In[]:=
ClearAll​​Clear[x]​​Clear[p,p1,p2,p3,p4]​​Clear[initialAngles,solutions,θValue,θsol,list]​​Clear[Plot1,Plot2,Plot3,Plot4,combinedPlot]​​Clear[i,j]​​Clear[w,h,A,L,R,ν,a1,a2,a3]​​Clear[θ,U]
Out[]=
ClearAll
In[]:=
w=4.7;​​h=3.4;​​A=25;​​ν=0.45;​​L=36*Pi;​​R=36;​​(*Steifigkeiten*)​​a1=4*A*π*w*
3
h
​​a2=4*A*π*
3
w
*h​​a3=
2*A*h*w*(
2
h
+
2
w
)
1+ν
Out[]=
58034.3
Out[]=
110898.
Out[]=
18542.3
In[]:=
θ[x_]:=q1+q2*x+q3*x^2​​U[θ_]:=Integrate[(1/2)*(a1/R^2*Cos[θ]^2+a2/R^2*Sin[θ]^2+a3/L^2*(θ')^2),{x,0,1}]​​θ'[x]​​U[θ[x]]​​​​result=NMinimize[{U[θ[x]],θ[0]==0,θ'[0]==0},{q3}]
Out[]=
q2+2q3x
Out[]=
1
∫
0
1
2
44.7795
2
Cos[q1+q2x+q3
2
x
]
+85.5692
2
Sin[q1+q2x+q3
2
x
]
+1.44964
2

′
(q1+q2x+q3
2
x
)

x
NMinimize
:The following constraints are not valid: {q10,q20}. Constraints should be equalities, inequalities, or domain specifications involving the variables.
Out[]=
NMinimize
1
∫
0
1
2
44.7795
2
Cos[q1+q2x+q3
2
x
]
+85.5692
2
Sin[q1+q2x+q3
2
x
]
+1.44964
2

′
(q1+q2x+q3
2
x
)

x,q10,q20,{q3}
​