b=1/4;

u[x_,y_]=(Cos[Pi (2 x+y)/Sqrt[3]]/4+(1-4 Cos[Pi b/Sqrt[3]]) Sin[Pi (2x+y)/Sqrt[3]]/(16 Sin[Pi b/Sqrt[3]])) Cos[Pi x];

Plot3D[u[x,y],{x,-1/2,1/2},{y,0,b},ViewPoint->{1.3, 1.4, 2.},BoxRatios->Automatic]

ub[x_,y_,bval_]=(Cos[Pi (2 x+y)/Sqrt[3]]/4+(1-4 Cos[Pi bval/Sqrt[3]]) Sin[Pi (2x+y)/Sqrt[3]]/(16 Sin[Pi bval/Sqrt[3]])) Cos[Pi x];

Animate[Plot3D[ub[x,y,bval],{x,-1/2,1/2},{y,0,bval},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,1},{-1,1}},BoxRatios->Automatic],{bval,0.1,1}]

Plot3D[ub[x,y,1.5],{x,-1/2,1/2},{y,0,1.5},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,1.5},{-0.5,0.8}},BoxRatios->Automatic]

Plot3D[ub[x,y,0.25],{x,-1/2,1/2},{y,0,0.25},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,0.25},{-0.3,0.4}},BoxRatios->Automatic]

Plot3D[ub[x,y,0.7],{x,-1/2,1/2},{y,0,0.7},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,0.7},{-0.3,0.4}},BoxRatios->Automatic]

u[x_,y_,a_,b_]=(Cos[Pi (2 x+y)/(a Sqrt[3])]/4+(1-4 Cos[Pi b/(a Sqrt[3])]) Sin[Pi (2x+y)/(a Sqrt[3])]/(16 Sin[Pi b/(a Sqrt[3])])) Cos[Pi x/a];

Plot3D[u[x,y,1,0.7],{x,-1/2,1/2},{y,0,0.7},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,0.7},{-0.3,0.4}},BoxRatios->Automatic]

Plot3D[u[x,y,1/2,0.7/2],{x,-1/2,1/2},{y,0,0.7},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,0.7},{-0.3,0.4}},BoxRatios->Automatic]

Plot3D[u[x,y,2,0.7/2],{x,-1/2,1/2},{y,0,0.7},ViewPoint->{1.3, 1.4, 2.},PlotRange->{{-1/2,1/2},{0,0.7},{-0.5,0.5}},BoxRatios->Automatic]