04006nam a22005775i 4500 978-3-031-56369-0 DE-He213 20251030112323.0 cr nn 008mamaa 240621s2024 sz | s |||| 0|eng d 9783031563690 978-3-031-56369-0 10.1007/978-3-031-56369-0 doi TJ1-1570 TGB bicssc TEC009070 bisacsh TGB thema Bielak, Jacobo. author. aut http://id.loc.gov/vocabulary/relators/aut 79053 The Finite Element Method [electronic resource] : A Primer / by Jacobo Bielak. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XIII, 288 p. 150 illus., 39 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Part 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. This 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. Mechanical engineering. 58323 Civil engineering. Electrical engineering. 65586 Numerical analysis. Engineering mathematics. 64145 Engineering Data processing. Mechanical Engineering. 58323 Civil Engineering. Electrical and Electronic Engineering. 65588 Numerical Analysis. Mathematical and Computational Engineering Applications. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031563683 Printed edition: 9783031563706 Printed edition: 9783031563713 https://doi.org/10.1007/978-3-031-56369-0 ZDB-2-ENG ZDB-2-SXE 60887 60887