LEADER 03754nam 22006735 450 001 9910254252803321 005 20220413170017.0 010 $a3-319-32580-9 024 7 $a10.1007/978-3-319-32580-4 035 $a(CKB)3710000000651928 035 $a(EBL)4517711 035 $a(SSID)ssj0001665891 035 $a(PQKBManifestationID)16454980 035 $a(PQKBTitleCode)TC0001665891 035 $a(PQKBWorkID)15000351 035 $a(PQKB)11150707 035 $a(DE-He213)978-3-319-32580-4 035 $a(MiAaPQ)EBC4517711 035 $a(PPN)193445182 035 $a(EXLCZ)993710000000651928 100 $a20160430d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe state of deformation in earthlike self-gravitating objects$b[electronic resource] /$fby Wolfgang H. Müller, Wolf Weiss 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (117 p.) 225 1 $aSpringerBriefs in Continuum Mechanics,$x2625-1329 300 $aDescription based upon print version of record. 311 $a3-319-32578-7 320 $aIncludes bibliographical references at the end of each chapters. 327 $aThe problem, its historical development and the shortcomings -- Analytical and numerical studies of the linear problem (small deformation theory) -- Numerical studies of the non-linear problem: shooting methods, finite differences, finite elements -- A radially symmetric composite shell model of the Earth. 330 $aThis book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis. 410 0$aSpringerBriefs in Continuum Mechanics,$x2625-1329 606 $aMechanics 606 $aMechanics, Applied 606 $aPlanetology 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 606 $aPlanetology$3https://scigraph.springernature.com/ontologies/product-market-codes/G18010 606 $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aPlanetology. 615 14$aSolid Mechanics. 615 24$aPlanetology. 615 24$aClassical Mechanics. 676 $a531 700 $aMüller$b Wolfgang H$4aut$4http://id.loc.gov/vocabulary/relators/aut$0254548 702 $aWeiss$b Wolf$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254252803321 996 $aThe State of Deformation in Earthlike Self-Gravitating Objects$92531925 997 $aUNINA