mws_civ_sle_txt_ludecomp_examples

mws_civ_sle_txt_ludecomp_examples - 04.07.1 Chapter 04.07...

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Unformatted text preview: 04.07.1 Chapter 04.07 LU Decomposition – More Examples Civil Engineering Example 1 To find the maximum stresses in a compound cylinder, the following four simultaneous linear equations need to solved.               × − =                           × − × − − × × − × − × × − × 007 . 10 887 . 7 10 6057 . 3 10 2857 . 4 15384 . 5 . 6 15384 . 5 . 6 10 4619 . 5 10 2857 . 4 10 4619 . 5 10 2857 . 4 10 2307 . 9 10 2857 . 4 3 4 3 2 1 5 7 5 7 5 7 5 7 c c c c In the compound cylinder, the inner cylinder has an internal radius of " 5 = a , and an outer radius " 5 . 6 = c , while the outer cylinder has an internal radius of " 5 . 6 = c and an outer radius of " 8 = b . Given 6 10 30 × = E psi, 3 . = ν , and that the hoop stress in the outer cylinder is given by ( )             − + + − = 2 4 3 2 1 1 1 r c c E ν ν ν σ θ , find the stress on the inside radius of the outer cylinder. Find the values of 1 c , 2 c , 3 c and 4 c using LU decomposition. Solution [ ] [ ][ ]                         = = 44 34 33 24 23 22 14 13 12 11 43 42 41 32 31 21 1 1 1 1 u u u u u u u u u u U L A       The [ ] U matrix is the same as the one found at the end of the forward elimination steps of the naïve Gauss elimination method. Forward Elimination of Unknowns Since there are four equations, there will be three steps of forward elimination of unknowns.               × − × − − × × − × − × × − × 5 7 5 7 5 7 5 7 10 6057 . 3 10 2857 . 4 15384 . 5 . 6 15384 . 5 . 6 10 4619 . 5 10 2857 . 4 10 4619 . 5 10 2857 . 4 10 2307 . 9 10 2857 . 4 04.07.2 Chapter 04.07 First step Divide Row 1 by 7 10 2857 . 4 × and multiply it by 7 10 2857 . 4 × , that is, multiply Row 1 by 1 10 2857 . 4 10 2857 . 4 7 7 = × × . Then subtract the result from Row 2....
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_civ_sle_txt_ludecomp_examples - 04.07.1 Chapter 04.07...

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