04352nam 22007095 450 991029992160332120200701010629.01-4939-7423-810.1007/978-1-4939-7423-8(CKB)4100000001381464(DE-He213)978-1-4939-7423-8(MiAaPQ)EBC6312199(MiAaPQ)EBC5590837(Au-PeEL)EBL5590837(OCoLC)1066189080(PPN)222225726(EXLCZ)99410000000138146420171205d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierFinite Element Concepts A Closed-Form Algebraic Development /by Gautam Dasgupta1st ed. 2018.New York, NY :Springer New York :Imprint: Springer,2018.1 online resource (XXXVI, 333 p. 45 illus.) Includes index.1-4939-7421-1 1. 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.This 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.Applied mathematicsEngineering mathematicsPartial differential equationsComputer mathematicsMechanical engineeringCivil engineeringMathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Computational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Mechanical Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T17004Civil Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T23004Applied mathematics.Engineering mathematics.Partial differential equations.Computer mathematics.Mechanical engineering.Civil engineering.Mathematical and Computational Engineering.Partial Differential Equations.Computational Science and Engineering.Mechanical Engineering.Civil Engineering.620.00151535Dasgupta Gautamauthttp://id.loc.gov/vocabulary/relators/aut1061151MiAaPQMiAaPQMiAaPQBOOK9910299921603321Finite Element Concepts2517687UNINA