Progetto Serbatoio

Definizione dati

Es=200000000;(*[(kN/(m^2))]*)
s1=0.006;(*[m]*)
s2=0.005;(*[m]*)
s3=0.004;(*[m]*)
R=2;(*[m]*)
ν=0.3;(*[-]*)
h1=4;(*[m]*)
h2=5;(*[m]*)
h3=6;(*[m]*)(* parte di serbatoio vuota*)
γs=78.25*1.3;(*[(kN/(m^3))]*)

Calcolo Delle Grandezze Caratteristiche

k1=(((Es s1))/(1-(ν^2)))

k2=(((Es s2))/(1-(ν^2)))

k3=(((Es s3))/(1-(ν^2)))

Definizione Carichi

P1[x_]=γs s1 (h1)+γs s2 (h2)+γs s3 (h3)
P2[x_]=γs s2 (h2)+γs s3 (h3)
P3[x_]=γs s3(h3)

Equazioni di Campo

EQ1=-k1 u1''[x]==P1[x];
EQ2=-k2 u2''[x]==P2[x];
EQ3=-k3 u3''[x]==P3[x];

sol=DSolve[{EQ1,EQ2,EQ3},{u1[x],u2[x],u3[x]},x]

Equazioni delle restanti grandezze

N1[x_]=-k1 u1'[x];
N2[x_]=-k2 u2'[x];
N3[x_]=-k2 u3'[x];

u1[x_]=u1[x]/.sol[[1]];
u2[x_]=u2[x]/.sol[[1]];
u3[x_]=u3[x]/.sol[[1]];

Condizioni al Contorno

cc1=u1[0]==0;
cc2=u1[h1]-u2[h1]==0;
cc3=N1[h1]-N2[h1]==0;
cc4=u2[h1+h2]-u3[h1+h2]==0;
cc5=N2[h1+h2]-N3[h1+h2]==0;
cc6=N3[h1+h2+h3]==-0.313*2*1.3;(*peso lineare della copertura*)

sol1=NSolve[{cc1,cc2,cc3,cc4,cc5,cc6},{C[1],C[2],C[3],C[4],C[5],C[6]},WorkingPrecision->10]

u1[x_]=u1[x]/.sol1[[1]];
u2[x_]=u2[x]/.sol1[[1]];
u3[x_]=u3[x]/.sol1[[1]];

Grafici

(*Spostamento della parete*)

s1=Plot[u1[x],{x,0,h1},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];
s2=Plot[u2[x],{x,h1,h2+h1},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];
s3=Plot[u3[x],{x,h1+h2,h2+h1+h3},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];

Show[s1,s2,s3,PlotRange->All]

(*Sforzo normale di meridiano*)

n1=Plot[N1[x],{x,0,h1},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];
n2=Plot[N2[x],{x,h1,h2+h1},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];
n3=Plot[N3[x],{x,h1+h2,h1+h2+h3},PlotRange->All,Filling->Axis,AxesOrigin->{0,0}];

Show[n1,n2,n3]

N3[x_]=-k2 u3'[h1+h2+h3]

N3[x_]=-k3 u3'[h1+h2]

N1[x_]=-k1 u1'[h1]

N1[x_]=-k1 u1'[0]