000 04552nam a22005655i 4500
001 978-3-030-55889-5
003 DE-He213
005 20220801215808.0
007 cr nn 008mamaa
008 201125s2021 sz | s |||| 0|eng d
020 _a9783030558895
_9978-3-030-55889-5
024 7 _a10.1007/978-3-030-55889-5
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.105
_223
100 1 _aHartmann, Friedel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_946504
245 1 0 _aStatics and Influence Functions
_h[electronic resource] :
_bFrom a Modern Perspective /
_cby Friedel Hartmann, Peter Jahn.
250 _a2nd ed. 2021.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2021.
300 _aXV, 464 p. 289 illus., 272 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v13
505 0 _aFoundation -- Betti's Theorem -- Finite Elements -- Betti Extended -- Stiffness Changes and Reanalysis -- Singularities -- Mixed formulations -- Nonlinear Problems.
520 _aThis extended and revised second edition is intended for engineering students and researchers working with finite element methods in structural and mechanical analysis. Discussing numerical structural analysis from first mechanical and mathematical principles, it establishes the central role of influence functions (Green's functions) in linear computational mechanics. The main features of the book are mentioned below. · Introducing Green's first and second identity as the core theorems of statics and mechanics. Formulation of the variational and energy principles of mechanics with an emphasis on the computational aspects and on the qualitative features of variational solutions. · Derivation of influence functions from duality principles, the distinction between weak and strong influence functions, the difference between monopoles and dipoles and how amputated dipoles lead to singularities, and how singularities on the boundary pollute the solution inside the domain - an unavoidable effect in 2-D and 3-D. · A detailed discussion of the various features of the finite element method and the key role of the notion of “shake-equivalence" as originally introduced by Turner et alt. Establishing that in linear finite element analysis the accuracy depends on the accuracy of the influence functions. Introducing Betti extended as a core theorem of finite element analysis. · A systematic treatment of the role which Green's functions play in reanalysis, sensitivity analysis, parameter identification and in optimization. Explaining why averaging material parameters succeeds and how local stiffness changes can be identified with the action of equilibrium forces f+. · Presenting a new technique, one-click reanalysis, which allows to make modifications to a structure by clicking on single elements and seeing directly the new shape, bypassing the need to solve the modified system. · Four programs for the solution of the Poisson equation, 2-D elasticity, plate-bending problems and planar frames are offered for download in this second edition. These are all-purpose programs but with a particular emphasis on influence functions. The frame program also demonstrates one-click reanalysis.
650 0 _aMechanics, Applied.
_93253
650 0 _aSolids.
_93750
650 0 _aBuildings—Design and construction.
_932147
650 0 _aMathematics—Data processing.
_931594
650 1 4 _aSolid Mechanics.
_931612
650 2 4 _aBuilding Construction and Design.
_932148
650 2 4 _aComputational Mathematics and Numerical Analysis.
_931598
700 1 _aJahn, Peter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_946505
710 2 _aSpringerLink (Online service)
_946506
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030558888
776 0 8 _iPrinted edition:
_z9783030558901
776 0 8 _iPrinted edition:
_z9783030558918
830 0 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v13
_946507
856 4 0 _uhttps://doi.org/10.1007/978-3-030-55889-5
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c77872
_d77872