LEADER 03986oam 2200529 450 001 9910483797903321 005 20210523015853.0 010 $a3-030-55889-4 024 7 $a10.1007/978-3-030-55889-5 035 $a(CKB)4100000011610319 035 $a(MiAaPQ)EBC6413395 035 $a(DE-He213)978-3-030-55889-5 035 $a(PPN)252508661 035 $a(EXLCZ)994100000011610319 100 $a20210523d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStatics and influence functions $efrom a modern perspective. /$fF. Hartmann, Peter Jahn 205 $a2nd ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (XV, 464 p. 289 illus., 272 illus. in color.) 225 1 $aSpringer Series in Solid and Structural Mechanics,$x2195-3511 ;$v13 311 $a3-030-55888-6 320 $aIncludes bibliographical references and index. 327 $aFoundation -- Betti's Theorem -- Finite Elements -- Betti Extended -- Stiffness Changes and Reanalysis -- Singularities -- Mixed formulations -- Nonlinear Problems. 330 $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. 410 0$aSpringer Series in Solid and Structural Mechanics,$x2195-3511 ;$v13 606 $aGreen's functions 606 $aStatics 606 $aMechanics 615 0$aGreen's functions. 615 0$aStatics. 615 0$aMechanics. 676 $a531.12 700 $aHartmann$b F$g(Friedel),$f1945-$040769 702 $aJahn$b Peter 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910483797903321 996 $aStatics and influence functions$92854045 997 $aUNINA