MIT2_092F09_lec23

MIT2_092F09_lec23 - 2.092/2.093 Finite Element Analysis of...

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Unformatted text preview: 2.092/2.093 Finite Element Analysis of Solids & Fluids I Fall 09 Lecture 23- Solution of K = M Prof. K. J. Bathe MIT OpenCourseWare Reading assignment: Chapters 10, 11 We have the solutions < 1 2 . . . n . Recall that: 1 2 n K i = i M i (1) In summary, a necessary and sucient condition for i is that Eq. (1) is satisfied. The orthogonality conditions are not sucient, unless q = n . In other words, vectors exist which are K- and M-orthogonal, but are not eigenvectors of the problem. = 1 . . . n (2) 1 zeros T M = I ; T K = = . . . (3) zeros n Assume we have an n q matrix P which gives us P T MP = I ; P T KP = A diagonal matrix q q q q Is a ii necessarily equal to i ? a 11 zeros a 22 . zeros . . If q = n , then A = , P = with some need for rearranging. If q < n , then P may contain eigenvectors (but not necessarily), and A may contain...
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.092 taught by Professor Klaus-jürgenbathe during the Fall '09 term at MIT.

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MIT2_092F09_lec23 - 2.092/2.093 Finite Element Analysis of...

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