One-dimensional finite amplitude wave propagation in a compressible elastic half-space
The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible half space is considered. The half space is subject on its surface to time dependent arbitrary normal and shear loadings. The problem is solved by employing a certain stable numerical scheme whi...
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| Published in | International journal of solids and structures Vol. 9; no. 3; pp. 363 - 378 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.03.1973
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| Online Access | Get full text |
| ISSN | 0020-7683 1879-2146 |
| DOI | 10.1016/0020-7683(73)90086-3 |
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| Abstract | The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible half space is considered. The half space is subject on its surface to time dependent arbitrary normal and shear loadings. The problem is solved by employing a certain stable numerical scheme which prevents almost all the numerical oscillations which usually occur near shocks when a standard finite difference scheme is applied.
иccлeдyeтcя зaдaчa pacнpocтpaнeния oднoмepнoй вoлны кoнeчнoй aмплитyды в нeлинeйнo yпpyгoм cжимaeмoм пoлyпpocтpaнcтвe. Пoлyпpocтpaнcтвo пoдвepжeнo нa eгo пoвepxнocтн дeйcтьиюзaвиcящeм oт вpeмeни, пpoнзвoльныx нaгpyзoк нopмaльнoй и cдвигa. зaдaчa peщaeтcя нyтeм нpимeнeния нeкoтopoй ycтoнчнвoй чнcлeннoй cxeмы кoтopaя пpeдoтвpaщaeт нoчтн вceм чиcлeнным кoлeбaнням, кoтopыe oбычнo пopиcxoдят близи yдapoв, для cлyчaя cтaндapтнoй cxeмы в кoнeчныx paзнocтяx. |
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| AbstractList | The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible halfspace is considered. The halfspace is subject on its surface to time dependent arbitrary normal and shear loadings. The problem is solved by employing a certain stable numerical scheme which prevents almost all the numerical oscillations which usually occur near shocks when a standard finite difference scheme is applied. The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible half space is considered. The half space is subject on its surface to time dependent arbitrary normal and shear loadings. The problem is solved by employing a certain stable numerical scheme which prevents almost all the numerical oscillations which usually occur near shocks when a standard finite difference scheme is applied. иccлeдyeтcя зaдaчa pacнpocтpaнeния oднoмepнoй вoлны кoнeчнoй aмплитyды в нeлинeйнo yпpyгoм cжимaeмoм пoлyпpocтpaнcтвe. Пoлyпpocтpaнcтвo пoдвepжeнo нa eгo пoвepxнocтн дeйcтьиюзaвиcящeм oт вpeмeни, пpoнзвoльныx нaгpyзoк нopмaльнoй и cдвигa. зaдaчa peщaeтcя нyтeм нpимeнeния нeкoтopoй ycтoнчнвoй чнcлeннoй cxeмы кoтopaя пpeдoтвpaщaeт нoчтн вceм чиcлeнным кoлeбaнням, кoтopыe oбычнo пopиcxoдят близи yдapoв, для cлyчaя cтaндapтнoй cxeмы в кoнeчныx paзнocтяx. |
| Author | Benveniste, Yako Aboudi, Jacob |
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| CitedBy_id | crossref_primary_10_1016_j_mechmat_2019_05_002 crossref_primary_10_1007_BF02175808 crossref_primary_10_1016_j_ijnonlinmec_2020_103502 crossref_primary_10_1016_0045_7825_76_90075_X crossref_primary_10_1016_S0022_460X_75_80131_3 crossref_primary_10_1016_0015_0568_74_90019_0 crossref_primary_10_1007_BF01601674 crossref_primary_10_1016_0020_7683_75_90023_2 crossref_primary_10_1016_0020_7683_74_90078_X crossref_primary_10_1016_0045_7825_75_90024_9 crossref_primary_10_1016_j_jmps_2019_103746 |
| Cites_doi | 10.1016/0021-9991(72)90087-3 10.1016/0022-5096(66)90022-6 10.1016/0020-7683(68)90040-1 10.1093/qjmam/19.3.259 10.1090/S0025-5718-1969-0247783-2 10.1093/qjmam/20.4.429 10.1016/0020-7683(66)90042-4 10.1122/1.548937 10.1007/BF01548245 |
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| References | Collins (BIB1) 1966; 19 Bland (BIB2) 1969 Fine, Shield (BIB3) 1966; 2 To be published. Numerical solution of quasi-conservative hyperbolic systems—the cylindrical shock problem. Davison (BIB14) 1966; 14 Collins (BIB13) 1967; 20 Abarbanel, Zwas (BIB11) 1969; 23 Aboudi (BIB9) 1971; 5 Jeffrey, Taniuti (BIB12) 1964 Truesdell, Noll (BIB7) 1960 and Davison (BIB4) 1968; 4 Malvern (BIB6) 1969 Blatz, Ko (BIB5) 1962; 6 Richtmyer, Morton (BIB8) 1967 Davison (10.1016/0020-7683(73)90086-3_BIB4) 1968; 4 Richtmyer (10.1016/0020-7683(73)90086-3_BIB8) 1967 Collins (10.1016/0020-7683(73)90086-3_BIB1) 1966; 19 Blatz (10.1016/0020-7683(73)90086-3_BIB5) 1962; 6 Davison (10.1016/0020-7683(73)90086-3_BIB14) 1966; 14 Bland (10.1016/0020-7683(73)90086-3_BIB2) 1969 Abarbanel (10.1016/0020-7683(73)90086-3_BIB11) 1969; 23 Aboudi (10.1016/0020-7683(73)90086-3_BIB9) 1971; 5 10.1016/0020-7683(73)90086-3_BIB10 Jeffrey (10.1016/0020-7683(73)90086-3_BIB12) 1964 Fine (10.1016/0020-7683(73)90086-3_BIB3) 1966; 2 Truesdell (10.1016/0020-7683(73)90086-3_BIB7) 1960 Malvern (10.1016/0020-7683(73)90086-3_BIB6) 1969 Collins (10.1016/0020-7683(73)90086-3_BIB13) 1967; 20 |
| References_xml | – year: 1960 ident: BIB7 article-title: The nonlinear field theories of mechanics publication-title: Handbuch der Physik III/III – year: 1964 ident: BIB12 article-title: Nonlinear Wave Propagation – year: 1969 ident: BIB2 article-title: Nonlinear Dynamic Elasticity – reference: and – reference: , Numerical solution of quasi-conservative hyperbolic systems—the cylindrical shock problem. – volume: 4 start-page: 301 year: 1968 end-page: 322 ident: BIB4 article-title: Peturbation theory of nonlinear elastic wave propagation publication-title: Int. J. Solids Struct – volume: 6 start-page: 223 year: 1962 end-page: 251 ident: BIB5 article-title: Application of finite elasticity theory to the deformation of rubbers publication-title: Trans. Soc. Rheology – year: 1967 ident: BIB8 article-title: Difference Methods for Initial-Value Problems – volume: 19 start-page: 259 year: 1966 end-page: 328 ident: BIB1 article-title: One-dimensional nonlinear wave propagation in incompressible elastic materials publication-title: Q. Jl Mech. Appl. Math – volume: 2 start-page: 605 year: 1966 end-page: 620 ident: BIB3 article-title: Second order effects in the propagation of elastic waves publication-title: Int. J. Solids Struct – volume: 20 start-page: 429 year: 1967 end-page: 452 ident: BIB13 article-title: The propagation and interaction of one-dimensional nonlinear waves in an incompressible isotropic elastic half-space publication-title: Q. Jl Mech. Appl. Math – year: 1969 ident: BIB6 article-title: Introduction to the Mechanics of a Continuous Medium – volume: 5 start-page: 279 year: 1971 end-page: 287 ident: BIB9 article-title: Wave propagation from a spherical cavity imbedded in an elasto-plastic medium publication-title: J. Engng Math – volume: 23 start-page: 549 year: 1969 end-page: 565 ident: BIB11 article-title: An iterative finite difference method for hyperbolic systems publication-title: Math. Comp – reference: To be published. – volume: 14 start-page: 249 year: 1966 end-page: 270 ident: BIB14 article-title: Propagation of plane waves of finite amplitude in elastic solids publication-title: J. Mech. Phys. Solids – ident: 10.1016/0020-7683(73)90086-3_BIB10 doi: 10.1016/0021-9991(72)90087-3 – volume: 14 start-page: 249 year: 1966 ident: 10.1016/0020-7683(73)90086-3_BIB14 article-title: Propagation of plane waves of finite amplitude in elastic solids publication-title: J. Mech. Phys. Solids doi: 10.1016/0022-5096(66)90022-6 – year: 1969 ident: 10.1016/0020-7683(73)90086-3_BIB6 – volume: 4 start-page: 301 year: 1968 ident: 10.1016/0020-7683(73)90086-3_BIB4 article-title: Peturbation theory of nonlinear elastic wave propagation publication-title: Int. J. Solids Struct doi: 10.1016/0020-7683(68)90040-1 – volume: 19 start-page: 259 year: 1966 ident: 10.1016/0020-7683(73)90086-3_BIB1 article-title: One-dimensional nonlinear wave propagation in incompressible elastic materials publication-title: Q. Jl Mech. Appl. Math doi: 10.1093/qjmam/19.3.259 – year: 1960 ident: 10.1016/0020-7683(73)90086-3_BIB7 article-title: The nonlinear field theories of mechanics – volume: 23 start-page: 549 year: 1969 ident: 10.1016/0020-7683(73)90086-3_BIB11 article-title: An iterative finite difference method for hyperbolic systems publication-title: Math. Comp doi: 10.1090/S0025-5718-1969-0247783-2 – volume: 20 start-page: 429 year: 1967 ident: 10.1016/0020-7683(73)90086-3_BIB13 article-title: The propagation and interaction of one-dimensional nonlinear waves in an incompressible isotropic elastic half-space publication-title: Q. Jl Mech. Appl. Math doi: 10.1093/qjmam/20.4.429 – volume: 2 start-page: 605 year: 1966 ident: 10.1016/0020-7683(73)90086-3_BIB3 article-title: Second order effects in the propagation of elastic waves publication-title: Int. J. Solids Struct doi: 10.1016/0020-7683(66)90042-4 – year: 1964 ident: 10.1016/0020-7683(73)90086-3_BIB12 – volume: 6 start-page: 223 year: 1962 ident: 10.1016/0020-7683(73)90086-3_BIB5 article-title: Application of finite elasticity theory to the deformation of rubbers publication-title: Trans. Soc. Rheology doi: 10.1122/1.548937 – year: 1969 ident: 10.1016/0020-7683(73)90086-3_BIB2 – year: 1967 ident: 10.1016/0020-7683(73)90086-3_BIB8 – volume: 5 start-page: 279 year: 1971 ident: 10.1016/0020-7683(73)90086-3_BIB9 article-title: Wave propagation from a spherical cavity imbedded in an elasto-plastic medium publication-title: J. Engng Math doi: 10.1007/BF01548245 |
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| Snippet | The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible half space is considered. The half space is subject... The problem of one-dimensional wave propagation of finite amplitude in a nonlinearly elastic compressible halfspace is considered. The halfspace is subject on... |
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| Title | One-dimensional finite amplitude wave propagation in a compressible elastic half-space |
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