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024 7 $a10.1007/978-1-4939-7423-8
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101 0 $aeng
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200 10$aFinite Element Concepts $eA Closed-Form Algebraic Development /$fby Gautam Dasgupta
205   $a1st ed. 2018.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2018.
215   $a1 online resource (XXXVI, 333 p. 45 illus.) 
300   $aIncludes index.
311   $a1-4939-7421-1 
327   $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.
330   $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.
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aPartial differential equations
606   $aComputer mathematics
606   $aMechanical engineering
606   $aCivil engineering
606   $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026
606   $aMechanical Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T17004
606   $aCivil Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T23004
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615  0$aPartial differential equations.
615  0$aComputer mathematics.
615  0$aMechanical engineering.
615  0$aCivil engineering.
615 14$aMathematical and Computational Engineering.
615 24$aPartial Differential Equations.
615 24$aComputational Science and Engineering.
615 24$aMechanical Engineering.
615 24$aCivil Engineering.
676   $a620.00151535
700   $aDasgupta$b Gautam$4aut$4http://id.loc.gov/vocabulary/relators/aut$01061151
801  0$bMiAaPQ
801  1$bMiAaPQ
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906   $aBOOK
912   $a9910299921603321
996   $aFinite Element Concepts$92517687
997   $aUNINA