Matlab code Shape Functions 1D Lagrangian - KratosWiki

http://kratos-wiki.cimne.upc.edu/index.php/Matlab_code_Shape_Functions_1D_Lagrangian[27-08-2014 07:30:38 PM]

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Matlab code Shape Functions 1D Lagrangian

% Shape Functions for 1D problems% polynomial Ni(x) = a1 + a2x + a3x^2 +...% Ni(xj)=1 if i=j, Ni(xj)=0 if i<>j

Np=101;x=linspace(0,1,Np);

% Linear case% Two nodes: x1, x2% Ni(x) = ai1 + ai2•x

xi(1)=0;xi(2)=1;

Ni(1,:)=shfunc(x,1,xi);Ni(2,:)=shfunc(x,2,xi);

mdibuja(x,Ni,'x','N1, N2','Linear Shape Funtions');

% Quadratic case% Three nodes: x1, x2, x3% Ni(x) = ai1 + ai2•x + ai3•x^2

xi(1)=0;xi(2)=0.5;xi(3)=1;

for num=1:length(xi) Ni(num,:)=shfunc(x,num,xi);end

mdibuja(x,Ni,'x','N1, N2, N3','Quadratic Shape Funtions');

% Cubic case% Four Nodes: x1, x2, x3, x4% Ni(x) = ai1 + ai2•x + ai3•x^2 + ai4•x^3

xi(1)=0;xi(2)=1/3;xi(3)=2/3;xi(4)=1;

for num=1:length(xi) Ni(num,:)=shfunc(x,num,xi);end

mdibuja(x,Ni,'x','N1, N2, N3, N4','Cubic Shape Funtions'); hold on;plot(xi,xi*0,'o');

% Five Nodes: x1, x2, x3, x4, x5% Ni(x) = ai1 + ai2•x + ai3•x^2 + ai4•x^3 + ai5•x^4

xi(1)=0;xi(2)=1/4;xi(3)=2/4;xi(4)=3/4;xi(5)=1;

for num=1:length(xi) Ni(num,:)=shfunc(x,num,xi);end

mdibuja(x,Ni,'x','N1, N2, N3, N4, N5','Five Node Shape Funtions'); hold on;plot(xi,xi*0,'o');

% Nine Nodes: x1, x2, x3, x4, x5, x6, x7, x8, x9

xi(1)=0;xi(2)=1/8;xi(3)=1/4;

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Matlab code Shape Functions 1D Lagrangian - KratosWiki

http://kratos-wiki.cimne.upc.edu/index.php/Matlab_code_Shape_Functions_1D_Lagrangian[27-08-2014 07:30:38 PM]

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xi(4)=3/8;xi(5)=1/2;xi(6)=5/8;xi(7)=3/4;xi(8)=7/8;xi(9)=1;

for num=1:length(xi) Ni(num,:)=shfunc(x,num,xi);end

mdibuja(x,Ni,'x','N1, N2, N3, N4, N5, N6, N7, N8, N9','Nine Node Shape Funtions'); hold on;plot(xi,xi*0,'o');

% Shape Functions for Lagrange polynomial% Ni(x)=num/den% num=(x-x1)*(x-x2)...(x-x{i-1})*(x-x{i+1})...(x-xn)% den=(xi-x1)*(xi-x2)...(xi-x{i-1})*(xi-x{i+1})...(xi-xn)

function ni=shfunc(x,i,xi)

num=1;den=1;

for j=1:length(xi) if(i~=j) num=num.*(x-xi(j)); den=den.*(xi(i)-xi(j)); endend

ni=num./den;

% plot including labels, grid and ajusting axis...function mdibuja(x,y,labx,laby,tit)

plot(x,y);miny=min(1.1*min(min(y)),0.9*min(min(y)));maxy=max(1.1*max(max(y)),0.9*max(max(y)));axis([min(x) max(x) floor(miny) ceil(maxy)]);grid;xlabel(labx);ylabel(laby);title(tit);

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