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# Untitled

a guest Dec 4th, 2011 25 Never
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1. ClearAll["Global`*"]
2. Er = 150*10^9;
3. Em = 75*10^9;
4. vr = 0.3;
5. vm = 0.25;
6. am = (0.25)*ar;
7.
8. wr1111 = (Er/((1 + vr) (1 - 2 vr)))*(1 - vr +
9.      e11 (1 - (2 vr^2)/(1 - vr)));
10. wr3333 = (Er (1 - vr))/((1 + vr) (1 - 2 vr));
11. wr1313 = wr3113 = Er/(2 (1 + vr));
12. wr1133 = (Er*vr)/((1 + vr) (1 - 2 vr));
13. wr1331 = (Er/(2 (1 + vr)))*(1 + 2 e11 (1 + vr)/(1 - vr));
14. wm1111 = (Em/((1 + vm) (1 - 2 vm)))*(1 - vm +
15.      e11 (1 - (2 vm^2)/(1 - vm)));
16. wm3333 = (Em (1 - vm))/((1 + vm) (1 - 2 vm));
17. wm1313 = wm3113 = Em/(2 (1 + vm));
18. wm1133 = (Em*vm)/((1 + vm) (1 - 2 vm));
19. wm1331 = (Em/(2 (1 + vm)))*(1 + 2 e11 (1 + vm)/(1 - vm));
20.
21. xim2 = Sqrt[cm + Sqrt[cm^2 - (wm3333*wm3113)/(wm1111*wm1331)]];
22. xir2 = Sqrt[cr + Sqrt[cr^2 - (wr3333*wr3113)/(wr1111*wr1331)]];
23. xim3 = Sqrt[cm - Sqrt[cm^2 - (wm3333*wm3113)/(wm1111*wm1331)]];
24. xir3 = Sqrt[cr - Sqrt[cr^2 - (wr3333*wr3113)/(wr1111*wr1331)]];
25. cm = (wm1111*wm3333 + wm1331*wm3113 - (wm1133 + wm1313)^2)/(
26.   2 (wm1111*wm1331));
27. cr = (wr1111*wr3333 + wr1331*wr3113 - (wr1133 + wr1313)^2)/(
28.   2 (wr1111*wr1331));
29.
30. b11 = ((wr1111*wr1313) + (xir2^-2*wr3113*wr1133)) Cosh[ar*xir2^-1];
31. b31 = (wr1133 + wr1313) xir2^-1 Sinh[ar*xir2^-2];
32. b12 = ((wr1111*wr1313) + (xir3^-2*wr3113*wr1133)) Cosh[ar*xir3^-1];
33. b32 = (wr1133 + wr1313) xir3^-1 Sinh[ar*xir3^-2];
34. b13 = -((wm1111*wm1313) + (xim2^-2*wm3113*wm1133)) Cosh[am*xim2^-1];
35. b33 = (wm1133 + wm1313) xim2^-1 Sinh[am*xim2^-2];
36. b14 = -((wm1111*wm1313) + (xim3^-2*wm3113*wm1133)) Cosh[am*xim3^-1];
37. b34 = (wm1133 + wm1313) xim3^-1 Sinh[am*xim3^-2];
38. b21 = ((wr1133*wr1133) + (wr1133*wr1313) - (wr1111*wr3333) + (xir2^-2*
39.        wr3113*wr3333)) xir2^-1 Sinh[ar*xir2^-1];
40. b22 = ((wr1133*wr1133) + (wr1133*wr1313) - (wr1111*wr3333) + (xir3^-2*
41.        wr3113*wr3333)) xir3^-1 Sinh[ar*xir3^-1];
42. b23 = ((wm1133*wm1133) + (wm1133*wm1313) - (wm1111*wm3333) + (xim2^-2*
43.        wm3113*wm3333)) xim2^-1 Sinh[am*xim2^-1];
44. b24 = ((wm1133*wm1133) + (wm1133*wm1313) - (wm1111*wm3333) + (xim3^-2*
45.        wm3113*wm3333)) xim3^-1 Sinh[am*xim3^-1];
46. b41 = (-wr1111 + xir2^-2 wr3113) Cosh[ar*xir2^-1];
47. b42 = (-wr1111 + xir3^-2 wr3113) Cosh[ar*xir3^-1];
48. b43 = (wm1111 - xim2^-2 wm3113) Cosh[am*xim2^-1];
49. b44 = (wm1111 - xim3^-2 wm3113) Cosh[am*xim3^-1];
50. bqs = {{b11, b12, b13, b14}, {b21, b22, b23, b24}, {b31, b32, b33,
51.     b34}, {b41, b42, b43, b44}} // MatrixForm
52.
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