Graphical Representation of Shape Functions for a Canonical Quadrilateral Element

Hi! I am a beginner user, I would like to plot a Quadrilateral shape function that I am studing. I know the theoretical functions and the graphical results (show bellow) but I am failing to plot the same graphics.

Just the first plot seems to be correct.

[s,t]=meshgrid(0:0.1:1,0:0.1:1)

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

subplot(2,2,1)

surf(s,t,N1)

[s,t]=meshgrid(0:0.1:1,0:0.1:1)

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

subplot(2,2,2)

surf(s,t,N2(s,t))

[s,t]=meshgrid(0:0.1:1,0:0.1:1)

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

subplot(2,2,3)

surf(s,t,N3(s,t))

[s,t]=meshgrid(0:0.1:1,0:0.1:1)

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

subplot(2,2,4)

surf(s,t,N4(s,t)

Thank you.

Answer 1

[Precise Simulation]

Check/compare with a reference implementation for the quadrilateral Q1 FEM shape function.

1. The local coordinates should go from -1..1 (not 0..1).

2. Switch order for the local coordinates 1+/-s/t (not s/t+/-1).

3. Use the elemetwise product operator ".*" between s/t (s and t are matrices and using "*" will result in matrix multiplication which is not correct).

    [s,t] = meshgrid(-1:0.1:1,0:0.1:1);
    
    N1 = 1/4*(1-t).*(1-s);
    subplot(2,2,1)
    surf(s,t,N1)
     
    N2 = @(s,t)1/4*(1-t).*(1+s);
    subplot(2,2,2)
    surf(s,t,N2(s,t))
    
    N3 = @(s,t)1/4*(1+t).*(1+s);
    subplot(2,2,3)
    surf(s,t,N3(s,t))
     
    N4 = @(s,t)1/4*(1+t).*(1-s);
    subplot(2,2,4)
    surf(s,t,N4(s,t))

[Jose vieira de neto]

Thanks Precise Simulation. It was I needed.