Development of a Transmitting Boundary for Numerical Wave Motion Calculations
NEWMARK (NATHAN M) CONSULTING ENGINEERING SERVICES URBANA IL
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A numerical discrete-element method of wave motion analysis is summarized and extended for problems involving infinite or semi-infinite solid media in plane and axi-symmetric conditions. Space discretization of a solid medium is accomplished through a lumped-parameter discrete-element model of the medium, whereas the time discretization is embedded within a general numerical integrator. This invariably leads to a system of finite difference equations thus, the required mathematical conditions for numerical stability can be developed on the basis of available finite difference theory. Explicit stability conditions for plane and axi-symmetric problems are presented. Calculations of wave motions in an infinite or semi-infinite space can be confined to a finite region or interest if the region is terminated by suitable transmitting boundaries such that no significant reflections are generated at these artificial boundaries. Based on the concept of a step-wise transmission of DAlembert forces, a general transmitting boundary was developed for the discrete-element method of analysis. The boundary was verified extensively through actual calculations of plane strain and axi-symmetric problems, including those with layered half-spaces, elastic-plastic systems, and a problem involving long calculation time.
- Numerical Mathematics