);

K = K+h*W1*W2*[B G]'*Dmatx*[B G]*Djacb;

end end

%

Young = Props(Matno(Ielem),1);

Poiss = Props (Matno(Ielem),2);

[PosgpP, WeigpP] = GaussqP (NgausP);

P=zeros(12,12);

for Igaus = 1:NgausP for Jgaus = 1: NgausP

r=PosgpP(Igaus); s=PosgpP(Jgaus);

W1=WeigpP(Igaus); W2=WeigpP(Jgaus);

[b,g] = bgmatps( Cartd , Xjabi , l , n ,Shape , SDeriv );

gamma = Young/(2*(1+Poiss));

P = P+h*W1*W2*gamma*[b ; g]*[b ; g]'*Djacb;

end end

Estiff = K+P;

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Lampiran 4 : Kode MATLAB untuk Matriks Kekakuan untuk M-Type

function Estiff = StifpsQ4( Coord , Lnods , Ielem , Props , NgausK , Ndofn , Matno , Ntype )

%Stiffness Matrix for Membran Elements using M-Type

Elcod=Coord(Lnods(Ielem,:),:);

E = Props(1);

v = Props(2);

h =Props(3);

%

K=zeros(12,12);

%

K = K+h*W1*W2*[B G]'*Dmatx*[B G]*Djacb;

end end

%

h_e=zeros(12,1);

V = 0;

[b,g] = bgmatps( Cartd , Xjabi , l , n ,Shape , SDeriv );

h_e = h_e+h*W1*W2*[b ; g]*Djacb;

V = V + h*W1*W2*Djacb;

end end

gamma = E/(2*(1+v));

Estiff = K+gamma/V*h_e*h_e';

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Lampiran 5 : Kode MATLAB untuk Tegangan dan Regangan

function Strsg = Stregps (Ielem, Lnods, Nnode, Ndofn, Xdisp, Coord, Props , Matno , Ntype)

% Calculating the stresses at the Gauss points for an element

%

% Input

% Ielem: Current element number

% Lnods: Element node numbers listed per each element

% Coord: Coordinate of the node

%

% Output

% Strsg: Stress components at element Gauss points

% Strsp: Principal stress values=(S1,S2,alpha)

% Identify the displacements of the element nodal points

% ---> Eldis Ncols=[];

for Inode=1:Nnode

Nodei=Lnods(Ielem,Inode);

for Idofn=1:Ndofn

Nrows(Idofn,:)=(Nodei-1)*Ndofn + Idofn;

end

Ncols=[Ncols; Nrows];

end

Eldis=Xdisp(Ncols,:);

Eldis12 = [];

Eldis3 = [];

for I = 1:Nnode

Eldis12((2*I-1):2*I,:) = Eldis((3*I-2):(3*I-1),:);

Eldis3(I,:) = Eldis(3*I,:);

end

% The elasticity matrix

% Elcod: Local array of nodal Cartesian coordinates of

% the element currently under consideration Elcod=Coord(Lnods(Ielem,:),:);

Ngaus = 2;

[Posgp, Weigp] = Gaussq (Ngaus);

Strsg=[];

for Igaus = 1:Ngaus for Jgaus = 1: Ngaus

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Lampiran 5 : Kode MATLAB untuk Tegangan dan Regangan (sambungan)

r=Posgp(Igaus); s=Posgp(Jgaus);

[Djacb, Xjabi, Cartd] = Jacob(Ielem, Deriv, Elcod);

IStrsg = Dmatx*(B*Eldis12+G*Eldis3);

Strsg = [Strsg IStrsg];

end end

clear Istrsg;

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Lampiran 6 : Kode MATLAB untuk Proses Utama dari Program

clear ;

%

% Input

%

Input_file_name='Input_NAFEMS2'; %input('Enter the input data file (excluding extension): ','s');

[Project_Title, Ndofn, NgausK, NgausP, Ntype , Npoin, Nelem, Nnode, Nsvab, Lnods, Coord, ...

Matno, Props, Ifpre, Fixed, Point] = Echo_data (Input_file_name);

%

Astiff= sparse(Nsvab,Nsvab);

Rload= zeros(Ndofn*Nnode,1);

for Ielem=1:Nelem IMatno=Matno(Ielem);

Estiff = StifpsQ4( Coord , Lnods , Ielem , Props , NgausK , ...

Ndofn , Matno , Ntype );

Mod_Estiff = Estiffps( Estiff );

Astiff= Astiff + Element2structure (Ielem, Mod_Estiff, Rload, ...

Lnods, Nsvab, Nnode, Ndofn);

end

clear Rload Ielem IMatno;

%

% Applying nodal point forces

%

Gload= Point; clear Point

%

% Imposing Displacement Boundary Conditions

%

[Mod_Astiff, Mod_Gload] = ...

Modify (Astiff, Gload, Nsvab, Ifpre, Fixed);

%

% The solution of equations

%

% Nonzero_Ifpre : Equation indices of fixed dofs or

% prescribed displacements

Nonzero_Ifpre = Nonzero_index (Ifpre, Fixed);

Xdisp = Solution (Mod_Astiff, Mod_Gload, Fixed, Nonzero_Ifpre);

% Scale=100;

% Plot_Deform( Project_Title, Lnods, Coord, Nelem, Npoin, ...

% Xdisp, Ndofn, Scale);

%

% Reactions

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Lampiran 6 : Kode MATLAB untuk Proses Utama dari Program (sambungan)

%

React= Reaction (Astiff, Gload, Xdisp, Ndofn, Nonzero_Ifpre)

%

% Stresses

%

%Ngaus=1;

delete Stress.txt Strep.txt Svm.txt

fid1=fopen('Stress.txt','at'); fid2=fopen('Strep.txt','at');

fid3=fopen('Svm.txt','at');

Stress=zeros(Nnode*Nelem,3);

Strsg = ... % Stress at Gauss Point

Stregps (Ielem, Lnods, Nnode, Ndofn, Xdisp, Coord, Props , Matno , Ntype);

%Strsp = Strepps (Strsg)

% Extrapolation to nodal points Strsex=[];

for Xi=-1:2:1 for Etha=-1:2:1

Strsex=[ Strsex Extrag2(Xi,Etha,Strsg)' ];

end end

Strsex=Strsex(:,[1 3 4 2]);

Stress( (Nnode*Ielem-3):(Nnode*Ielem), : )= Strsex';

Strsp = Strepps (Strsex);

Strsvm = Strevm (Strsex, Props(1,2));

fprintf(fid1,'%e %e %e\n',Strsex); fprintf(fid1,'\n');

fprintf(fid2,'%e %e %e\n',Strsp); fprintf(fid2,'\n');

fprintf(fid3,'%e %e %e %e\n',Strsvm);

end

fclose(fid1); fclose(fid2); fclose(fid3);

clear Ielem Imatno;

tic;

toc;

%

% Strain Energy

% SE=0;

Estiff = StifpsQ4( Coord , Lnods , Ielem , Props , NgausK , ...

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Lampiran 6 : Kode MATLAB untuk Proses Utama dari Program (sambungan)

Ndofn , Matno , Ntype );

Mod_Estiff = Estiffps( Estiff );

Eldis= Edisps( Ielem, Lnods, Nnode, Ndofn, Xdisp);

SE= SE + 0.5* Eldis' * Mod_Estiff* Eldis;

end

% SE-0.5*Xdisp'*Astiff*Xdisp

%

% Plotting

%

Ask_G='y';

while Ask_G == 'y' disp('Plotting option:')

disp('1. Undeformed shape of the structure') disp('2. Deformed shape of the structure') disp('3. Stress contours')

disp('4. Principal stress contours')

disp('5. Effective von Mises stress contours') disp('6. Exit')

Plot_case=input('Which one do you want to plot? ');

fprintf('\n\n')

for icase=1:size(Plot_case,2) switch Plot_case(1,icase) case 1

Plot_Undeform (Project_Title, Lnods, Coord, Nelem, Npoin);

case 2

Scale=input('Scale for the deformed plot (enter 0 for autoscale): ') Plot_Deform( Project_Title, Lnods, Coord, Nelem, Npoin, ...

Xdisp, Ndofn, Scale);

case 3

Plot_Stress (Lnods, Coord, Nelem, 'Stress.txt');

case 4

Plot_Strep (Lnods, Coord, Nelem, 'Strep.txt');

case 5

Plot_Strevm (Lnods, Coord, Nelem, 'Svm.txt') otherwise

Ask_G='n';

end end end

disp('Congratulations! The project has been completed.') disp('Check the results carefully!!')

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