As indicated in figure 133 the elemental indices

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Unformatted text preview: } c3 1 ;1 ;1 3 7 7 7 7 7 7 7 7 7 7 5 Figure 1.3.3: Assembly of the rst three element sti ness matrices into the global sti ness matrix. j ; 1 and j and columns j ; 1 and j . Some modi cations are needed for the rst and last elements to account for the boundary conditions. The summations of AM and (V f )j proceed in the same manner and, using (1.3.13) j and (1.3.15), we obtain N X j =0 AM = dT Mc j (1.3.17a) N X where j =0 (V f )j = dT l 2 4 61 6 M = qh 6 6 66 4 2 6 l= h6 4 66 1 41 ... ... ... 141 14 f0 + 4f1 + f2 f1 + 4f2 + f3 ... fN 2 + 4fN 1 + fN ; ; (1.3.17b) 3 7 7 7 7 7 5 3 7 7: 7 5 (1.3.17c) (1.3.17d) 16 Introduction The matrix M and the vector l are called the global mass matrix and global load vector, respectively. Substituting (1.3.16a) and (1.3.17a,b) into (1.3.9a,b) gives dT (K + M)c ; l] = 0: (1.3.18) As noted in Section 1.2, the requirement that (1.3.9a) hold for all V to satisfying (1.3.18) for all choices of d. This is only possible when N 2 S0 (K + M)c = l: is equivalent...
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