Fundamentals of Finite Element Analysis phần 9 ppsx

... diagonal matrix. Hutton: Fundamentals of Finite Element Analysis 10. Structural Dynamics Text © The McGraw−Hill Companies, 2004 10.5 Beam Elements 4 09 As in the case of the bar element, transverse ... very often in structural analysis. It can be shown, by comparison to a damped single degree -of- freedom system that ␣ + ␤␻ 2 i = 2␻ i ␨ i (10.152) Hutton: Fundamentals of...

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... Basic Concepts of the Finite Element Method Text © The McGraw−Hill Companies, 2004 1.5 Examples of Finite Element Analysis 15 0.00 197 Љ Z X 0.25Љ 0.488Љ Figure 1 .9 Finite element model of a thin-walled heat ... the domain. (c) Additional elements showing a partial finite element mesh of the domain. Hutton: Fundamentals of Finite Element Analysis 1. Basic C...

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... Stress Analysis. 2d ed. New York: McGraw-Hill, 199 8. 2. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications, 194 4. Hutton: Fundamentals of Finite Element ... which form the finite element approximation to the solution of the differential equation(s) gov- erning the response of a structural system. Hutton: Fundamentals of Fini...

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... Matrix 1234567 1 19, 627.2 2 .94 4 ×10 6 − 19, 627.2 2 .94 4 ×10 6 000 2 2 .94 4 ×10 6 5.888 ×10 8 −2 .94 4 ×10 6 2 .94 4 ×10 8 000 3 − 19, 627.2 −2 .94 4 ×10 6 66,350.4 0 − 19, 627.2 2 .94 4 ×10 6 −27, 096 4 2 .94 4 ×10 6 2 .94 4 ... 11.78 ×10 8 −2 .94 4 ×10 6 2 .94 4 ×10 8 0 50 0 − 19, 627.2 −2 .94 4 ×10 6 19, 627.2 −2 .94 4 ×10 6 0 6 0 0 2 .94 4 ×10 6 2 .94 4 ×10 8 −2 .94 4 ×10 6 5.8 89...

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... y 3 ) Figure 6 .9 Three-node triangle having an element coordinate system attached to the element. Hutton: Fundamentals of Finite Element Analysis 6. Interpolation Functions for General Element Formulation Text © ... – °F. Formulate a four -element finite element model of this problem and solve for the nodal temperatures and Hutton: Fundamentals of Finite Element...

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... )dr (6 .98 ) Hutton: Fundamentals of Finite Element Analysis 6. Interpolation Functions for General Element Formulation Text © The McGraw−Hill Companies, 2004 6.8 Isoparametric Formulation 199 Writing ... 6 .98 and 6 .99 , we find I = 1  −1 1  −1 f (r, s)dr ds = m  j=1 n  i=1 W j W i f (r i , s j ) (6.106) Hutton: Fundamentals of Finite Element Analysis 6. Interpo...

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... 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 Hutton: Fundamentals of Finite Element Analysis 7. ... z 1 ) 3 (r 3 , z 3 ) Figure 7. 19 Cross section of a three-node axisymmetric element. Recall that the element is a body of revolution. Hutton: Fundamentals of...

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... 51.535 49. 121 23 40.55 39. 36 57.836 55. 499 24 18 .98 18.28 68.142 65.425 45 67.88 65. 89 41.706 40. 799 46 103.87 100.74 42.3 59 41.018 This solution is actually for a cylinder in a uniform stream of ... assumed. In the context of finite element analysis, can the flow problem and the heat transfer problem be solved independently? U Q Hutton: Fundamentals of Finite Element...

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... 264.42 154.44 1731.5 Element 99 21 89. 0 2 49. 14 480.57 2236.4 p(x,y) xy z Figure 9. 12 Example of a thin plate subjected to bending. Hutton: Fundamentals of Finite Element Analysis 9. Applications in ... 2004 9. 7 Strain and Stress Computation 371 Table 9. 1 Stress Values (psi) Computed at Node 107 of Example 9. 4 ␴ x ␴ y ␶ xy Element 1 20 49. 3 187.36 118.4 Element...

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... method, 280 key parameter, 285 time step, 2 79, 285 what is it, 2 79 Finite element, 2, 12 Finite element analysis (FEA). See Finite element method (FEM) Finite element formulation axisymmetric heat ... ft 12 ft 9 ft 18 ft 18 ft 18 ft 18 ft 9 ft12 ft 700 lb 400 lb 3 1 25 8 4 6 7 600 lb 3 m 9 m 3 m 3 m 4 m 4 m 4 m 5 kN 9 kN 9 kN 5 kN 12 4 5 7 9 36810 Hutton: Fun...

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