mostibra

20 Reputation

3 Badges

4 years, 135 days

MaplePrimes Activity


These are replies submitted by mostibra

i changed and still doesnt work@tomleslie 

@tomleslie  that was of a great help since the first answer you provide you directed me to the right way

@tomleslie  but i still have a problem with the results themselves they are so big and going bigger each time i hit enter
 

M := .4556;

.4556

(1)

K := 18;

18

(2)

c := .2865;

.2865

(3)

Nabla(t) := .1``

.1

(4)

``

N := 10``

10

(5)

``

``

a__1 := 4/.1^2*.4556+2/(.1)*.2865``

187.9700000

(6)

``

``

a__2 := 4/(.1)*.4556+.2865``

18.51050000

(7)

``

``

a__3 := .4556``

.4556

(8)

``

````

fu := Array(0 .. 10):

p:=Array(0..10):
  p[0]:=0:
  for i from 0 to 9 do
      p[i+1]:=(u__doubledot[i+1]*(1))+(u__dot[i+1]*(3))+(u[i+1]*(2)):
      phat[i+1]:= p[i+1]+((6)*u[i])+((7)*u__dot[i])+((8)*u__doubledot[i]):
      u[i+1]:= phat[i+1]/(2):
      u__dot[i+1]:=(u[i+1]/(2))-u[i]:
      u__doubledot[i+1]:= (4*(u[i+1]-u[i])/(4)^2)-(4*u__dot[i+1]/(4))-(u__doubledot[i]):
  end do;

0.4364546378e16

 

0.4364546378e16

 

0.2424747988e15

 

0.1347082216e14

 

0.9645108663e17

 

0.1329220357e19

 

0.1418990812e19

 

0.7883282289e17

 

0.4137126473e16

 

0.3117420309e20

 

0.2157868181e21

 

0.2448845710e21

 

0.1360469839e20

 

0.6769837543e18

 

0.5352092674e22

 

0.2479742758e23

 

0.2980564747e23

 

0.1655869304e22

 

0.7838804072e20

 

0.6484182279e24

 

0.2261291556e25

 

0.2869415656e25

 

0.1594119809e24

 

0.7200351857e22

 

0.6216601234e26

 

0.1739975511e27

 

0.2324183385e27

 

0.1291212992e26

 

0.5579285702e24

 

0.5016604021e28

 

0.1173498768e29

 

0.1645797307e29

 

0.9143318372e27

 

0.3788408326e26

 

0.3540359156e30

 

0.7117400112e30

 

0.1045606983e31

 

0.5808927683e29

 

0.2312850209e28

 

0.2242342807e32

 

0.3953955326e32

 

0.6071752047e32

 

0.3373195582e31

 

0.1293104778e30

 

0.1298446675e34

 

0.2039677073e34

 

0.3267702553e34

 

0.1815390307e33

 

0.6712306128e31

 

0.6969939512e35

(9)

 

``


 

Download hw_4_structural.mw



phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL



Download case5analytic.mw

phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL


Download case5analytic.mw

phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL


Download case5analytic.mw

phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL


Download case5analytic.mw

phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL


Download case5analytic.mw

phi := -(1/2)*x^2+2*cos((3.14*(1/20))*x)*(c__1*cosh((3.14*(1/20))*y)+c__2*sinh((3.14*(1/20))*y)+c__3*y*cosh((3.14*(1/20))*y)+c__4*y*sinh((3.14*(1/20))*y));

-(1/2)*x^2+2*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(1)

diff(phi, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(2)

NULL

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y))

(3)

-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0);

-1-0.4929800000e-1*cos(.1570000000*x)*(`#msub(mi("c"),mi("1"))`*cosh(.1570000000*y)+`#msub(mi("c"),mi("2"))`*sinh(.1570000000*y)+`#msub(mi("c"),mi("3"))`*y*cosh(.1570000000*y)+`#msub(mi("c"),mi("4"))`*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0)

(4)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = .75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`+.1180222905*`#msub(mi("c"),mi("2"))`+.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(5)

eval(-1-0.4929800000e-1*cos(.1570000000*x)*(c__1*cosh(.1570000000*y)+c__2*sinh(.1570000000*y)+c__3*y*cosh(.1570000000*y)+c__4*y*sinh(.1570000000*y)) = piecewise(abs(x) < 5, -1, 0), y = -.75);

-1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*`#msub(mi("c"),mi("1"))`-.1180222905*`#msub(mi("c"),mi("2"))`-.7552054088*`#msub(mi("c"),mi("3"))`+0.8851671788e-1*`#msub(mi("c"),mi("4"))`) = piecewise(abs(x) < 5, -1, 0)

(6)

``

diff(-phi, x, y);

.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y))

(7)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = -.75);

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4)

(8)

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0

(9)

eval(.3140000000*sin(.1570000000*x)*(.1570000000*c__1*sinh(.1570000000*y)+.1570000000*c__2*cosh(.1570000000*y)+c__3*cosh(.1570000000*y)+.1570000000*c__3*y*sinh(.1570000000*y)+c__4*sinh(.1570000000*y)+.1570000000*c__4*y*cosh(.1570000000*y)), y = .75);

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4)

(10)

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0;

.3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0

(11)

s := solve({.3140000000*sin(.1570000000*x)*(-0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3-.2365895397*c__4) = 0, .3140000000*sin(.1570000000*x)*(0.1852949961e-1*c__1+.1580896656*c__2+1.020837670*c__3+.2365895397*c__4) = 0, -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1-.1180222905*c__2-.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0), -1-0.4929800000e-1*cos(.1570000000*x)*(1.006940545*c__1+.1180222905*c__2+.7552054088*c__3+0.8851671788e-1*c__4) = piecewise(abs(x) < 5, -1, 0)}, {c__1, c__2, c__3, c__4});

{`#msub(mi("c"),mi("1"))` = -(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x), `#msub(mi("c"),mi("2"))` = 0., `#msub(mi("c"),mi("3"))` = 0., `#msub(mi("c"),mi("4"))` = (1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))/cos(.1570000000*x)}

(12)

phi1 := subs({c__1 = -20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x), c__2 = 0., c__3 = 0., c__4 = 1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.)/cos(.1570000000*x)}, phi);

-(1/2)*x^2+2*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(13)

syy1 := diff(phi1, x, x);

-1-0.4929800000e-1*cos(.1570000000*x)*(-(20.28463654*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+(1.588676174*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))-.6280000000*sin(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-(3.184687937*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+(.2494221593*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2)+2*cos(.1570000000*x)*(-20.28463654*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)/cos(.1570000000*x)-6.369375874*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*cosh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2-(.9999920122*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3-(.4999960061*(piecewise(abs(x) < 5., -1., 0.)+1.))*cosh(.1570000000*y)/cos(.1570000000*x)+1.588676174*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)/cos(.1570000000*x)+.4988443186*piecewise(x = -5., Float(undefined), x = 5., Float(undefined), 0.)*y*sinh(.1570000000*y)*sin(.1570000000*x)/cos(.1570000000*x)^2+(0.7831855802e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)*sin(.1570000000*x)^2/cos(.1570000000*x)^3+(0.3915927901e-1*(piecewise(abs(x) < 5., -1., 0.)+1.))*y*sinh(.1570000000*y)/cos(.1570000000*x))

(14)

``NULL


Download case5analytic.mw

@Carl Love 

@Ronan thank u very much



phi := sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh(Pi/(4*y))+c__4*y*sinh((1/4)*Pi*y));

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(1)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(2)

diff((2), y);

sin((1/4)*Pi*x)*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(3)

diff((3), y);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c*`2`*sinh((1/4)*pi*y)*pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

(4)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(5)

diff((5), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(6)

diff((6), x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(7)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(8)

diff((8), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(9)

diff((9), y);

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*pi*y)*pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(10)

``

(11)

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y));

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(12)

eval( (12), [x = 0]);

0

(13)

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y));

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c*`2`*sinh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(14)

eval( (14), [x = 20]);

0

(15)

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c*`2`*sinh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2) = 0;

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c*`2`*sinh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2) = 0

(16)

eval( (16), [y = 9]);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((9/4)*Pi)*Pi^2+(1/16)*c*`2`*sinh((9/4)*Pi)*Pi^2+(1/11664)*c__3*cosh((1/36)*Pi)*Pi^2+(1/2)*c__4*cosh((9/4)*Pi)*Pi+(9/16)*c__4*sinh((9/4)*Pi)*Pi^2) = 0

(17)

evalf[5]( (17) );

sin(.78540*x)*(362.25*c__1+362.25*c*`2`+0.84938e-3*c__3+4182.6*c__4) = 0.

(18)

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c*`2`*sinh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2) = -sin((1/4)*pi*x);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c*`2`*sinh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2) = -sin((1/4)*pi*x)

(19)

eval( (19), [y = -9]);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((9/4)*Pi)*Pi^2-(1/16)*c*`2`*sinh((9/4)*Pi)*Pi^2-(1/11664)*c__3*cosh((1/36)*Pi)*Pi^2+(1/2)*c__4*cosh((9/4)*Pi)*Pi+(9/16)*c__4*sinh((9/4)*Pi)*Pi^2) = -sin((1/4)*pi*x)

(20)

evalf[5]( (20) );

sin(.78540*x)*(362.25*c__1-362.25*c*`2`-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*pi*x)

(21)

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(22)

eval( (22), [y = 9]);

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((9/4)*Pi)*Pi+(1/4)*c*`2`*cosh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi+c__4*sinh((9/4)*Pi)+(9/4)*c__4*cosh((9/4)*Pi)*Pi) = 0

(23)

evalf[5]( (23) );

.78540*cos(.78540*x)*(461.22*c__1+461.22*c*`2`+.99617*c__3+4738.2*c__4) = 0.

(24)

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+(1/4)*c*`2`*cosh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(25)

eval( (25), [y = -9]);

(1/4)*cos((1/4)*Pi*x)*Pi*(-(1/4)*c__1*sinh((9/4)*Pi)*Pi+(1/4)*c*`2`*cosh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi-c__4*sinh((9/4)*Pi)-(9/4)*c__4*cosh((9/4)*Pi)*Pi) = 0

(26)

evalf[5]( (26) );

.78540*cos(.78540*x)*(-461.22*c__1+461.22*c*`2`+.99617*c__3-4738.2*c__4) = 0.

(27)

s:=solve({(sin.78540*x)*(362.25*c__1-362.25*c*`2`-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*Pi*x),.78540*cos(.78540*x)*(461.22*c__1+461.22*c*`2`+.99617*c__3+4738.2*c__4) = 0,.78540*cos(.78540*x)*(-461.22*c__1+461.22*c*`2`+.99617*c__3-4738.2*c__4) = 0,sin(.78540*x)*(362.25*c__1+362.25*c*`2`+0.84938e-3*c__3+4182.6*c__4 = 0},{c1,c2,c3,c4,x});

Error, `}` unexpected

 

NULL



Download analytical_case_1.mw

@Ronan 

Thank you very much

phi := sin(alpha*X)*(c1*cosh(alpha*Y)+c2*sinh(alpha*Y)+c3*Y*cosh(alpha*Y)+c4*Y*sinh(alpha*Y));
sin(alpha X) (c1 cosh(alpha Y) + c2 sinh(alpha Y)

+ c3 Y cosh(alpha Y) + c4 Y sinh(alpha Y))
alpha := (1/4)*pi;
1
- pi
4
`&sigma;X` := diff(phi, Y, Y);
/1 \ /1 /1 \ 2 1 /1 \ 2
sin|- pi X| |-- c1 cosh|- pi Y| pi + -- c2 sinh|- pi Y| pi
\4 / \16 \4 / 16 \4 /

1 /1 \ 1 /1 \ 2
+ - c3 sinh|- pi Y| pi + -- c3 Y cosh|- pi Y| pi
2 \4 / 16 \4 /

1 /1 \ 1 /1 \ 2\
+ - c4 cosh|- pi Y| pi + -- c4 Y sinh|- pi Y| pi |
2 \4 / 16 \4 / /
sigmaY := diff(phi, X, X);
1 /1 \ 2 / /1 \ /1 \
- -- sin|- pi X| pi |c1 cosh|- pi Y| + c2 sinh|- pi Y|
16 \4 / \ \4 / \4 /

/1 \ /1 \\
+ c3 Y cosh|- pi Y| + c4 Y sinh|- pi Y||
\4 / \4 //
sigmaXY := -(diff(phi, X, Y));
1 /1 \ /1 /1 \ 1 /1 \
- - cos|- pi X| pi |- c1 sinh|- pi Y| pi + - c2 cosh|- pi Y| pi
4 \4 / \4 \4 / 4 \4 /

/1 \ 1 /1 \ /1 \
+ c3 cosh|- pi Y| + - c3 Y sinh|- pi Y| pi + c4 sinh|- pi Y|
\4 / 4 \4 / \4 /

1 /1 \ \
+ - c4 Y cosh|- pi Y| pi|
4 \4 / /
B.Cs1(x = 0, `&sigma;x` = 0, x = 20, `&sigma;x` = 0);
B . (Cs1(x = 0, &sigma;x = 0, x = 20, &sigma;x = 0))
B.Cs2(y = 9, sigmaXY = 0, sigmaY = 0);
/ / 1 /1 \ /1 /1 \
B . |Cs2|y = 9, - - cos|- pi X| pi |- c1 sinh|- pi Y| pi
\ \ 4 \4 / \4 \4 /

1 /1 \ /1 \
+ - c2 cosh|- pi Y| pi + c3 cosh|- pi Y|
4 \4 / \4 /

1 /1 \ /1 \
+ - c3 Y sinh|- pi Y| pi + c4 sinh|- pi Y|
4 \4 / \4 /

1 /1 \ \ 1 /1 \ 2 / /1
+ - c4 Y cosh|- pi Y| pi| = 0, - -- sin|- pi X| pi |c1 cosh|- pi Y
4 \4 / / 16 \4 / \ \4

\ /1 \ /1 \ /1 \\
| + c2 sinh|- pi Y| + c3 Y cosh|- pi Y| + c4 Y sinh|- pi Y|| = 0
/ \4 / \4 / \4 //

\\
||
//
B.cs3(y = -9, `&sigma;XY` = 0, y = -9, sigmaY = sin((1/4)*pi*x));
/ / 1 /1 \ 2 /
B . |cs3|y = -9, &sigma;XY = 0, y = -9, - -- sin|- pi X| pi |c1
\ \ 16 \4 / \

/1 \ /1 \ /1 \
cosh|- pi Y| + c2 sinh|- pi Y| + c3 Y cosh|- pi Y|
\4 / \4 / \4 /

/1 \\ /1 \\\
+ c4 Y sinh|- pi Y|| = sin|- pi x|||
\4 // \4 ///
solve := phi, B.cs1, Bcs2, Bcs3;
Error, attempting to assign to `solve` which is protected. Try declaring `local solve`; see ?protect for details.

 

i will follow that

Thanks @Kitonum 

What if I want to plot it in 2d

Thank you very much.

Zero otherwise. 

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