WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

TOPOLOGY OPTIMIZATION WITH PADÉ APPROXIMANTS 1629
˜Q T j
= N
Q j,N+1−ku
k=1
∗ k
Equation (A16) is inserted into Equation (A10)
Bu ′ = Bu ′ 0 −
N
ũ ju
j=1
+ j
+ N
˜biI + u +
i=1
u ′ N+1
N+1−i uN+1
j=1
N
ũ j ˜Q T
j
u ′ i −
N
Q j,N+1−iũj
j=1
in which it has been used that ˜b0 = B.
Equation (A19) can now be used to identify the components of the matrices Di and Ei
and
for i = 1, N.
h T ū ′ i
(A18)
(A19)
D0 = I, E0 = 0 (A20)
DN+1 =− 1
B
N
ũ ju + j , EN+1 = 0 (A21)
j=1
Di = 1
˜biI + u
B
+
N+1−i uN+1
j=1
Ei =− 1
N
Q j,N+1−iũj
B j=1
N
ũ j ˜Q T
j
h T
ACKNOWLEDGEMENTS
(A22)
(A23)
The author wishes to thank Professors M. P. Bendsøe, Department of Mathematics and P. C. Madsen,
Department of Informatics and Mathematical Modelling at the Technical University of Denmark for helpful
suggestions and discussions.
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Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 72:1605–1630
DOI: 10.1002/nme