Inverse Reconstruction of Moving Contact Loads on an Elastic Half-Space Using Prescribed Surface Displacement

TL;DR

This paper develops an analytical and inverse modeling framework to reconstruct moving surface loads on an elastic half-space using prescribed surface displacements, incorporating elastodynamic effects and enabling efficient contact pressure determination.

Contribution

It introduces a Green's function-based inverse method with Fourier regularization for reconstructing moving contact loads from surface displacement data, accounting for dynamic effects.

Findings

Reconstructed contact pressure is smooth and symmetric within the contact region.

Stress fields are derived analytically and show patterns similar to photoelastic fringes.

As Mach number increases, stress asymmetry becomes more pronounced.

Abstract

This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the displacement and stress fields generated by a point load traveling at a constant velocity along the surface, explicitly incorporating elastodynamic effects through Mach number dependence. These moving-load solutions serve as building blocks for constructing more general loading scenarios via linear superposition. Based on Green's functions, an inverse problem is formulated to reconstruct the unknown surface traction responsible for a given surface displacement. The inverse analysis is performed through a Fourier-domain inversion with regularization, which enables a direct and computationally efficient determination of the contact pressure without iterative forward simulations. This framework is applied to a rigid wheel-ground contact problem, where the imposed displacement is dictated by the wheel geometry. The reconstructed surface traction exhibits a smooth, symmetric distribution within the contact region, while the resulting subsurface stress fields are obtained in closed analytical form and involve dilogarithm functions. The principal stress difference reveals characteristic spatial patterns similar to photoelastic fringes, and their asymmetry increases with the Mach number, reflecting the dynamic nature of the moving contact.