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Transient analysis of geometrically linear and non‐linear structures by a combined finite‐element‐Riccati‐transfer substructure method
Author(s) -
Zhu Jinghua,
Xue Huiyu
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360906
Subject(s) - substructure , finite element method , mathematics , transient (computer programming) , riccati equation , matrix (chemical analysis) , transformation (genetics) , transfer matrix method (optics) , transfer matrix , linear system , mathematical analysis , computer science , partial differential equation , physics , structural engineering , materials science , engineering , biochemistry , chemistry , composite material , computer vision , gene , operating system , optics
The combined finite‐element‐Riccati‐transfer substructure method is applied to the transient analysis of the structures under various excitations with small and large displacements, respectively. The advantages include reductions in the order of standard transfer equation systems, in the computational efforts, and in the propagation of round‐off errors produced in recursive multiplications of the transfer matrices. Meanwhile, a methodology for analysing transfer substructures is, in combination with exact dynamic condensation and generalized Riccati transformation, proposed to develop the finite element and transfer matrix (FETM) techniques. The Newmark method and Wilson‐θ method are used for time integrations with respect to linear and non‐linear problems. The modified Newton‐Raphson method is employed for equilibrium iteration in each time step. Numerical examples are presented to demonstrate the high efficiency and accuracy of the proposed method for the transient responses of plates. The results from these examples agree well with those obtained by other methods.