In[]:=
(*Assignment-5*)​​(*PropertiesofLaminate*)​​El=40;Glt=0.5;vlt=0.25;vtl=0.01;D1=(1-(vlt*vtl));​​Q=
(25/D1)
(vlt*(1*(1/D1)))
0
(vlt*(1*(1/D1)))
(1/D1)
0
0
0
(0.5)
;​​T=
2
(Cos[k])
2
(Sin[k])
2Sin[k]Cos[k]
2
(Sin[k])
2
(Cos[k])
-2Sin[k]Cos[k]
-Sin[k]Cos[k]
Sin[k]Cos[k]
2
(Cos[k])
-
2
(Sin[k])
;​​iT=
2
(Cos[k])
2
(Sin[k])
Sin[k]Cos[k]
2
(Sin[k])
2
(Cos[k])
-Sin[k]Cos[k]
-2Sin[k]Cos[k]
2Sin[k]Cos[k]
2
(Cos[k])
-
2
(Sin[k])
;​​(Qi=(Inverse[T].Q.iT)Et);​​(Q0=Qi/.{k->0°});​​(Q90=Qi/.{k->90°});​​Q2=((Q0+Q90)/2);​​(*Case-1(a)*)​​(*AMatrixfor
°
0
Laminate*)​​A=((Q0*((0)-(-h/2)))+(Q0*((h/2)-(-0))));​​(*BMatrixfo
°
0
Laminate*)​​B=((0.5)*((Q0((-
2
(h/2)
))+Q0(
2
(h/2)
))));​​(*DMatrixfor
°
0
Laminate*)​​D1=((1/3)*((Q0*(((0)^3)-(((-h/2)^3)))+(Q0*(((h/2)^3)-((0)^3))))));​​w=WSin
mπx
a
Sin
nπy
a
;​​wxxxx=D[w,{x,4}];​​wxxyy=D[w,{x,2},{y,2}];​​wyyyy=D[w,{y,4}];​​wxx=D[w,{x,2}];​​Nx=
2
π
D1[[1,1]]
2
m1
a
+(2D1[[1,2]]+4D1[[3,3]])
2
1
b
+D1[[2,2]]
2
a
m1
4
1
b
;​​m1=List[1,2,3];​​M=Simplify
Nx
2
b
2
π
D1[[2,2]]
/.{a->cb};​​PlotM,{c,0,10},GridLinesAutomatic,Frame->True,PlotLabelStyle["0° Laminate",FontSize->18],PlotLegendsLineLegend[{"m=1","m=2","m=3"}],FrameLabel"Plate aspect Ratio (a / b)","
N
x
2
b
2
π
D
2,2
"​​
Out[]=
m=1
m=2
m=3