Mathematical Problems in Engineering / 2015 / Article / Tab 2

Research Article

Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

Table 2

Comparison of ECT and FCT.


Fundamental theories ① Implicit function theorem
② Morse lemma     
③ Thorn splitting lemma 
Research contentThe non-Morse critical point (or singular) of the potential function
Potential functionElementary function (polynomial functions) Functional
State variables
Non-Morse critical points
Control variables
Catastrophic conditions

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