Foundation of the Wave Finite Element Method

Abstract

As a simple mechanical model, we consider a rectilinear homogeneous elastic rod of length L and constant cross-sectional area A. The rod moves along its x-axis with velocity v₀ and is loaded by forces F ⁺₀ and F ^-₀ = -F ⁺₀ applied to its ends (Fig.1.1a). The positive index refers to the right end, the negative index to the left end. The positive direction of the forces is taken to coincide with that of the x-axis; therefore, a positive (tensile) stress in the rod is determined as σ₀ = F ⁺₀ / A = -F ^-₀ / A (Fig.1.1b).