A NUMERICAL METHOD FOR THE ANALYSIS OF STRESS WAVE PROPAGATION IN ELASTIC SOLIDS (CAGNIARD)
Abstract
This research originated in the problem of fatigue failure due to impact in the tips of compressor reed valves. Photomicrographic analysis has indicated that these failures are due to stress waves that propagate from the impact site and reflect from the boundaries forming the valve tip. The purpose of this work is to produce a numerical method for computing the patterns of stress wave propagation in bounded elastic bodies. The solution to this problem is based on the exact ray theory for elastic wave propagation in the half space due to Cagniard. A Green's function for the problem of an oblique line impact on the surface of an elastic half space is formulated. An efficient convolution integration algorithm is developed for numerically extending this solution to the problem of arbitrarily complicated loadings on an elastic half space. Particular attention is paid to the accurate integration of the wave front singularities in the solution. Finally, a second algorithm is developed, based on the principle of superposition, for the purpose of computing the patterns of elastic wave propagation in bodies of arbitrarily complicated shape. The methods described above are developed for the case of plane strain. Results are shown for line impacts on three fundamental geometries: the half space, the infinite plate, and the quarter space. In addition, results are shown for time varying line loads, spatially distributed impacts, and more general loadings on the infinite plate.
Degree
Ph.D.
Subject Area
Mechanical engineering
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