It should be noted that "Bifurcation-Theory" as applicable to Structural Engineering Systems and/or Computational Mechanics, is the Mathematical-Analysis of changes and variations in the "Qualitative" or "Topological" Surface-Structure. This can include "Integral-Curves" of a family of "Vector-Fields", and the respective "Solutions" of a family of "Differential-Equations". Furthermore, a "Bifurcation" is typically induced, at the time a relatively small, "smooth" change is made to the subject "Parameter-Values" of a system (i.e. referenced herein as the "Bifurcation-Parameters") that results in a sudden "Qualitative" or "Topological" change in its behavior. Generally, this most frequently applies to "Dynamic-type" of systems, but may also be noted in other "interactive-type of systems".
Can we Benefit from using "Bifurcation-Theory", as applicable to Structural Engineering Systems and/or Computational Mechanics, at this point in time? and/or do you feel there will be a broader acceptance of the "Bifurcation-Theory" in the near future for "Structural-type of Systems"?
The ASME Boiler and Pressure Vessel Code (BPVC) Section VIII Division 2 Part 5 allows bifurcation analysis to evaluate pressure vessels protection against structural buckling (structural instability). In paragraph 5.4.1.2 the code defines the design factor (a kind of safety factor) considering the type of analysis: "The design factor to be used in a structural stability assessment is based on the type of buckling analysis performed. The following design factors shall be the minimum values for use with shell components when the buckling loads are determined using a numerical solution (i.e. bifurcation buckling analysis or elastic-plastic collapse analysis)...". In my experience, the bifurcation bucking assessments are preferred by the designers instead of elastic-plastic collapse assessments because of computational costs.
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