Authors: D.I. Nazarov

Title of the article: Catastrophe theory: a construction crash bifurcation principle in geomechanics problems and structural analysis minings buildings and structures

Year: 2026, Issue: 1, Pages: 90-103

Branch of knowledge: 2.8.6. Geomechanics, destruction of rocks by explosion, mine aerogasdynamics and mining thermophysics

Index UDK: 622.279.6

DOI: 10.26730/1999-4125-2026-1-90-103

Abstract: Major designing tool for geomechanical engineering in the last time has become specialized FEA computer program such as: Plaxis, Fidesys, Midas, Rocscience, for structural analysis mining buildings and structures - Lira, SCAD-office, SAP2000, ETABS, and for complex problems - ANSYS, Abaqus, Comsol. The accuracy of modeling results is not only actualing scientifics problem, but also a requirement of federal laws in the part of designing very dangerous, technically complex and unique objects. The validity of the results of a FEA program is legally accepted as unreliable and needed verification with another FEM program, and including scientific and technical support by experts of both the design and building processes. Current FEM programs used for designs geomechanical problem and structural analysis mining buildings and structures is based on modern physical and mathematical models of finite element analysis theory, and don’t using the bifurcation model of structures. Analyzing the skill FEM program for solving buckling and geometric nonlinear (large deflection) state shows the impossibility of correctly determining the crash criterion excluding using the bifurcation criterion. The impossibility authentically solves the crash structure for buckling and geometric nonlinear (large deflection) model is shown by examples and is grounded by useless exactly physical definition and corresponding mathematical formulations for these bases definition: static force, static loading, buckling, crash capacity. The bifurcations criterion as a physical process leading to the structures crash, show both in analytical analysis and in the example of real building structures to crash subjected, this criterion (unfortunately don’t uses by either FEM or current design standards) shows the need to take it into structural analysis as crash criterion.

Key words: сatastrophe theory bifurcation critical load buckling finite element method crash mechanics of materials geomechanics structural analysis

Receiving date: 14.08.2025

Approval date: 15.01.2026

Publication date: 19.03.2026

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