Variational Mechanics for Mining Infrastructure Design: A Systematic Review from Hamilton’s Principle to Physics-Constrained Optimization and Digital Twins

This article presents a systematic synthesis of variationally grounded approaches for the design and optimization of mining structural infrastructure. This study is motivated by the critical need to ensure stiffness, reliability, and operational availability under severe loading, mass constraints, and aggressive environmental conditions. Methodologically, the study situates structural modeling and synthesis within the continuity of the principle of stationary action. It demonstrates that, in the quasi-static regime, structural equilibrium is obtained as the stationarity of the total potential energy; consequently, the finite element method (FEM) arises naturally as a Ritz–Galerkin approximation of this underlying variational statement. On this basis, topology optimization is interpreted as a physics-constrained optimization problem wherein the design is posed as an outer optimality level acting over an energetically defined state. It is worth noting that SIMP-based formulations require explicit regularization to define the effective problem being solved. Emphasis is placed on the traceability between physical assumptions, discretization choices, regularization, and the resulting structural interpretations. The core contribution of this paper is a systematic literature review that consolidates evidence across variational mechanics, FEM-based optimization, and industrial applications, identifying recurrent methodological patterns and gaps that currently limit transfer to mining practice. Furthermore, a fully specified illustrative case is included to demonstrate reporting discipline and methodological consistency, rather than as a validation of a new optimization method. The conclusions highlight that a variational reading provides a coherent theoretical backbone for structural analysis, synthesis, simulation, and physics-based digital twins, while also clarifying the extensions required for industrial deployment, such as stability constraints, manufacturability, and multiphysics coupling within Mining 4.0 workflows.