
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 discreteelement method of wave motion analysis is summarized and extended for problems involving infinite or semiinfinite solid media in plane and axisymmetric conditions. Space discretization of a solid medium is accomplished through a lumpedparameter discreteelement 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 axisymmetric problems are presented. Calculations of wave motions in an infinite or semiinfinite 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 stepwise transmission of D'Alembert forces, a general transmitting boundary was developed for the discreteelement method of analysis. The boundary was verified extensively through actual calculations of plane strain and axisymmetric problems, including those with layered halfspaces, elasticplastic 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