TY - CHAP
T1 - Random Imperfection (II)
AU - Ikeda, Kiyohiro
AU - Murota, Kazuo
N1 - Publisher Copyright:
© Springer New York 2010.
PY - 2010
Y1 - 2010
N2 - It was clarified in Chapter 5, for simple critical points, that the probabilistic properties of critical loads can be formulated in an asymptotic sense (when imperfections are small). In this chapter, this formulation is extended to a Dn-equivariant system that potentially has simple and double bifurcation points. For a simple critical point of a Dn-equivariant system, which is either a limit point or a pitchfork bifurcation point (cf., §8.3.1), the relevant results presented in Chapter 5are applicable.
AB - It was clarified in Chapter 5, for simple critical points, that the probabilistic properties of critical loads can be formulated in an asymptotic sense (when imperfections are small). In this chapter, this formulation is extended to a Dn-equivariant system that potentially has simple and double bifurcation points. For a simple critical point of a Dn-equivariant system, which is either a limit point or a pitchfork bifurcation point (cf., §8.3.1), the relevant results presented in Chapter 5are applicable.
KW - Bifurcation Point
KW - Critical Load
KW - Multivariate Normal Distribution
KW - Probability Density Function
KW - Reliability Function
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U2 - 10.1007/978-1-4419-7296-5_10
DO - 10.1007/978-1-4419-7296-5_10
M3 - Chapter
AN - SCOPUS:85068135425
T3 - Applied Mathematical Sciences (Switzerland)
SP - 271
EP - 286
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -