20000e 02 30000e 02 10000e 02 20000e 02 30000e

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Unformatted text preview: 0 (b) (a) The element contributions to 18944 the nodal forces. 6250 (b) The nodal forces. (c) The nodal forces resolved into 10825 components. 10 (c) Chapter 23 Page 32 K. Haghighi Note: p 2i−1 = p19 = −10825 N @ node p 2i = p 20 = −6250 N 10 p 2i−1 = p 23 = −18944 N @ node p 2i = p 24 = −10938 N 12 p 2i−1 = p 35 = −8119 N @ node p 2i = p 36 = −4688 N 18 Chapter 23 Page 33 K. Haghighi Element Stresses: Once elem. disp’s are known, then {σ(e )}= [D]([B]{u(e )}− {εT}) constant w/in linear ∆ elem. (a disadvantage) usually at the centroid. Chapter 23 Page 34 K. Haghighi Example: A thin plate subjected to a distributed load in the middle third of one side. The bottom surface is free to move horizontally relative to the support. 20 20 10000 N / cm2 20 () E = 20 106 N / cm2 µ = 0.25 t = 3.0 cm 30 cm Lubricated surface Chapter 23 Page 35 K. Haghighi Grid: y 150000 N 150000 N 13 14 (15) (13) (14) 9 10 ( 9) (7) ( 8) 5 1 10 ( 2) 2 11 (11) (12) (10) 6 ( 3) (1) (18) (16) ( 4) 3 10 horizontal disp. of nodes 1, 5, 9, 13=0 & vertical disp. of nodes 1, 2, 3, 4=0 16 15 (17 ) 7 ( 5) 10 ( 6) 4 10 12 10 8 10 x Chapter 23 Page 36 K. Haghighi Input Data: Title Parameters Material properties X-coordinates Y-coordinates Element data Known nodal forces Known nodal displacements 16 18 0 20000000. 0.25 3.0 0. 10. 20. 30. 0. 10. 20. 30. 0. 10. 20. 30. 0. 10. 20. 30. 0. 0. 0. 0. 10. 10. 10. 10. 20. 20. 20. 20. 30. 30. 30. 30. 5 1 6 1 6 2 2 1 6 3 7 2 7 4 3 2 7 5 8 3 8 6 4 3 9 7 10 5 10 8 6 5 10 9 11 6 11 10 7 6 11 11 12 7 12 12 8 7 13 13 14 9 14 14 10 9 14 15 15 10 15 16 11 10 15 17 16 11 16 18 12 11 26 − 150000. 28 − 150000. 0 1 0. 2 0. 4 0. 6 0. 8 0. 9 0. 17 0. 25 0. 0 Chapter 23 Page 37 K. Haghighi Output: Elasticity Example Problem NN = 16 NE = 18 Nodal Coordinates Node X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0. 0. 0. 0. .10000E + 02 .20000E + 02 .20000E + 02 .10000E + 02 .20000E + 02 .30000E + 02 .10000E + 02 .20000E + 02 .30000E + 02 .10000E + 02 .20000E + 02 .30000E + 02 Parameter Values EM = .20000E + 08 PR = .25000E + 00 TH = .30000E + 01 Y 0. 0. 0. 0. .10000E + 02 .10000E + 02 .10000E + 02 .10000E + 02 .20000E + 02 .20000E + 02 .20000E...
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This document was uploaded on 01/29/2014.

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