Fundamentals of Finite Element Analysis phần 4 pps

... −2.26000 −2.26 4. 52 −2.26 0 0 0 −2.26 6.66 4. 40 0 00 4. 40 8.80 4. 40 000 4. 40 4. 40                  T 1 T 2 T 3 T 4 80            =            40 00 0 0 0 −q 5            ␲(0.06) 2 4 =            11.31 0 0 0 −0.0028q 5            Accounting ... Integrals of the form  V L a 1 L b 2 L c 3 L d 4 dV (6.65)...

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... 3.77(10 4 ) 3771 3 4. 0(10 4 ) 40 00 4 1.33(10 4 ) 1333 5 5.33(10 4 ) 5333 6 −5.67(10 4 ) −5657 7 2.67(10 4 ) 2667 8 4. 00(10 4 ) 40 00 Hutton: Fundamentals of Finite Element Analysis 2. Stiffness ... 3(10 5 )          0. 64 0 −0 .48 −0. 64 0 0 .48 000 000 −0 .48 0 0.36 0 .48 0 −0.36 −0. 64 0 0 .48 0. 64 0 −0 .48 000 000 0 .48 −0 −0.36 −0 .48 0 0.36...

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... −2. 944 ×10 6 66,350 .4 0 −19,627.2 2. 944 ×10 6 −27,096 4 2. 944 ×10 6 2. 944 ×10 8 0 11.78 ×10 8 −2. 944 ×10 6 2. 944 ×10 8 0 50 0 −19,627.2 −2. 944 ×10 6 19,627.2 −2. 944 ×10 6 0 6 0 0 2. 944 ×10 6 2. 944 ... equations as EI z L 3          96 24L −96 24L 00 24L 8L 2 −24L 4L 2 00 −96 −24L 192 0 −96 24L 24L 4L 2 016L 2 −24L 4L 2 00−96 −24L 96 24L 0024L 4L 2 24L 8L 2       ...

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... the effect of external forces, the Hutton: Fundamentals of Finite Element Analysis 10. Structural Dynamics Text © The McGraw−Hill Companies, 20 04 444 CHAPTER 10 Structural Dynamics 4. Ginsberg, ... Fundamentals of Finite Element Analysis 10. Structural Dynamics Text © The McGraw−Hill Companies, 20 04 10 .4 Bar Elements: Consistent Mass Matrix 40 5 or ␻ 2  ␻ 2 −...

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... postprocessing.) Hutton: Fundamentals of Finite Element Analysis 1. Basic Concepts of the Finite Element Method Text © The McGraw−Hill Companies, 20 04 2 CHAPTER 1 Basic Concepts of the Finite Element Method mathematical ... tension. Hutton: Fundamentals of Finite Element Analysis 1. Basic Concepts of the Finite Element Method Text © The McGraw−Hill Co...

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... = 1 4 (1 − r )(1 − s) N 2 (r, s) = 1 4 (1 + r )(1 − s) EXAMPLE 7 .4 1 34 s r 2 Figure 7.9 Element node numbering for Example 7 .4; the length of each edge is 1 in. Hutton: Fundamentals of Finite Element ... correct. 910111213 12 67 8 345 4 3 6 1 2 5 3 4 1 2 Hutton: Fundamentals of Finite Element Analysis 7. Applications in Heat Transfer Text © The McGraw−Hi...

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... become 1. 145 1 ˙ T 2 + 0. 940 8(80) − 0. 940 8 T 2 = q 1 A 1. 145 1 ˙ T 4 − 0. 940 8 T 4 + 0. 940 8(30) =−q 5 A respectively. The three remaining equations are then written as   4. 58 04 1. 145 1 0 1. 145 1 4. 58 04 ... fin. (b) Finite element model. (c) Element 1 edge convection. (d) Element 2 edge convection. (b) 4 1 2 5 4 7 2 1 3 6 9 8 3 (c) 1 1 25 4 (d) 2 4 58 7...

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... 38.735 38 .4 16 123.63 122.17 40 .533 40 .510 20 142 .48 137 .40 44 .903 42 .9 14 21 100.03 99.37 47 .109 45 .215 22 67.10 64. 67 51.535 49 .121 23 40 .55 39.36 57.836 55 .49 9 24 18.98 18.28 68. 142 65 .42 5 45 67.88 ... solution; 40 elements. (b) Streamlines ( ␺ = constant) for finite element solution of Example 8.1. (b) 6 7 2 5 4 3 1 24 23 22 27 42 46 35 41 51 48...

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... Example 9 .4 ␴ x ␴ y ␶ xy ␴ e Element 1 2553.5 209.71 179.87 247 5.8 Element 2 1922.7 351.69 43 .55 17 74. 8 Element 12 1827.5 2 64. 42 1 54. 44 1731.5 Element 99 2189.0 249 . 14 480.57 2236 .4 p(x,y) xy z Figure ... Node 107 of Example 9 .4 ␴ x ␴ y ␶ xy Element 1 2 049 .3 187.36 118 .4 Element 2 2 149 .4 315.59 91.89 Element 12 1987.3 322.72 2 04. 13 Element 99 1853...

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... 42 6 matrix, 42 8 over/underdamped, 42 6, 42 7 physical forms, 42 4 ratio, 42 6 Rayleigh, 43 0, 43 2 software packages, 43 2 structural, 42 8 Damping matrix, 42 8 Damping ratio, 42 6 Dashpot, 42 5 Deflected beam element, ... 389 Coefficient matrix, 45 2 Cofactor matrix, 45 2 Cofactors, 45 1 Column matrix, 44 7 Column vector, 44 7 Commutative, 44 9 Compatibility, 165 Compatib...

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