Global instabilities of pyramidal trusses
DOI:
https://doi.org/10.5540/tcam.2026.027.e01852Keywords:
multiple bifurcation, snap-through, pyramidal trussesAbstract
This paper presents an exact analytical study of global instabilities in pyramidal trusses under large displacements. Using the stationarity of total potential energy and Green-Lagrange strain, non-linear equilibrium equations are derived for a 3-bar isostatic truss. The tangent stiffness matrix yields 6 critical points: 2 limit points and 2 double bifurcation points. Multiple bifurcation is shown to occur universally for α > 45◦, independent of bar count m ≥ 3 and alignment. Closed-form expressions for primary and secondary paths, validated via eigenvalue analysis, establish a generalized buckling threshold with direct implications for lightweight lattice design.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 W. T. M. Silva, G.F. Barrozo, A.A.A. Portela
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
