Abstract:
This paper presents a novel optimisation approach for analysing cracked structural systems, consisting of four key steps. The first step (called the Golden Derivative) derives an equation at the discontinuity specific to cracked systems. The cracked system is transformed into an equivalent intact system for analysis in the second step. The third step converts the unique cracked system equation into a finite element equation, revealing epistemic uncertainty that leads to the formulation of Persian curves (PCs). These curves are developed using the following three methods: numerical experimentation, equivalent springs and logical reasoning, with consistent outcomes validating their effectiveness. The uncertainty is linked to the crack effect equation from fracture mechanics in the final step. It is shown by applying mathematical differentiation that this crack effect and classical fracture mechanics inherently involve epistemic uncertainty. A proposed remedy addresses this issue. The derivation of PC is based on pure mathematics and logical reasoning (bridging probabilistic and deterministic methods) making the results applicable across various fields for analysing real-world data.