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Nonlinear dynamic analysis of frame structures. (English) Zbl 0626.73056

A geometrically nonlinear dynamic analysis method is presented for frames which may be subjected to finite rotations in three-dimensional space. The proposed method is based on the static geometrically nonlinear analysis method reported by Y. Yoshida, T. Nomura and the first author [Comput. Methods Appl. Mech. Eng. 32, 285-309 (1982; Zbl 0492.73042)], in which the governing incremental equilibrium equation is represented by the coordinates after the deformation themselves rather than conventional displacements. The governing dynamic equilibrium equation for each element is obtained from the static equation by adding the inertia term. In the solution procedure, a modified Steffensen iteration process is introduced and combined with the two-step approximation and iterative correction solution procedure developed for static analysis. A numerical example of a curved cantilever beam under lateral loads indicates the effectiveness of the proposed method in cases with three-dimensional finite rotations. Forced vibration analyses of a two-hinged shallow arch are conducted under centrally concentrated loading with several loading amplitudes.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74B20 Nonlinear elasticity
74H55 Stability of dynamical problems in solid mechanics

Citations:

Zbl 0492.73042
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