The demo is the verification of the Principle of Minimum Potential Energy , which serves as the foundational variational principle for the Finite Element Method (FEA). The script explicitly solves the stiffness matrix equation ( $K d = F$ ) to find the equilibrium displacement ( $d$ ), and then mathematically confirms that this specific displacement corresponds exactly to the global minimum of the Total Potential Energy functional ( $\Pi=U-W$ ). This demonstrates that solving the static force equilibrium in FEA is fundamentally equivalent to finding the system's lowest energy configuration, proving the stability and uniqueness of the calculated structural solution.
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%% Proof and Derivation
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