Impact loading on mechanical structures and components produces stress conditions that are large in magnitude and fluctuate with time which are difficult for the engineer to assess for design. The Stress Wave Propagation (SWP) is a classical methodology to account for these large stress levels. Due to the highly mathematical approach of stress wave theory along with consideration of boundary conditions interactions in the struck solid, the stress wave propagation method generates closed solutions to impact problems that are only 1-D in nature [1, 2]. In engineering practice, most mechanical problems are more complex than 1-D and thus numerical methods need to be applied to provide engineering solutions. The Finite Element Method (FEM) is a numerical technique that is commonly used in static and dynamic loading conditions to provide engineering solution to complex geometry and loading. In this paper, the FEM is examined to determine if this methodology is robust enough to accurately represent Stress Wave Propagation in solid mediums by the capturing wave propagation velocities, boundary reflections and transmissions along with large transient stress magnitudes using simple 2-D axisymmetrical elements. The most complex 1-D problem and perhaps the most practical solved problem by the Stress Wave Propagation is the Split Hopkinson Bar (SHB) test. The purpose of this test is to determine the dynamic strength of materials. A finite element (FE) model of an as-built SHB test apparatus was developed. In the same function as the strain gages, two nodes were used to extract the strain time histories from the FE model of the apparatus bars. It was found that the pseudo-strain gages of the FEA compared well to the SWP theory. The pulse magnitudes of strains, strain rates and stress were found extremely similar and exhibited magnitudes within 4% between SWP and direct examination.
This model replicating a dynamic impact event demonstrated that the FEA can be used to solve complex impact problems involving stress wave propagation with the use of simple 2-D axisymmetric elements reducing computation time.
Finite Element Analysis of Torsional Stress Wave Propagation
