Multi-Dimensional Wave Propagation in Solids Due to Impact Loading by the Method of Characteristics. Case 1. Computational Method for Two-Dimensional Waves in a Linear Elastic Solid.
TECHNION - ISRAEL INST OF TECH HAIFA DEPT OF AERONAUTICAL ENGINEERING
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A computational method is presented for the solution of multi-dimensional hyperbolic partial differential equations governing the dynamic deformation of solids. The method is based on characteristics formulation of the hyperbolic differential equations. Thus generated waves are located in the medium and the differential equations holding along these waves are obtained. The algorithm consists of a new method which evaluates the unknown variables along the leading wave and then couples the first generator to the motion behind it. The unknowns along the leading wave are resolved by means of kinematic and dynamic conditions existing across this wave. The entire multi-dimensional solution domain is then linked to the leading wave by the method of characteristics. The mathematical avenues used to develop this computational method are potentially capable of solving multi-dimensional wave problems in various types of solids. As a first step in the report, the described technique is confined to field equations defining the deformation of a linear elastic solid in two-space and time independent variables. Author