Tesina di Teoria delle Strutture

Definizione dati

P1=-2;
P2=-45;
Ei1=83498;
Ei2=186867;
Et=210000000;
At=0.1;
R1=12;
R2=87;
a=7.5;
Km1=0;
Km2=0;

(*KN,KN m^2,m,KN,m^2*)

Angoli e lunghezza dei tiranti

θ1=ArcCos[a/R1]
θ2=ArcCos[a/(2 R1)]

θ3=ArcCos[a/R2]
θ4=ArcCos[a/(2 R2)]

c1c2=R2 Sin[θ3]-R1 Sin[θ1]

h0=c1c2-(R2-R1)
h1=c1c2-(R2 Sin[θ4]-R1 Sin[θ2])
h2=c1c2-(R2 Sin[θ4]-R1 Sin[θ2])

ARCO1=R1 (Pi-2θ1);
N[%]
ARCO2=R2 (Pi-2θ3);
N[%]

PENDENZA=100*Tan[ArcCos[a/(ARCO2/2)]];
N[%]

Definizione della rigidezza dei tiranti

K0=Et*At/h0
K1=Et*At/h1
K2=Et*At/h2

(*KN/m*)

Equazioni sulle molle

f0=K0*(v2[Pi/2 R1]-v6[Pi/2 R2]);
N[%]
f1=K1*(v1[θ2 R1]*Sin[θ2]-v5[θ4 R2]*Sin[θ4]+u1[θ2 R1]*Cos[θ2]-u5[θ4 R2]*Cos[θ4]);
N[%]
f2=K2*(v3[(Pi-θ2) R1]*Sin[θ2]-v7[(Pi-θ4) R2]*Sin[θ4]-u3[(Pi-θ2) R1]*Cos[θ2]+u7[(Pi-θ4) R2]*Cos[θ4]);
N[%]
fm1=Km1*(v4[(Pi-θ1) R1]*Cos[θ1]+u4[(Pi-θ1) R1]*Sin[θ1]);
N[%]
fm2=Km2*(v8[(Pi-θ3) R2]*Cos[θ3]-u8[(Pi-θ3) R2]*Sin[θ3])
N[%]

Equazioni di campo

EQ1=-Ei1*( R1^2 u1''''''[s]+2 u1''''[s]+u1''[s]/(R1^2))==2P1 Cos[s/R1];
EQ2=-Ei1*( R1^2 u2''''''[s]+2 u2''''[s]+u2''[s]/(R1^2))==2P1 Cos[s/R1];
EQ3=-Ei1 *(R1^2 u3''''''[s]+2 u3''''[s]+u3''[s]/(R1^2))==2P1 Cos[s/R1];
EQ4=-Ei1 *(R1^2 u4''''''[s]+2 u4''''[s]+u4''[s]/(R1^2))==2P1 Cos[s/R1];
EQ5=-Ei2 *(R2^2 u5''''''[s]+2u5''''[s]+u5''[s]/(R2^2))==2P2 Cos[s/R2];
EQ6=-Ei2 *(R2^2 u6''''''[s]+2u6''''[s]+u6''[s]/(R2^2))==2P2 Cos[s/R2];
EQ7=-Ei2*( R2^2 u7''''''[s]+2u7''''[s]+u7''[s]/(R2^2))==2P2 Cos[s/R2];
EQ8=-Ei2 *(R2^2 u8''''''[s]+2u8''''[s]+u8''[s]/(R2^2))==2P2 Cos[s/R2];

sol=DSolve[{EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8},{u1[s],u2[s],u3[s],u4[s],u5[s],u6[s],u7[s],u8[s]},s];

Equazioni delle restanti grandezze

v1[s_]=-R1 u1'[s];
v2[s_]=-R1 u2'[s];
v3[s_]=-R1 u3'[s];
v4[s_]=-R1 u4'[s];
v5[s_]=-R2 u5'[s];
v6[s_]=-R2 u6'[s];
v7[s_]=-R2 u7'[s];
v8[s_]=-R2 u8'[s];

φ1[s_]=-R1 u1''[s]-1/R1 u1[s];
φ2[s_]=-R1 u2''[s]-1/R1 u2[s];
φ3[s_]=-R1 u3''[s]-1/R1 u3[s];
φ4[s_]=-R1 u4''[s]-1/R1 u4[s];
φ5[s_]=-R2 u5''[s]-1/R2 u5[s];
φ6[s_]=-R2 u6''[s]-1/R2 u6[s];
φ7[s_]=-R2 u7''[s]-1/R2 u7[s];
φ8[s_]=-R2 u8''[s]-1/R2 u8[s];

M1[s_]=Ei1 (-R1 u1'''[s]-1/R1 u1'[s]);
M2[s_]=Ei1 (-R1 u2'''[s]-1/R1 u2'[s]);
M3[s_]=Ei1 (-R1 u3'''[s]-1/R1 u3'[s]);
M4[s_]=Ei1 (-R1 u4'''[s]-1/R1 u4'[s]);
M5[s_]=Ei2 (-R2 u5'''[s]-1/R2 u5'[s]);
M6[s_]=Ei2 (-R2 u6'''[s]-1/R2 u6'[s]);
M7[s_]=Ei2 (-R2 u7'''[s]-1/R2 u7'[s]);
M8[s_]=Ei2 (-R2 u8'''[s]-1/R2 u8'[s]);

T1[s_]=Ei1 (+R1 u1''''[s]+1/R1 u1''[s]);
T2[s_]=Ei1 (+R1 u2''''[s]+1/R1 u2''[s]);
T3[s_]=Ei1 (+R1 u3''''[s]+1/R1 u3''[s]);
T4[s_]=Ei1 (+R1 u4''''[s]+1/R1 u4''[s]);
T5[s_]=Ei2 (+R2 u5''''[s]+1/R2 u5''[s]);
T6[s_]=Ei2 (+R2 u6''''[s]+1/R2 u6''[s]);
T7[s_]=Ei2 (+R2 u7''''[s]+1/R2 u7''[s]);
T8[s_]=Ei2 (+R2 u8''''[s]+1/R2 u8''[s]);

N1[s_]=R1 Ei1 (+R1 u1'''''[s]+1/R1 u1'''[s])+P1 R1 Sin[s/R1];
N2[s_]=R1 Ei1 (+R1 u2'''''[s]+1/R1 u2'''[s])+P1 R1 Sin[s/R1];
N3[s_]=R1 Ei1 (+R1 u3'''''[s]+1/R1 u3'''[s])+P1 R1 Sin[s/R1];
N4[s_]=R1 Ei1 (+R1 u4'''''[s]+1/R1 u4'''[s])+P1 R1 Sin[s/R1];
N5[s_]=R2 Ei2 (+R2 u5'''''[s]+1/R2 u5'''[s])+P2 R2 Sin[s/R2];
N6[s_]=R2 Ei2 (+R2 u6'''''[s]+1/R2 u6'''[s])+P2 R2 Sin[s/R2];
N7[s_]=R2 Ei2 (+R2 u7'''''[s]+1/R2 u7'''[s])+P2 R2 Sin[s/R2];
N8[s_]=R2 Ei2 (+R2 u8'''''[s]+1/R2 u8'''[s])+P2 R2 Sin[s/R2];

u1[s_]=u1[s]/.sol[[1]];
u2[s_]=u2[s]/.sol[[1]];
u3[s_]=u3[s]/.sol[[1]];
u4[s_]=u4[s]/.sol[[1]];
u5[s_]=u5[s]/.sol[[1]];
u6[s_]=u6[s]/.sol[[1]];
u7[s_]=u7[s]/.sol[[1]];
u8[s_]=u8[s]/.sol[[1]];

Condizioni al contorno

cc1=u1[θ1 R1]==0;
cc2=v1[θ1 R1]==0;
cc3=φ1[θ1 R1]==0;
cc4=u5[θ3 R2]==0;
cc5=v5[θ3 R2]==0;
cc6=φ5[θ3 R2]==0;

cc7=u1[θ2 R1]-u2[θ2 R1]==0;
cc8=v1[θ2 R1]-v2[θ2 R1]==0;
cc9=φ1[θ2 R1]-φ2[θ2 R1]==0;
cc10=M1[θ2 R1]-M2[θ2 R1]==0;
cc11=N2[θ2 R1]-N1[θ2 R1]-f1*Cos[θ2]==0;
cc12=T2[θ2 R1]-T1[θ2 R1]-f1*Sin[θ2]==0;

cc13=u5[θ4 R2]-u6[θ4 R2]==0;
cc14=v5[θ4 R2]-v6[θ4 R2]==0;
cc15=φ5[θ4 R2]-φ6[θ4 R2]==0;
cc16=M5[θ4 R2]-M6[θ4 R2]==0;
cc17=N6[θ4 R2]-N5[θ4 R2]+f1*Cos[θ4]==0;
cc18=T6[θ4 R2]-T5[θ4 R2]+f1*Sin[θ4]==0;

cc19=u2[Pi/2 R1]-u3[Pi/2 R1]==0;
cc20=v2[Pi/2 R1]-v3[Pi/2 R1]==0;
cc21=φ2[Pi/2 R1]-φ3[Pi/2 R1]==0;
cc22=M2[Pi/2 R1]-M3[Pi/2 R1]==0;
cc23=N2[Pi/2 R1]-N3[Pi/2 R1]==0;
cc24=T3[Pi/2 R1]-T2[Pi/2 R1]-f0==0;

cc25=u6[Pi/2 R2]-u7[Pi/2 R2]==0;
cc26=v6[Pi/2 R2]-v7[Pi/2 R2]==0;
cc27=φ6[Pi/2 R2]-φ7[Pi/2 R2]==0;
cc28=M6[Pi/2 R2]-M7[Pi/2 R2]==0;
cc29=N6[Pi/2 R2]-N7[Pi/2 R2]==0;
cc30=T7[Pi/2 R2]-T6[Pi/2 R2]+f0==0;

cc31=u3[(Pi-θ2) R1]-u4[(Pi-θ2) R1]==0;
cc32=v3[(Pi-θ2) R1]-v4[(Pi-θ2) R1]==0;
cc33=φ3[(Pi-θ2) R1]-φ4[(Pi-θ2) R1]==0;
cc34=M3[(Pi-θ2) R1]-M4[(Pi-θ2) R1]==0;
cc35=N4[(Pi-θ2) R1]-N3[(Pi-θ2) R1]+f2*Cos[θ2]==0;
cc36=T4[(Pi-θ2) R1]-T3[(Pi-θ2) R1]-f2*Sin[θ2]==0;

cc37=u7[(Pi-θ4) R2]-u8[(Pi-θ4) R2]==0;
cc38=v7[(Pi-θ4) R2]-v8[(Pi-θ4) R2]==0;
cc39=φ7[(Pi-θ4) R2]-φ8[(Pi-θ4) R2]==0;
cc40=M7[(Pi-θ4) R2]-M8[(Pi-θ4) R2]==0;
cc41=N8[(Pi-θ4) R2]-N7[(Pi-θ4) R2]-f2*Cos[θ4]==0;
cc42=T8[(Pi-θ4) R2]-T7[(Pi-θ4) R2]+f2*Sin[θ4]==0;

cc43=v4[(Pi-θ1) R1]*Sin[θ1]-u4[(Pi-θ1) R1]*Cos[θ1]==0;
cc44=T4[(Pi-θ1) R1]*Cos[θ1]+N4[(Pi-θ1) R1]*Sin[θ1]-fm1==0;
cc45=φ4[(Pi-θ1) R1]==0;
cc46=T8[(Pi-θ3) R2]*Cos[θ3]+N8[(Pi-θ3) R2]*Sin[θ3]-fm2==0;
cc47=v8[(Pi-θ3) R2]*Sin[θ3]-u8[(Pi-θ3) R2]*Cos[θ3]==0;
cc48=φ8[(Pi-θ3) R2]==0;

sol1=NSolve[{cc1,cc2,cc3,cc4,cc5,cc6,cc7,cc8,cc9,cc10,cc11,cc12,cc13,cc14,cc15,cc16,cc17,cc18,cc19,cc20,cc21,cc22,cc23,cc24,cc25,cc26,cc27,cc28,cc29,cc30,cc31,cc32,cc33,cc34,cc35,cc36,cc37,cc38,cc39,cc40,cc41,cc42,cc43,cc44,cc45,cc46,cc47,cc48},{C[1],C[2],C[3],C[4],C[5],C[6],C[7],C[8],C[9],C[10],C[11],C[12],C[13],C[14],C[15],C[16],C[17],C[18],C[19],C[20],C[21],C[22],C[23],C[24],C[25],C[26],C[27],C[28],C[29],C[30],C[31],C[32],C[33],C[34],C[35],C[36],C[37],C[38],C[39],C[40],C[41],C[42],C[43],C[44],C[45],C[46],C[47],C[48]},WorkingPrecision->110]

u1[s_]=u1[s]/.sol1[[1]];
u2[s_]=u2[s]/.sol1[[1]];
u3[s_]=u3[s]/.sol1[[1]];
u4[s_]=u4[s]/.sol1[[1]];
u5[s_]=u5[s]/.sol1[[1]];
u6[s_]=u6[s]/.sol1[[1]];
u7[s_]=u7[s]/.sol1[[1]];
u8[s_]=u8[s]/.sol1[[1]];

Forze sulle molle

K1*(v1[θ2 R1]*Sin[θ2]-v5[θ4 R2]*Sin[θ4]+u1[θ2 R1]*Cos[θ2]-u5[θ4 R2]*Cos[θ4])
K0*(v2[Pi/2 R1]-v6[Pi/2 R2])
K2*(v3[(Pi-θ2) R1]*Sin[θ2]-v7[(Pi-θ4) R2]*Sin[θ4]-u3[(Pi-θ2) R1]*Cos[θ2]+u7[(Pi-θ4) R2]*Cos[θ4])

Grafici

(*SPOSTAMENTO TANGENZIALE*)

g1=Plot[u1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g2=Plot[u2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g3=Plot[u3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g4=Plot[u4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g5=Plot[u5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g6=Plot[u6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g7=Plot[u7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g8=Plot[u8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange->All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange->All]

(*SPOSTAMENTO NORMALE*)

g1=Plot[v1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g2=Plot[v2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g3=Plot[v3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g4=Plot[v4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g5=Plot[v5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g6=Plot[v6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g7=Plot[v7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g8=Plot[v8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange->All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange->All]

(*ROTAZIONI*)

g1=Plot[φ1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g2=Plot[φ2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g3=Plot[φ3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g4=Plot[φ4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g5=Plot[φ5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g6=Plot[φ6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g7=Plot[φ7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];
g8=Plot[φ8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange->All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange->All]

(*MOMENTO FLETTENTE*)

g1=Plot[-M1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g2=Plot[-M2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g3=Plot[-M3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g4=Plot[-M4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g5=Plot[-M5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g6=Plot[-M6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g7=Plot[-M7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g8=Plot[-M8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange->All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange->All]

(*SFORZO TAGLIANTE*)

g1=Plot[T1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g2=Plot[T2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g3=Plot[T3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g4=Plot[T4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g5=Plot[T5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g6=Plot[T6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g7=Plot[T7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g8=Plot[T8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange-> All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange->All]

(*SFORZO NORMALE*)

g1=Plot[N1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g2=Plot[N2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g3=Plot[N3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g4=Plot[N4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g5=Plot[N5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g6=Plot[N6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g7=Plot[N7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g8=Plot[N8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];

Show[g1,g2,g3,g4,AxesOrigin->{R1 Pi/2,0},PlotRange-> All]
Show[g5,g6,g7,g8,AxesOrigin->{R2 Pi/2,0},PlotRange-> All]

Grafici Parametrici

(*Spostamento qualitativo dell'arco*)

p1=ParametricPlot[{R1 Cos[s/R1],R1 Sin[s/R1]},{s,θ1 R1,(Pi-θ1) R1  },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Blue,Thickness[0.002]}];
p2=ParametricPlot[{R2 Cos[s/R2],R2 Sin[s/R2]-(R2 Sin[θ3]-R1 Sin[θ1]) },{s,θ3 R2,(Pi-θ3) R2 },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Blue,Thickness[0.002]}];

p3=ParametricPlot[{(R1*Cos[s/R1]-20*u1[s]*Sin[s/R1]+20*v1[s]*Cos[s/R1]),(R1*Sin[s/R1]+20*u1[s]*Cos[s/R1]+20*v1[s]*Sin[s/R1])},{s,θ1 R1,θ2 R1  },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p4=ParametricPlot[{(R1*Cos[s/R1]-20*u2[s]*Sin[s/R1]+20*v2[s]*Cos[s/R1]),(R1*Sin[s/R1]+20*u2[s]*Cos[s/R1]+20*v2[s]*Sin[s/R1])},{s,θ2 R1 ,(Pi/2) R1    },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p5=ParametricPlot[{(R1*Cos[s/R1]-20*u3[s]*Sin[s/R1]+20*v3[s]*Cos[s/R1]),(R1*Sin[s/R1]+20*u3[s]*Cos[s/R1]+20*v3[s]*Sin[s/R1])},{s,(Pi/2) R1,(Pi-θ2) R1  },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p6=ParametricPlot[{(R1*Cos[s/R1]-20*u4[s]*Sin[s/R1]+20*v4[s]*Cos[s/R1]),(R1*Sin[s/R1]+20*u4[s]*Cos[s/R1]+20*v4[s]*Sin[s/R1])},{s,(Pi-θ2) R1  ,(Pi-θ1) R1  },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];

p7=ParametricPlot[{(R2*Cos[s/R2]-10*u5[s]*Sin[s/R2]+10*v5[s]*Cos[s/R2]),(R2*Sin[s/R2]+10*u5[s]*Cos[s/R2]+10*v5[s]*Sin[s/R2])-(R2 Sin[θ3]-R1 Sin[θ1])},{s,θ3 R2 ,θ4 R2 },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p8=ParametricPlot[{(R2*Cos[s/R2]-10*u6[s]*Sin[s/R2]+10*v6[s]*Cos[s/R2]),(R2*Sin[s/R2]+10*u6[s]*Cos[s/R2]+10*v6[s]*Sin[s/R2])-(R2 Sin[θ3]-R1 Sin[θ1])},{s,θ4 R2 ,Pi/2 R2 },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p9=ParametricPlot[{(R2*Cos[s/R2]-10*u7[s]*Sin[s/R2]+10*v7[s]*Cos[s/R2]),(R2*Sin[s/R2]+10*u7[s]*Cos[s/R2]+10*v7[s]*Sin[s/R2])-(R2 Sin[θ3]-R1 Sin[θ1])},{s,Pi/2 R2 ,(Pi-θ4) R2 },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
p10=ParametricPlot[{(R2*Cos[s/R2]-10*u8[s]*Sin[s/R2]+10*v8[s]*Cos[s/R2]),(R2*Sin[s/R2]+10*u8[s]*Cos[s/R2]+10*v8[s]*Sin[s/R2])-(R2 Sin[θ3]-R1 Sin[θ1])},{s,(Pi-θ4) R2 ,(Pi-θ3) R2 },AxesOrigin->{0,R1 Sin[θ1]},PlotStyle->{Red,Thickness[0.003]}];
Show[p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,PlotRange->All]

Show[p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,PlotRange->{{-7,-8},{9.3,10}}]

Spostamento relativo degli archi

v4[(Pi-θ1) R1]*Cos[θ1]+u4[(Pi-θ1) R1]*Sin[θ1]
v8[(Pi-θ3) R2]*Cos[θ3]+u8[(Pi-θ3) R2]*Sin[θ3]

v4[(Pi-θ1) R1]*Cos[θ1]+u4[(Pi-θ1) R1]*Sin[θ1]-v8[(Pi-θ3) R2]*Cos[θ3]-u8[(Pi-θ3) R2]*Sin[θ3]

Linea delle pressioni

g1=Plot[M1[s]/N1[s],{s,θ1 R1,θ2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g2=Plot[M2[s]/N2[s],{s,θ2 R1,Pi/2 R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g3=Plot[M3[s]/N3[s],{s,Pi/2 R1,(Pi-θ2) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g4=Plot[M4[s]/N4[s],{s,(Pi-θ2) R1,(Pi-θ1) R1},AxesOrigin->{R1 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g5=Plot[M5[s]/N5[s],{s,θ3 R2, θ4 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g6=Plot[M6[s]/N6[s],{s,θ4 R2, Pi/2 R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g7=Plot[M7[s]/N7[s],{s,Pi/2 R2,(Pi-θ4) R2},AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];
g8=Plot[M8[s]/N8[s],{s,(Pi-θ4) R2,(Pi-θ3) R2 },AxesOrigin->{R2 Pi/2,0},PlotRange-> All,Filling->Axis,FillingStyle->Directive[Opacity[0.5],Red]];

Show[g1,g2,g3,g4,PlotRange->{500,-1000}]
Show[g5,g6,g7,g8,PlotRange->{150000,-100000}]