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dershapefunc2D.m
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dershapefunc2D.m
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function [vwp,vdNr,ngp,swp,sdNr,nsgp,sNr,Nr]=dershapefunc2D(nen,stress_flag)
if nen == 4 && stress_flag == 0
nf = 4; % Number of faces
ngp=4; % Number of area Gauss points
nsgp = 3; % Number of surface Gauss points
nD = 2; % Number of dimensions
g2=1/sqrt(3); % Area Gauss point position (magnitude)
%% ========= 4 node quad shape function and derivative values ========== %%
gp = [-1 -1 1 1; -1 1 1 -1 ]'.*g2; % Area Gauss point position
vwp=ones(4,1); % Area Guass point weights
r = (ngp*nD);
xsi=gp(:,1); eta=gp(:,2); % Reference coodinate position
vdNr(1:2:r,1) = -(1 - eta)./4; % Area shape function derivative values
vdNr(1:2:r,2) = -(1 + eta)./4;
vdNr(1:2:r,3) = (1 + eta)./4;
vdNr(1:2:r,4) = (1 - eta)./4;
vdNr(2:2:r,1) = -(1 - xsi)./4;
vdNr(2:2:r,2) = (1 - xsi)./4;
vdNr(2:2:r,3) = (1 + xsi)./4;
vdNr(2:2:r,4) = -(1 + xsi)./4;
r = r/nD;
Nr(1:r,1) = (1 - xsi).*(1 - eta)./4; % Area shape function values
Nr(1:r,2) = (1 - xsi).*(1 + eta)./4;
Nr(1:r,3) = (1 + xsi).*(1 + eta)./4;
Nr(1:r,4) = (1 + xsi).*(1 - eta)./4;
g1=sqrt(3/5); % Surface Gauss point position (magnitude)
gp = [-1 -1 -1 -g1 0 g1 1 1 1 g1 0 -g1 ; % Surface Gauss point position
-g1 0 g1 1 1 1 g1 0 -g1 -1 -1 -1]'; %
w1 = (5/9); w2 = (8/9); % Edge Guass point weight
swp = [w1 w2 w1];
r = nsgp*nf*nD;
xsi = gp(:,1); eta=gp(:,2); % Reference coodinate position
sdNr(1:2:r,1) = -(1 - eta)./4; % Edge shape function derivatives
sdNr(1:2:r,2) = -(1 + eta)./4;
sdNr(1:2:r,3) = (1 + eta)./4;
sdNr(1:2:r,4) = (1 - eta)./4;
sdNr(2:2:r,1) = -(1 - xsi)./4;
sdNr(2:2:r,2) = (1 - xsi)./4;
sdNr(2:2:r,3) = (1 + xsi)./4;
sdNr(2:2:r,4) = -(1 + xsi)./4;
r=r/nD;
sNr(1:r,1) = (1-xsi).*(1-eta)./4; % Edge shape functions
sNr(1:r,2) = (1-xsi).*(1+eta)./4;
sNr(1:r,3) = (1+xsi).*(1+eta)./4;
sNr(1:r,4) = (1+xsi).*(1-eta)./4;
elseif nen==8 && stress_flag == 0
nf = 4; % Number of faces
ngp=9; % Number of area Gauss points
nsgp = 4; % Number of surface Gauss points
nD = 2; % Number of dimensions
g1=sqrt(3/5); % Area Gauss point position (magnitude)
%% ========= 8 node quad shape function and derivative values ========== %%
gp = [-1 -1 -1 0 1 1 1 0 0; % Area Gaus point position
-1 0 1 1 1 0 -1 -1 0]'.*g1; %
w1 = (5/9)^2; w2 = (8/9).*(5/9); w3=(8/9)^2; % Area Gauss point weights
vwp=[w1 w2 w1 w2 w1 w2 w1 w2 w3]; %
r = (ngp*nD);
xsi=gp(:,1); eta=gp(:,2); % Reference coordinate position
vdNr(1:2:r,1) = ((1 - eta).*((2.*xsi)+eta))./4; % Area shape function derivative values
vdNr(1:2:r,2) = -(1 - eta.^2)./2;
vdNr(1:2:r,3) = ((1 + eta).*((2.*xsi)-eta))./4;
vdNr(1:2:r,4) = -xsi.*(1 + eta);
vdNr(1:2:r,5) = ((1 + eta).*((2.*xsi)+eta))./4;
vdNr(1:2:r,6) = (1 - eta.^2)./2;
vdNr(1:2:r,7) = ((1 - eta).*((2.*xsi)-eta))./4;
vdNr(1:2:r,8) = -xsi.*(1 - eta);
vdNr(2:2:r,1) = ((1 - xsi).*((2*eta)+xsi))./4;
vdNr(2:2:r,2) = -eta.*(1-xsi);
vdNr(2:2:r,3) = (1-xsi).*((2*eta) - xsi)./4;
vdNr(2:2:r,4) = (1 - (xsi.^2))./2;
vdNr(2:2:r,5) = (1 + xsi).*((2*eta)+xsi)./4;
vdNr(2:2:r,6) = -eta.*(1+xsi);
vdNr(2:2:r,7) = (1 + xsi).*((2*eta)-xsi)./4;
vdNr(2:2:r,8) = -(1 - xsi.^2)./2;
r = r/nD;
Nr(1:r,1) = (1 - xsi).*(1 - eta).*(-xsi-eta-1)./4; % Area shape function values
Nr(1:r,2) = (1 - xsi).*(1 - eta.^2)./2;
Nr(1:r,3) = (1 - xsi).*(1 + eta).*(-xsi+eta-1)./4;
Nr(1:r,4) = (1 - xsi.^2).*(1 + eta)./2;
Nr(1:r,5) = (1 + xsi).*(1 + eta).*( xsi+eta-1)./4;
Nr(1:r,6) = (1 + xsi).*(1 - eta.^2)./2;
Nr(1:r,7) = (1 + xsi).*(1 - eta).*(xsi-eta-1)./4;
Nr(1:r,8) = (1 - xsi.^2).*(1 - eta)./2;
g1=sqrt((3/7)+(2/7)*sqrt(6/5)); g2=sqrt((3/7)-(2/7)*sqrt(6/5)); % Surface Gauss point position (magnitude)
gp = [-1 -1 -1 -1 -g1 -g2 g2 g1 1 1 1 1 g1 g2 -g2 -g1; % Surface Gauss point position
-g1 -g2 g2 g1 1 1 1 1 g1 g2 -g2 -g1 -1 -1 -1 -1]';
w1 = (18-sqrt(30))/36; w2 = (18+sqrt(30))/36; % Edge Guass point weight
swp = [w1 w2 w2 w1];
r = nsgp*nf*nD;
xsi = gp(:,1); eta=gp(:,2); % Reference coordinate position
sdNr(1:2:r,1) = ((1 - eta).*((2.*xsi)+eta))./4; % Surface shape function derivative values
sdNr(1:2:r,2) = -(1 - eta.^2)./2;
sdNr(1:2:r,3) = ((1 + eta).*((2.*xsi)-eta))./4;
sdNr(1:2:r,4) = -xsi.*(1 + eta);
sdNr(1:2:r,5) = ((1 + eta).*((2.*xsi)+eta))./4;
sdNr(1:2:r,6) = (1 - eta.^2)./2;
sdNr(1:2:r,7) = ((1 - eta).*((2.*xsi)-eta))./4;
sdNr(1:2:r,8) = -xsi.*(1 - eta);
sdNr(2:2:r,1) = ((1 - xsi).*((2*eta)+xsi))./4;
sdNr(2:2:r,2) = -eta.*(1-xsi);
sdNr(2:2:r,3) = (1-xsi).*((2*eta) - xsi)./4;
sdNr(2:2:r,4) = (1 - (xsi.^2))./2;
sdNr(2:2:r,5) = (1 + xsi).*((2*eta)+xsi)./4;
sdNr(2:2:r,6) = -eta.*(1+xsi);
sdNr(2:2:r,7) = (1 + xsi).*((2*eta)-xsi)./4;
sdNr(2:2:r,8) = -(1 - xsi.^2)./2;
r = r/nD;
sNr(1:r,1) = (1 - xsi).*(1 - eta).*(-xsi-eta-1)./4; % Surface shape function values
sNr(1:r,2) = (1 - xsi).*(1 - eta.^2)./2;
sNr(1:r,3) = (1 - xsi).*(1 + eta).*(-xsi+eta-1)./4;
sNr(1:r,4) = (1 - xsi.^2).*(1 + eta)./2;
sNr(1:r,5) = (1 + xsi).*(1 + eta).*(xsi+eta-1)./4;
sNr(1:r,6) = (1 + xsi).*(1 - eta.^2)./2;
sNr(1:r,7) = (1 + xsi).*(1 - eta).*(xsi-eta-1)./4;
sNr(1:r,8) = (1 - xsi.^2).*(1 - eta)./2;
elseif nen==4 && stress_flag == 1
gp = [-1 -1 1 1
-1 1 1 -1 ]';
ngp=size(gp,1);
r1 = (ngp*2);
xsi=gp(:,1) ;
eta=gp(:,2) ;
r=r1;
vdNr(1:2:r,1) = -(1 - eta)./4;
vdNr(1:2:r,2) = -(1 + eta)./4;
vdNr(1:2:r,3) = (1 + eta)./4;
vdNr(1:2:r,4) = (1 - eta)./4;
vdNr(2:2:r,1) = -(1 - xsi)./4;
vdNr(2:2:r,2) = (1 - xsi)./4;
vdNr(2:2:r,3) = (1 + xsi)./4;
vdNr(2:2:r,4) = -(1 + xsi)./4;
vwp=[];swp=[]; sdNr =[]; nsgp=[];sNr=[];Nr=[];
elseif nen==8 && stress_flag == 1
gp = [-1 -1 -1 0 1 1 1 0;
-1 0 1 1 1 0 -1 -1]';
ngp=size(gp,1);
r1 = (ngp*2);
xsi=gp(:,1) ;
eta=gp(:,2) ;
r=r1;
vdNr(1:2:r,1) = ((1 - eta).*((2.*xsi)+eta))./4;
vdNr(1:2:r,2) = -(1 - eta.^2)./2;
vdNr(1:2:r,3) = ((1 + eta).*((2.*xsi)-eta))./4;
vdNr(1:2:r,4) = -xsi.*(1 + eta);
vdNr(1:2:r,5) = ((1 + eta).*((2.*xsi)+eta))./4;
vdNr(1:2:r,6) = (1 - eta.^2)./2;
vdNr(1:2:r,7) = ((1 - eta).*((2.*xsi)-eta))./4;
vdNr(1:2:r,8) = -xsi.*(1 - eta);
vdNr(2:2:r,1) = ((1 - xsi).*((2*eta)+xsi))./4;
vdNr(2:2:r,2) = -eta.*(1-xsi);
vdNr(2:2:r,3) = (1-xsi).*((2*eta) - xsi)./4;
vdNr(2:2:r,4) = (1 - (xsi.^2))./2;
vdNr(2:2:r,5) = (1 + xsi).*((2*eta)+xsi)./4;
vdNr(2:2:r,6) = -eta.*(1+xsi);
vdNr(2:2:r,7) = (1 + xsi).*((2*eta)-xsi)./4;
vdNr(2:2:r,8) = -(1 - xsi.^2)./2;
vwp=[];swp=[]; sdNr =[]; nsgp=[];sNr=[];Nr=[];
end