7 5 cn 1 14 d1 d2 2 1 6 1 p6 dn 1 h 6 6 4

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Unformatted text preview: been shown for clarity. With all matrices and vectors having the same dimension, the summation is ; N X j =1 where 2 2 6 ;1 6 p6 K= h6 6 6 6 4 AS = dT Kc j ;1 2 ;1 (1.3.16a) ;1 2 ;1 ... ... ... ;1 2 ;1 ;1 2 3 7 7 7 7 7 7 7 5 (1.3.16b) c = c1 c2 cN 1 ]T (1.3.16c) d = d1 d2 dN 1]T : (1.3.16d) ; ; The matrix K is called the global sti ness matrix. It is symmetric, positive de nite, and tridiagonal. In the form that we have developed the results, the summation over elements is regarded as an assembly process where the element sti ness matrices are added into their proper places in the global sti ness matrix. It is not necessary to actually extend the dimensions of the element matrices to those of the global sti ness matrix. As indicated in Figure 1.3.3, the elemental indices determine the proper location to add a local matrix into the global matrix. Thus, the 2 2 element sti ness matrix Kj is added to rows 1.3. A Simple Finite Element Problem p AS = d1 h 1] c1 1 |{z} p AS = d1 d2] h 2 | 15 c1 {z 1 } c2 p AS = d2 d3] h 3 | 1 ;1 2 2 6 ;1 6 6 6 p6 K= h6 6 6 6 6 4 ;1 ;1 2 ;1 ;1 1 c2 {z 1...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.

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