Accession Number : AD0722087

Title :   Development of a Transmitting Boundary for Numerical Wave Motion Calculations

Descriptive Note : Final rept.

Corporate Author : NEWMARK (NATHAN M) CONSULTING ENGINEERING SERVICES URBANA IL

Personal Author(s) : Ang, A H -S ; Newmark, N M

PDF Url : AD0722087

Report Date : Apr 1971

Pagination or Media Count : 166

Abstract : 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 D'Alembert 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.

Descriptors :   *SEISMIC WAVES, *SHOCK WAVES, DIFFERENCE EQUATIONS, EQUATIONS OF MOTION, LOADS(FORCES), NUMERICAL ANALYSIS, NUMERICAL INTEGRATION, PARTIAL DIFFERENTIAL EQUATIONS, SHEAR STRESSES, STRAIN(MECHANICS), WAVE PROPAGATION

Subject Categories : Seismology
      Numerical Mathematics
      Armor

Distribution Statement : APPROVED FOR PUBLIC RELEASE