Engine Deep Dive • `fea_engine.py`

Deterministic FEA Stress Analysis Engine

Calculates Von Mises stress, bending moments ($M = \frac{F \cdot L}{4}$), and safety factors against material yield limits automatically.

Mathematical Methodology

ZylForge FEA Stress Engine evaluates beam loading using the classical Euler-Bernoulli flexural formula:

$$\sigma_{bending} = \frac{M}{Z} = \frac{F \cdot L \cdot y}{4 \cdot I}$$

Where $F$ is the point load in Newtons, $L$ is beam length in mm, $I$ is moment of inertia ($mm^4$), and $Z$ is section modulus ($mm^3$). The safety factor ($SF$) is certified by comparing maximum Von Mises stress ($\sigma_{max}$) against material yield strength ($\sigma_{yield}$):

$$SF = \frac{\sigma_{yield}}{\sigma_{max}} > 1.0$$
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