Progetto Serbatoio

Definizione dati

Es=200000000;(*[(kN/(m^2))]*)
h=0.00487;(*[m]*)
R=2;(*[m]*)
ν=0.3;(*[-]*)
l1=15;(*[m]*)
γ=9.3157*1.3;(*[(kN/(m^3))]*)

Ds=(((Es (h^3)))/(12 (1-(ν^2))))(*[kNm]*)
 β=(((((Es*h)/(4 Ds (R^2)))))^(1/4))(*[(1/m)]*)
λ=2Pi/ β(*[m]*)
Lc=1/ β(*[m]*)
tipotubo= (l1/λ) (* se l>>λ tubo lungo, altrimenti tubo corto *)
rigidezzamolle= ((Es h)/(R^2)) (* se l>>λ tubo lungo, altrimenti tubo corto *)

Definizione Equazioni

Pin[x_]=γ(l1-x);

v1[x_]=Exp[-x β](C[1] Cos[β x]+C[2] Sin[β x])+Exp[x β](C[3] Cos[β x]+C[4] Sin[β x])+((Pin[x])/(Es h))×(R^2)

Equazioni delle restanti grandezze

φ1[x_]=v1'[x];
M1[x_]=Ds v1''[x];
T1[x_]=-Ds v1'''[x];
N1[x_]=((Es h)/R)v1[x];

Condizioni al Contorno

cc1=v1[0]==0;
cc2=φ1[0]==0;
cc3=M1[l1]==0;
cc4=v1[l1]==0;

SOL=NSolve[{cc1,cc2,cc3,cc4},{C[1],C[2],C[3],C[4]},WorkingPrecision->10]

v1[x_]=v1[x]/.SOL[[1]];
φ1[x_]=v1'[x];
M1[x_]=Ds  v1''[x];
T1[x_]=-Ds  v1'''[x];
N1[x_]=((Es h)/R)v1[x];

Grafici

s1=Plot[v1[x],{x,0,l1},PlotRange->All,Filling->Axis]

r1=Plot[φ1[x],{x,0,l1},PlotRange->All,Filling->Axis]

t1=Plot[T1[x],{x,0,l1},PlotRange->All,Filling->Axis]

T1[x_]=-Ds  v1'''[0]

m1=Plot[M1[x],{x,0,l1},PlotRange->All,Filling->Axis]

M1[x_]=Ds  v1''[0]

n1=Plot[N1[x],{x,0,l1},PlotRange->All,Filling->Axis]

N1[x_]=((Es h)/R)v1[0.823]

φ1[x_]=v1'[0.823]