TY - CHAP

T1 - Random Imperfection (II)

AU - Ikeda, Kiyohiro

AU - Murota, Kazuo

PY - 2010/1/1

Y1 - 2010/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=85068135425&partnerID=8YFLogxK

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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 -