-

Intro_Solid_Mechanics_Adeeb/10.1.3.1.py

@@ -4,14 +4,14 @@
 s = Matrix([[x1*x2,5,0],[5,x1,0],[0,0,0]])
 x = Matrix([[x1,x2,x3]])
 pb1,pb2,pb3 =[-sum([diff(s[i,j],x[i]) for i in range(3)]) for j in range(3)]
-display("\u03C1b_1 =",pb1)
-display("\u03C1b_2 =",pb2)
-display("\u03C1b_3 =",pb3)
+print("\u03C1b_1 =",pb1)
+print("\u03C1b_2 =",pb2)
+print("\u03C1b_3 =",pb3)
 a,b,t = sp.symbols("a b t")
 ustar = Matrix([a*x1 + b*x2, 0])
-display("u* =",ustar)
+print("u* =",ustar)
 gradustar = Matrix([[diff(i,j) for j in x[:2]]for i in ustar])
-display("\u2207u* =",gradustar)
+print("\u2207u* =",gradustar)
 ustara = ustar.subs({x1:2})
 ustarb = ustar.subs({x2:1})
 ustarc = ustar.subs({x1:0})
@@ -25,22 +25,22 @@
 tb = (s*nb).subs({x2:1})
 tc = (s*nc).subs({x1:0})
 td = (s*nd).subs({x2:0})
-display("t_A =",ta,"t_B =",tb,"t_C =",tc,"t_D =",td)
+print("t_A =",ta,"t_B =",tb,"t_C =",tc,"t_D =",td)
 estar = sp.Rational("1/2")*(gradustar+gradustar.T)
-display("\u03B5* =",estar)
+print("\u03B5* =",estar)
 ststrain = sum([s[i]*estar[i] for i in range(4)])
-display("ststrain =",ststrain)
+print("ststrain =",ststrain)
 IVW = integrate(ststrain,(x1,0,2),(x2,0,1),(x3,0,t))
-display("Internal Virtual Work =",IVW)
+print("Internal Virtual Work =",IVW)
 EVWBodyForces = integrate(pb1*ustar[0],(x1,0,2),(x2,0,1),(x3,0,t))
-display("External Virtual Work|_{Body Forces} =",EVWBodyForces)
+print("External Virtual Work|_{Body Forces} =",EVWBodyForces)
 EVWa = integrate((ta.dot(ustara)).subs({x1:2}),(x2,0,1),(x3,0,t))
-display("External Virtual Work|_A =",EVWa)
+print("External Virtual Work|_A =",EVWa)
 EVWb = integrate((tb.dot(ustarb)).subs({x2:1}),(x1,0,2),(x3,0,t))
-display("External Virtual Work|_B =",EVWb)
+print("External Virtual Work|_B =",EVWb)
 EVWc = integrate((tc.dot(ustarc)).subs({x1:0}),(x2,0,1),(x3,0,t))
-display("External Virtual Work|_C =",EVWc)
+print("External Virtual Work|_C =",EVWc)
 EVWd = integrate((td.dot(ustard)).subs({x2:0}),(x1,0,2),(x3,0,t))
-display("External Virtual Work|_D =",EVWd)
+print("External Virtual Work|_D =",EVWd)
 EVW = simplify(EVWBodyForces+EVWa+EVWb+EVWc+EVWd)
-display("External Virtual Work = Internal Virtual Work =",EVW)
+print("External Virtual Work = Internal Virtual Work =",EVW)

Intro_Solid_Mechanics_Adeeb/10.1.3.2.py

@@ -10,29 +10,29 @@
 q = -5*x
 s = dsolve(EI*y(x).diff(x,4)-q,y(x),ics={y1:0,y2:0,yp1:0,yp2:0})
 y = s.rhs
-display("y(x) =",y)
+print("y(x) =",y)
 th = simplify(diff(y,x))
 M = simplify(EI*diff(y,x,x))
 V = simplify(EI*diff(y,x,x,x))
-display("th =",th,"M =",M,"V =",V)
+print("th =",th,"M =",M,"V =",V)
 M1 = M.subs({x:0})
 M2 = M.subs({x:L})
 V1 = V.subs({x:0})
 V2 = V.subs({x:L})
-display("M@x=0",M1,"M@x=L",M2,"V@x=0",V1,"V@x=L",V2)
+print("M@x=0",M1,"M@x=L",M2,"V@x=0",V1,"V@x=L",V2)
 ystar = a*x**2
 thstar = diff(ystar,x)
 ystar1 = ystar.subs({x:0})
 ystar2 = ystar.subs({x:L})
 thstar1 = thstar.subs({x:0})
 thstar2 = thstar.subs({x:L})
-display("y*@x=0",ystar1,"y*@x=L",ystar2,"\u03B8*@x=0",thstar1,"\u03B8*@x=L",thstar2)
+print("y*@x=0",ystar1,"y*@x=L",ystar2,"\u03B8*@x=0",thstar1,"\u03B8*@x=L",thstar2)
 IVW = integrate(M*diff(ystar,x,x),(x,0,L))
-display("Internal Virtual Work =",IVW)
+print("Internal Virtual Work =",IVW)
 EVWq = integrate(q*ystar,(x,0,L))
-display("EVWq =",EVWq)
+print("EVWq =",EVWq)
 EVW1 = V1*ystar1-M1*thstar1
 EVW2 = M2*thstar2-V2*ystar2
-display("EVW1 =",EVW1,"EVW2 =",EVW2)
+print("EVW1 =",EVW1,"EVW2 =",EVW2)
 EVW = EVWq+EVW1+EVW2
-display("External Virtual Work = Internal Virtual Work =",EVW)
+print("External Virtual Work = Internal Virtual Work =",EVW)

Intro_Solid_Mechanics_Adeeb/10.2.3.py

@@ -5,19 +5,19 @@
 s = solve(Equil,th)
 s=[(i.expand(complex=True)).evalf() for i in s]
 degs = [(i/sp.pi*180).evalf() for i in s]
-display("Equilibrium =",Equil)
-display("there are 4 real roots of  the above expression")
-display(s)
-display("\u03B8_1 =",degs[1])
-display("\u03B8_2 =",degs[2])
-display("\u03B8_3 =",degs[3])
-display("\u03B8_4 =",degs[0]+360)
+print("Equilibrium =",Equil)
+print("there are 4 real roots of  the above expression")
+print(s)
+print("\u03B8_1 =",degs[1])
+print("\u03B8_2 =",degs[2])
+print("\u03B8_3 =",degs[3])
+print("\u03B8_4 =",degs[0]+360)
 PE = 750/2*(2*sin(th))**2-140*th-900*sin(th)
 DPE = diff(PE,th)
 D2PE = diff(DPE,th)
-display("Potential Energy =",PE)
-display("Derivative of PE",DPE,"Second Derivative of Pe",D2PE)
-display("D2PE@\u03B8=\u03B8_1 =",D2PE.subs({th:s[1]}))
-display("D2PE@\u03B8=\u03B8_2 =",D2PE.subs({th:s[2]}))
-display("D2PE@\u03B8=\u03B8_3 =",D2PE.subs({th:s[3]}))
-display("D2PE@\u03B8=\u03B8_4 =",D2PE.subs({th:s[0]+2*sp.pi}))
+print("Potential Energy =",PE)
+print("Derivative of PE",DPE,"Second Derivative of Pe",D2PE)
+print("D2PE@\u03B8=\u03B8_1 =",D2PE.subs({th:s[1]}))
+print("D2PE@\u03B8=\u03B8_2 =",D2PE.subs({th:s[2]}))
+print("D2PE@\u03B8=\u03B8_3 =",D2PE.subs({th:s[3]}))
+print("D2PE@\u03B8=\u03B8_4 =",D2PE.subs({th:s[0]+2*sp.pi}))

Intro_Solid_Mechanics_Adeeb/11.1.1.1.b.py

@@ -5,13 +5,13 @@
 u = a2*x**2+a1*x
 uL = u.subs(x,L)
 PE = integrate((1/2)*E*A*(u.diff(x)**2), (x,0,L)) - P*uL - integrate(c*x*u, (x,0,L))
-display("Potential Energy: ", PE)
+print("Potential Energy: ", PE)
 Eq1 = PE.diff(a2)
 Eq2 = PE.diff(a1)
-display("Minimize PE: ", Eq1, Eq2)
+print("Minimize PE: ", Eq1, Eq2)
 s = solve((Eq1, Eq2), (a2, a1))
-display("Solve: ", s)
+print("Solve: ", s)
 u = u.subs({a1:s[a1], a2:s[a2]})
-display("Best second degree Polynomial(Rayleigh Ritz method): ", u)
+print("Best second degree Polynomial(Rayleigh Ritz method): ", u)
 stress = E * u.diff(x)
-display("stress: ", simplify(stress))
+print("stress: ", simplify(stress))

Intro_Solid_Mechanics_Adeeb/11.1.1.1.c.py

@@ -5,14 +5,14 @@
 u = a3*x**3+a2*x**2+a1*x
 uL = u.subs(x,L)
 PE = integrate((1/2)*E*A*(u.diff(x)**2), (x,0,L)) - P*uL - integrate(c*x*u, (x,0,L))
-display("Potential Energy: ", PE)
+print("Potential Energy: ", PE)
 Eq1 = PE.diff(a2)
 Eq2 = PE.diff(a1)
 Eq3 = PE.diff(a3)
-display("Minimize PE: ", Eq1, Eq2, Eq3)
+print("Minimize PE: ", Eq1, Eq2, Eq3)
 s = solve((Eq1, Eq2, Eq3), (a2, a1, a3))
-display("Solve: ", s)
+print("Solve: ", s)
 u = u.subs({a1:s[a1], a2:s[a2], a3:s[a3]})
-display("Best third degree Polynomial(Rayleigh Ritz method): ", u)
+print("Best third degree Polynomial(Rayleigh Ritz method): ", u)
 stress = E * u.diff(x)
-display("stress: ", simplify(stress))
+print("stress: ", simplify(stress))

Intro_Solid_Mechanics_Adeeb/11.1.1.1.d.py

@@ -7,8 +7,8 @@
 u2 = u(x).diff(x).subs(x,L)
 Ax = 25/100*(5/10-25/200*x)
 Ax1 = Ax.subs(x,L)
-display("Area: ", Ax)
+print("Area: ", Ax)
 s = dsolve(E*u(x).diff(x,2)*Ax+E*u(x).diff(x)*Ax.diff(x), u(x), ics = {u1:0, u2:200/E/Ax1})
 u = s.rhs.subs({E:100000, L:2, P:200})
 stress = (E * u.diff(x)).subs({E:100000, L:2, P:200})
-display("displacement and stress: ", u, stress)
+print("displacement and stress: ", u, stress)

Intro_Solid_Mechanics_Adeeb/11.1.1.1.e.py

@@ -6,59 +6,59 @@
 sp.init_printing(use_latex = "mathjax")
 x, a1, a2, a3, E, P = symbols("x a_1 a_2 a_3 E P")
 Ax = 25/100*(5/10-25/200*x)
-display("Exact")
+print("Exact")
 u = Function("u")
 u1_1 = u(x).subs(x,0)
 u2_1 = u(x).diff(x).subs(x,L)
 Ax1 = Ax.subs(x,L)
-display("Area: ", Ax)
+print("Area: ", Ax)
 s = dsolve(E*u(x).diff(x,2)*Ax+E*u(x).diff(x)*Ax.diff(x), u(x), ics = {u1_1:0, u2_1:200/E/Ax1})
 u = s.rhs.subs({E:100000, L:2, P:200})
 stress0 = (E * u.diff(x)).subs({E:100000, L:2, P:200})
-display("displacement and stress: ", u, stress0)
-display("First Degree")
+print("displacement and stress: ", u, stress0)
+print("First Degree")
 u1 = a1*x 
 uL = u1.subs(x,L)
 PE = integrate((1/2)*E*((u1.diff(x))**2)*Ax, (x,0,L)) - P*uL
 PE = PE.subs({E:100000, L:2, P:200})
-display("Potential Energy: ", PE)
+print("Potential Energy: ", PE)
 Eq1 = PE.diff(a1)
-display("Minimize:", Eq1)
+print("Minimize:", Eq1)
 s = solve(Eq1,a1)
-display("Solve: ", s)
+print("Solve: ", s)
 u1 = u1.subs(a1,s[0])
-display("Best First degree Polynomial(Rayleigh Ritz method): ", u1)
+print("Best First degree Polynomial(Rayleigh Ritz method): ", u1)
 stress1 = (E * u1.diff(x)).subs(E,100000)
-display("stress: ", stress1)
-display("Second Degree")
+print("stress: ", stress1)
+print("Second Degree")
 u2 = a1*x+a2*x**2
 PE2 = integrate((1/2)*E*((u2.diff(x))**2)*Ax, (x,0,L)) - P*u2.subs(x,L)
 PE2 = PE2.subs({E:100000, L:2, P:200})
-display("Potential Energy: ", PE2)
+print("Potential Energy: ", PE2)
 Eq1_2 = PE2.diff(a1)
 Eq2_2 = PE2.diff(a2)
 s = solve((Eq1_2, Eq2_2),a1, a2)
-display("Minimize:", Eq1_2, Eq2_2)
-display("Solve: ", s)
+print("Minimize:", Eq1_2, Eq2_2)
+print("Solve: ", s)
 u2 = u2.subs({a1:s[a1], a2:s[a2]})
-display("Best Second degree Polynomial(Rayleigh Ritz method): ", u2)
+print("Best Second degree Polynomial(Rayleigh Ritz method): ", u2)
 stress2 = (E * u2.diff(x)).subs(E,100000)
-display("stress: ", stress2)
-display("Third Degree")
+print("stress: ", stress2)
+print("Third Degree")
 u3 = a1*x+a2*x**2+a3*x**3
 PE3 = integrate((1/2)*E*((u3.diff(x))**2)*Ax, (x,0,L)) - P*u3.subs(x,L)
 PE3 = PE3.subs({E:100000, L:2, P:200})
-display("Potential Energy: ", PE3)
+print("Potential Energy: ", PE3)
 Eq1_3 = PE3.diff(a1)
 Eq2_3 = PE3.diff(a2)
 Eq3_3 = PE3.diff(a3)
 s = solve((Eq1_3, Eq2_3, Eq3_3),a1, a2, a3)
-display("Minimize:", Eq1_3, Eq2_3, Eq3_3)
-display("Solve: ", s)
+print("Minimize:", Eq1_3, Eq2_3, Eq3_3)
+print("Solve: ", s)
 u3 = u3.subs({a1:s[a1], a2:s[a2], a3:s[a3]})
-display("Best Third degree Polynomial(Rayleigh Ritz method): ", u3)
+print("Best Third degree Polynomial(Rayleigh Ritz method): ", u3)
 stress3 = (E * u3.diff(x)).subs(E,100000)
-display("stress: ", stress3)
+print("stress: ", stress3)
 fig, ax = plt.subplots(1,2, figsize = (15,6))
 plt.setp(ax[0], xlabel = "X1 m ", ylabel = "u(m)")
 plt.setp(ax[1], xlabel = "X1 m", ylabel = "Stress(Pa)")
@@ -71,7 +71,7 @@
 stress1_list = [stress1.subs({x:i}) for i in x1]
 stress2_list = [stress2.subs({x:i}) for i in x1]
 stress3_list = [stress3.subs({x:i}) for i in x1]
-display("Comparison")
+print("Comparison")
 ax[0].plot(x1, u_list, 'blue', label = "exact")
 ax[0].plot(x1, u1_list, 'orange', label = "u1")
 ax[0].plot(x1, u2_list, 'green', label = "u2")

Intro_Solid_Mechanics_Adeeb/11.1.1.1.f.py

@@ -6,65 +6,65 @@
 sp.init_printing(use_latex = "mathjax")
 x, a1, a2, a3, a4, E, p, A, L= symbols("x a_1 a_2 a_3 a_4 E p A L")
 p = 5*x**2
-display("Exact")
+print("Exact")
 u = Function("u")
 u1_1 = u(x).subs(x,0)
 u2_1 = u(x).subs(x,L)
 s = dsolve(E*u(x).diff(x,2)+ p/A, u(x), ics = {u1_1:0, u2_1:0})
 u = s.rhs.subs({E:100000, L:2, A:(25/100)**2})
 stress0 = (E * u.diff(x)).subs({E:100000, L:2, A:(25/100)**2})
-display("displacement and stress: ", u, stress0)
-display("Second Degree")
+print("displacement and stress: ", u, stress0)
+print("Second Degree")
 u2 = a1*x+a2*x**2
 sol = solve(u2.subs(x,L), a2)
 u2 = u2.subs(a2,sol[0])
-display("a2:", sol)
-display(u2)
+print("a2:", sol)
+print(u2)
 PE2 = (1/2)*(integrate(E*A*((u2.diff(x))**2), (x,0,L))) - integrate(p*u2, (x,0,L))
 PE2 = PE2.subs({E:100000, L:2, A:(25/100)**2})
-display("Potential Energy: ", PE2)
+print("Potential Energy: ", PE2)
 Eq1_2 = PE2.diff(a1)
 sol1 = solve(Eq1_2,a1)
-display("a1:", sol1)
+print("a1:", sol1)
 u2 = u2.subs(a1,sol1[0]).subs(L,2)
-display("Best Second degree Polynomial(Rayleigh Ritz method): ", u2)
+print("Best Second degree Polynomial(Rayleigh Ritz method): ", u2)
 stress2 = (E * u2.diff(x)).subs(E,100000)
-display("stress: ", stress2)
-display("Third Degree")
+print("stress: ", stress2)
+print("Third Degree")
 u3 = a1*x+a2*x**2+a3*x**3
 sol = solve(u3.subs(x,L), a3)
-display("a3: ", sol)
+print("a3: ", sol)
 u3 = u3.subs(a3,sol[0])
 PE3 = (1/2)*(integrate(E*A*((u3.diff(x))**2), (x,0,L))) - integrate(p*u3, (x,0,L))
 PE3 = PE3.subs({E:100000, L:2, A:(25/100)**2})
-display("Potential Energy: ", PE3)
+print("Potential Energy: ", PE3)
 Eq1_3 = PE3.diff(a1)
 Eq2_3 = PE3.diff(a2)
 sol1 = solve((Eq1_3, Eq2_3),a1, a2)
-display("Minimize:", Eq1_3, Eq2_3)
-display("Solve: ", sol1)
+print("Minimize:", Eq1_3, Eq2_3)
+print("Solve: ", sol1)
 u3 = u3.subs({a1:sol1[a1], a2:sol1[a2], L:2})
-display("Best Third degree Polynomial(Rayleigh Ritz method): ", u3)
+print("Best Third degree Polynomial(Rayleigh Ritz method): ", u3)
 stress3 = (E * u3.diff(x)).subs(E,100000)
-display("stress: ", stress3)
-display("Fourth Degree")
+print("stress: ", stress3)
+print("Fourth Degree")
 u4 = a1*x+a2*x**2+a3*x**3+a4*x**4
 sol = solve(u4.subs(x,L), a4)
-display("a4: ", sol)
+print("a4: ", sol)
 u4 = u4.subs(a4,sol[0])
 PE4 = (1/2)*(integrate(E*A*((u4.diff(x))**2), (x,0,L))) - integrate(p*u4, (x,0,L))
 PE4 = PE4.subs({E:100000, L:2, A:(25/100)**2})
-display("Potential Energy: ", PE4)
+print("Potential Energy: ", PE4)
 Eq1_4 = PE4.diff(a1)
 Eq2_4 = PE4.diff(a2)
 Eq3_4 = PE4.diff(a3)
 sol1 = solve((Eq1_4, Eq2_4, Eq3_4),(a1, a2, a3))
-display("Minimize:", Eq1_4, Eq2_4, Eq3_4)
-display("Solve: ", sol1)
+print("Minimize:", Eq1_4, Eq2_4, Eq3_4)
+print("Solve: ", sol1)
 u4 = u4.subs({a1:sol1[a1], a2:sol1[a2], a3:sol1[a3]}).subs(L,2)
-display("Best Fourth degree Polynomial(Rayleigh Ritz method): ", u3)
+print("Best Fourth degree Polynomial(Rayleigh Ritz method): ", u3)
 stress4 = (E * u4.diff(x)).subs(E,100000)
-display("stress: ", stress4)
+print("stress: ", stress4)
 fig, ax = plt.subplots(1,2, figsize = (15,6))
 plt.setp(ax[0], xlabel = "X1 m ", ylabel = "u(m)")
 plt.setp(ax[1], xlabel = "X1 m", ylabel = "Stress(Pa)")
@@ -77,7 +77,7 @@
 stress2_list = [stress2.subs({x:i}) for i in x1]
 stress3_list = [stress3.subs({x:i}) for i in x1]
 stress4_list = [stress4.subs({x:i}) for i in x1]
-display("Comparison")
+print("Comparison")
 ax[0].plot(x1, u_list, 'blue', label = "exact")
 ax[0].plot(x1, u2_list, 'orange', label = "u2")
 ax[0].plot(x1, u3_list, 'green', label = "u3")

Intro_Solid_Mechanics_Adeeb/11.1.1.1.py

@@ -8,4 +8,4 @@
 a = dsolve(u(x).diff(x,2) + C*x/(E*A), u(x), ics = {u1:0, u2:P/(E*A)})
 u = a.rhs
 sigma = E * u.diff(x)
-display("displacement and stress: ", u, simplify(sigma))
+print("displacement and stress: ", u, simplify(sigma))