000 03810nam a22005895i 4500
001 978-1-4939-7423-8
003 DE-He213
005 20220801221400.0
007 cr nn 008mamaa
008 171205s2018 xxu| s |||| 0|eng d
020 _a9781493974238
_9978-1-4939-7423-8
024 7 _a10.1007/978-1-4939-7423-8
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620
_223
100 1 _aDasgupta, Gautam.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_955717
245 1 0 _aFinite Element Concepts
_h[electronic resource] :
_bA Closed-Form Algebraic Development /
_cby Gautam Dasgupta.
250 _a1st ed. 2018.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2018.
300 _aXXXVI, 333 p. 45 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _a1. Bar -- 2. Trusses -- 3. 2-D Llinear Interpolation -- 4. Triangular Elements -- 5. Taig’s Convex Quadrilateral Elements -- 6. Irons patch test -- 7. Eight DOFs -- 8. Incompressibility -- 9. Conclusions.
520 _aThis text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs. The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aDifferential equations.
_955718
650 0 _aMathematics—Data processing.
_931594
650 0 _aMechanical engineering.
_95856
650 0 _aCivil engineering.
_910082
650 1 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aDifferential Equations.
_955719
650 2 4 _aComputational Science and Engineering.
_955720
650 2 4 _aMechanical Engineering.
_95856
650 2 4 _aCivil Engineering.
_910082
710 2 _aSpringerLink (Online service)
_955721
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9781493974214
776 0 8 _iPrinted edition:
_z9781493974221
776 0 8 _iPrinted edition:
_z9781493984817
856 4 0 _uhttps://doi.org/10.1007/978-1-4939-7423-8
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c79609
_d79609