A Method for Determining Load Paths Based on Fermat’s Principle

Abstract

Load path analysis serves as the foundation for establishing mechanical models of D-regions in structural components. This paper proposes a method based on Fermat’s principle for the automatic generation of load paths within structural members. First, based on the governing equations of elastodynamics and utilizing the Wentzel–Kramers–Brillouin–Jeffreys high-frequency asymptotic expansion, we demonstrate a geometric analogy between the ray paths of high-frequency body waves in inhomogeneous media and load flow transmission paths. Subsequently, by constructing a virtual refractive index field applicable to material inhomogeneity and damage degradation, we transform the determination of load paths into an optimal routing problem subject to boundary, obstacle, and topological constraints and introduce a numerical solution employing Bezier curve parameterization coupled with a hybrid Monte Carlo and hill-climbing algorithm. Finally, analyses of several classical cases indicate that the proposed method can automatically generate load paths characterized by both physical autonomy and geometric smoothness, demonstrating high accuracy and broad applicability.