random22552255

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These are questions asked by random22552255

restart; with(LinearAlgebra); with(plots); with(SolveTools); eq1 := m1*m2*x^4+(c1*m2+c2*m1+c2*m2)*x^3+(c1*c2+k1*m2+k2*m1+k2*m2)*x^2+(c1*k2+c2*k1)*x+k1*k2

m1*m2*x^4+(c1*m2+c2*m1+c2*m2)*x^3+(c1*c2+k1*m2+k2*m1+k2*m2)*x^2+(c1*k2+c2*k1)*x+k1*k2

(1)

m1 := 2;
m2 := 4;
c1 := 1;
c2 := 0;
k1 := 3;
k2 := 2;

2

 

4

 

1

 

0

 

3

 

2

(2)

eq1

8*x^4+4*x^3+24*x^2+2*x+6

(3)

``

sol1 := evalf(solve(8*x^4+4*x^3+24*x^2+2*x+6 = 0))

-0.2293604281e-1+.5263956354*I, -.2270639572+1.627879522*I, -.2270639572-1.627879522*I, -0.2293604281e-1-.5263956354*I

(4)

assign(sol1)

Error, invalid left hand side in assignment

 

NULL

``

Download complex_numbers.mw


 

restart

with(LinearAlgebra)

InvT := Matrix([[c^2, s^2, -2*s*c], [s^2, c^2, 2*s*c], [s*c, -s*c, c^2-s^2]])

Matrix(%id = 18446746411704779590)

(1)

T := Matrix([[c^2, s^2, 2*s*c], [s^2, c^2, -2*s*c], [-s*c, s*c, c^2-s^2]])

Matrix(%id = 18446746411704773678)

(2)

c := cos(p)

cos(p)

(3)

s = sin(p)

s = sin(p)

(4)

Q := Matrix([[Q11, Q12, 0], [Q12, Q22, 0], [0, 0, Q66]])

Matrix(%id = 18446746411704759470)

(5)

Q11 := E1/(-v12*v21+1); Q12 := E2/(-v12*v21+1); Q66 := G12

E1/(-v12*v21+1)

 

E2/(-v12*v21+1)

 

G12

(6)

E1 := 0.233e12; E2 := 0.231e11; v21 := 0.2e-1; v12 := .2; G12 := 0.717e10

0.233e12

 

0.231e11

 

0.2e-1

 

.2

 

0.717e10

(7)

R := Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 2]])

Matrix(%id = 18446746411704747062)

(8)

Qbar := Matrix([[Qb11, Qb12, Qb16], [Qb12, Qb22, Qb26], [Qb16, Qb26, Qb66]])

Matrix(%id = 18446746411704742726)

(9)

InvR := MatrixInverse(R)

Matrix(%id = 18446746411704745726)

(10)

eq1 := Qbar = InvT.Q.R.T.InvR

Matrix(%id = 18446746411704742726) = Matrix(%id = 18446746411704732718)

(11)

plot(Qb11, p = 0 .. 9)

Warning, expecting only range variable p in expression Qb11 to be plotted but found name Qb11

 

 

NULL


 

Download plotting_elements_of_matrix.mw


 

restart

sigma := 7.500*10^7+2.005*10^7*sinh(22985.642*z)-2.097*10^7*cosh(22985.642*z)

75000000.00+20050000.00*sinh(22985.642*z)-20970000.00*cosh(22985.642*z)

(1)

sigma_debond := 5.403*10^7

54030000.00

(2)

mid := 0.1653e-3

0.1653e-3

(3)

L := 0.2184e-3

0.2184e-3

(4)

plot(sigma, z = mid .. L)

 

plot(sigma_debond, z = 0 .. mid)

 

``


 

Download join_curves.mw


 

restart; eq2 := ef*epsilon+x1*sinh(y1*L/r1)+x2*cosh(y1*L/r1)-.1*(ef*epsilon+x2) = 0; eq3 := ef*epsilon+x1*sinh(-y1*L/r1)+x2*cosh(-y1*L/r1)-.1*(ef*epsilon+x2) = 0; sol1 := solve({eq2, eq3}, {x1, x2})

.9*ef*epsilon+x1*sinh(y1*L/r1)+x2*cosh(y1*L/r1)-.1*x2 = 0

 

.9*ef*epsilon-x1*sinh(y1*L/r1)+x2*cosh(y1*L/r1)-.1*x2 = 0

 

{x1 = 0., x2 = -9.*ef*epsilon/(10.*cosh(y1*L/r1)-1.)}

(1)

assign(sol1); 1; x1, x2

0., -9.*ef*epsilon/(10.*cosh(y1*L/r1)-1.)

(2)

x1;

0.

(3)

x2;

-9.*ef*epsilon/(10.*cosh(y1*L/r1)-1.)

(4)

eq4 := ef*epsilon+x1*sinh(y1*z/r1)+x2*cosh(y1*z/r1);

ef*epsilon-9.*ef*epsilon*cosh(y1*z/r1)/(10.*cosh(y1*L/r1)-1.)

(5)

avg_eq4 := Typesetting:-delayDotProduct(1/L, int(eq4, z));

1/L.(ef*epsilon*z-9.*ef*epsilon*r1*sinh(y1*z/r1)/((10.*cosh(y1*L/r1)-1.)*y1))

(6)

Ecomp := Typesetting:-delayDotProduct(simplify((eval(subs(z = L, avg_eq4)-subs(z = 0, avg_eq4)))/epsilon), Vf)+(1-Vf)*Em;

(1/L.(ef*epsilon*(10.*L*y1*cosh(y1*L/r1)-L*y1-9.*r1*sinh(y1*L/r1))/((10.*cosh(y1*L/r1)-1.)*y1)))/epsilon.Vf+(1-Vf)*Em

(7)

tau := .5*(diff(eq4, z))*r1;

-4.5*ef*epsilon*sinh(y1*z/r1)*y1/(10.*cosh(y1*L/r1)-1.)

(8)

L := lfact*r1;

lfact*r1

 

0.65e-5

(9)

ef := 0.75e11;

0.75e11

 

0.326e10

 

.3

 

.5

(10)

Theo_Ecomp := Vf*ef+(1-Vf)*Em;

0.39130e11

(11)

y1 := 2*Em/((1+nu)*ef*ln(1/Vf))

0.9647560684e-1

(12)

Ecomp

0.5979989095e17*(1/lfact.(epsilon*(0.6270914445e-5*lfact*cosh(0.9647560685e-1*lfact)-0.6270914445e-6*lfact-0.585e-4*sinh(0.9647560685e-1*lfact))/(10.*cosh(0.9647560685e-1*lfact)-1.)))/epsilon+0.1630e10

(13)

epsilon := 0.1e-2;

0.1e-2

(14)

plot(Ecomp, lfact = 1 .. 500)

 

lfact := 90.81506;

90.81506

(15)

eq4

0.75e8-21149.64968*cosh(14842.40105*z)

(16)

plot(eq4, z = 0 .. L)

 

plot(tau, z = 0 .. L)

 

NULL


 

Download Fuly_bonded_updated.mw

Warning: Solutions may have been lost;  Pleas help, i have uploaded .mw file

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