Mathematical design and graphical solution of the multiple bifurcation equations of a 4-DoF benchmark model. (September 2021)

• Record Type: Journal Article
• Authors: Tanaka, Masato; Ikeda, Kiyohiro; Hsiao, Kuo Mo; Fujii, Fumio
• Is Part Of: Thin-walled structures. Volume 166(2021)
• Publication Date: 2021-09
• Subjects: 00-01 -- 99-00; Benchmark model -- Multiple bifurcation -- Rank deficiency two -- Block-diagonalized Jacobian matrix -- Bifurcation equations -- Graphical solution; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2021.108010
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: A 4 degree-of-freedom (DoF) benchmark model of multiple bifurcation (MB) in compound stability problems of nonlinear structures is proposed. In the MB model, the governing equations are designed to be highly simplified when two critical modes exist in the singular Jacobian matrix. The resulting MB equations can be solved analytically through manual calculation. To verify the applicability, graphical solution methods are applied to solve the MB equations and visualize the multiple path branching through a graphical monitor. The proposed benchmark model and graphical strategies can help understand the stability phenomenology and MB in the stability design of large-scale finite element models. Highlights: A 4 degree-of-freedom benchmark model of multiple bifurcation is proposed. The model is suitable for compound stability problems involving nonlinear structures. The model is useful for understanding stability phenomenology. The model facilitates stability design of large-scale finite-element models.