03823nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001300172072001600185072002300201072001500224100008400239245008600323250001800409264007500427300006700502336002600569337002600595338003600621347002400657505068300681520129001364650003502654650002302689650003502712650002402747650003602771650003402807650003502841650002302876650005002899650002402949650006102973710003403034773002603068776003603094776003603130776003603166856004603202912001403248912001403262999001703276978-3-031-56369-0DE-He21320251030112323.0cr nn 008mamaa240621s2024    sz |    s    |||| 0|eng d  a97830315636909978-3-031-56369-07 a10.1007/978-3-031-56369-02doi 4aTJ1-1570 7aTGB2bicssc 7aTEC0090702bisacsh 7aTGB2thema1 aBielak, Jacobo.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97905314aThe Finite Element Methodh[electronic resource] :bA Primer /cby Jacobo Bielak.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXIII, 288 p. 150 illus., 39 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPart I Fundamental Concepts, Implementation, and Applications -- Chapter 1 Prototype One-Dimensional Boundary-Value Problem (BVP) – Governing Differential Equation and Variational Formulations with Examples -- Chapter 2 Finite Elements for the Prototype One-Dimensional BVP -- Chapter 3 Prototype Two-Dimensional (2D) Problem – Variational Formulations.-Chapter 4 Finite Elements for the Model Two-Dimensional BVP -- Part II Extensions -- Chapter 5 Problems With Singularities -- Chapter 6 Three-Dimensional Boundary-Value Problems -- Chapter 7 Initial Boundary-Value Problems -- Chapter 8 Spectral Elements -- Chapter 9 One-Dimensional Fourth-Order Boundary Value Problems.  aThis textbook introduces the widely used numerical technique FEM in various engineering disciplines for the analysis of structures, heat transfer, fluid dynamics, and other physical phenomena. Appropriate for interested senior undergraduate engineering students and beginner graduate students in a one-semester introductory course, this book provides a clear understanding of the main issues in FEM. Looking at the FEM as a variational approximation method that uses localized piecewise polynomial basis functions for the solution of boundary-value problems (BVP) and initial boundary-value problems (IBVP), the book uses examples to apply this technique to various problems of physical interest, e.g., elasticity, heat conduction, advection-diffusion, etc. One-dimensional (1D) problems are presented first to make it easier to grasp the fundamental concepts associated with the formulation and application of the FEM; then, the methodology is extended to more challenging 2D and 3D problems that involve somewhat greater mathematical complexity. For simplicity, the book deals with problems that are specified in terms of a single set of state variables, such as displacements or temperature. Finally, due to the introductory nature of this text, only linear problems are considered. 0aMechanical engineering.958323 0aCivil engineering. 0aElectrical engineering.965586 0aNumerical analysis. 0aEngineering mathematics.964145 0aEngineeringxData processing.14aMechanical Engineering.95832324aCivil Engineering.24aElectrical and Electronic Engineering.96558824aNumerical Analysis.24aMathematical and Computational Engineering Applications.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303156368308iPrinted edition:z978303156370608iPrinted edition:z978303156371340uhttps://doi.org/10.1007/978-3-031-56369-0  aZDB-2-ENG  aZDB-2-SXE  c60887d60887