Finite Element Analysis - Thermomechanics of Solids Part 9 pptx

... ) () () rzt t t u r u r w z u z w r a a a ua wa = ()                 =               ∂ ∂ ∂ ∂ ∂ ∂ + ∂ ∂ 1 2 1 1 1 1 1 ββ ΦΦ ΦΦ γγ γγ T 0 0 07 49_ Frame_C 09 Page 130 Wednesday, February 19, 2003 5: 09 PM © 2003 by CRC CRC Press LLC 138 Finite Element Analysis: Thermomechanics of Solids 7. The stress-strain relations in two-dimensional ... ν () () ˆ D...

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... () U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 ′ = ′ AB T GCG 07 49_ Frame_C02 Page 40 Wednesday, February 19, 2003 5:00 PM © 2003 by CRC CRC Press LLC 36 Finite Element Analysis: Thermomechanics of Solids As proof, (2. 59) Now, the eigenvalues of A ⊗ ... AA AI 3 1 2 23 −+−=III0, 07 49_ Frame_C02 Page 29 Wednesday, February 19, 2003 5:00 PM © 2003 by C...

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... . δδ ((.))dS dS ∫∫ =       07 49_ Frmae_C03 Page 43 Wednesday, February 19, 2003 5:01 PM © 2003 by CRC CRC Press LLC 44 Finite Element Analysis: Thermomechanics of Solids 2. δ ( f ) ... 0 EA du dx 2 2 0= . E,A L P 07 49_ Frmae_C03 Page 44 Wednesday, February 19, 2003 5:01 PM © 2003 by CRC CRC Press LLC 48 Finite Element Analysis: Thermomechanics of...

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... , 11 2 11 2 2 2 θθ θ θ θθθ θ E L = − −                 θ θ θ θ 2 2 2 2 0 0 000 . 07 49_ Frame_C04 Page 64 Wednesday, February 19, 2003 5:33 PM © 2003 by CRC CRC Press LLC 60 Finite Element Analysis: Thermomechanics of Solids and (4.37) The divergence of v is given ... φ θθθ φφφ φθ φ 11 11 11 cos cos cos cos 07 49_ Frame_C04 Page 59 Wednesday, February 19, 2003 5...

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... ij L kk L ij =+2 µλδ () () . 07 49_ Frame_C06 Page 95 Wednesday, February 19, 2003 5:06 PM © 2003 by CRC CRC Press LLC 98 Finite Element Analysis: Thermomechanics of Solids Now, (6.17) From Chapter ... kk L = 3Κ () . z v x E 07 49_ Frame_C06 Page 106 Wednesday, February 19, 2003 5:06 PM © 2003 by CRC CRC Press LLC 96 Finite Element Analysis: Thermomechanics of...

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... −ES 07 49_ Frame_C07 Page 1 09 Wednesday, February 19, 2003 5:07 PM © 2003 by CRC CRC Press LLC 114 Finite Element Analysis: Thermomechanics of Solids in which B T is the thermal analog of the ... −+= ∫∫∫∫ TT ττ 07 49_ Frame_C07 Page 114 Wednesday, February 19, 2003 5:07 PM © 2003 by CRC CRC Press LLC 116 Finite Element Analysis: Thermomechanics of Solids Note th...

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... 07 49_ Frame_C08 Page 117 Wednesday, February 19, 2003 5:08 PM © 2003 by CRC CRC Press LLC 120 Finite Element Analysis: Thermomechanics of Solids There are two classes of errors in finite -element ... hardware and soft- ware, especially computer-aided design (CAD) systems. Today, a number of highly developed, user-friendly finite -element codes are available commercially....

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... 07 49_ Frame_C10 Page 1 39 Wednesday, February 19, 2003 6:04 PM © 2003 by CRC CRC Press LLC 142 Finite Element Analysis: Thermomechanics of Solids Multiplying by the variation of T ... = γγ ρ 3 E,A,L,ρ P m k 07 49_ Frame_C10 Page 140 Wednesday, February 19, 2003 6:04 PM © 2003 by CRC CRC Press LLC 150 Finite Element Analysis: Thermomechanics of Solids...

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... ,KM+= λ j 2 0 07 49_ Frame_C11 Page 1 59 Wednesday, February 19, 2003 5:13 PM © 2003 by CRC CRC Press LLC 162 Finite Element Analysis: Thermomechanics of Solids Since the jk th entries of X T MX and ... ++ ++L 07 49_ Frame_C11 Page 158 Wednesday, February 19, 2003 5:13 PM © 2003 by CRC CRC Press LLC 154 Finite Element Analysis: Thermomechanics of Solids Startin...

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... tn mm m m t t ××××γγΣΣθθ11 07 49_ Frame_C13 Page 175 Wednesday, February 19, 2003 5: 19 PM © 2003 by CRC CRC Press LLC 180 Finite Element Analysis: Thermomechanics of Solids 13.5 EXERCISES 1. Find ... Y AALY uL vY p f/ // / − −                       =           () () uL L () 07 49_ Frame_C13 Page 180 Wednesday, February 19, 2003 5: 19 PM © 2003...

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