Overview
The textbook is suitable for a two semester undergraduate or a one semester graduate course
Suitable for engineering, applied mathematics and physics students
Modeled for Civil, mechanical, bio-engineering and engineering mechanics disciplines
Self-study, in styling the book, encourages researchers towards innovative and independent thinking
Synthesizes numerics and graphics through symbolic computation
Mathematica® routines, for transformation and closed form integration on arbitrary convex, concave and curved regions, can be easily integrated in any C++ code for production runs
Also, appropriate for animation and augmented reality industries for color distribution and morphology
Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
Keywords
- Closed-form computation
- Generalized Barycentric coordinates
- Continuum mechanics
- Differential equations/problem solutions
- FEM
- Mathematica
- Fluid mechanics and Nano mechanics
- Linear algebra, progaming concepts
- Bio-morphometry
- Rayleigh modes
- Richard Courant
- Scalar problems
- Steady temperature distribution
- Stochastic FE
- Structural Engineering
- Walther Ritz
- partial differential equations
About this book
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.
Authors and Affiliations
About the author
Dr. Gautam Dasgupta has been a member of Columbia University faculty since 1977. He has published in the areas of engineering mechanics and computer mathematics including graphics and music. He constructed numerical forms of the viscoelastic correspondence principle, introduced the cloning algorithm to model frequency responses of infinite (unbounded) media with finite elements, derived stochastic shape and Green's functions for finite and boundary element, and proved the Almansi Theorem for anisotropic continua.
Bibliographic Information
Book Title: Finite Element Concepts
Book Subtitle: A Closed-Form Algebraic Development
Authors: Gautam Dasgupta
DOI: https://doi.org/10.1007/978-1-4939-7423-8
Publisher: Springer New York, NY
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Science+Business Media, LLC 2018
Hardcover ISBN: 978-1-4939-7421-4Published: 06 December 2017
Softcover ISBN: 978-1-4939-8481-7Published: 30 August 2018
eBook ISBN: 978-1-4939-7423-8Published: 05 December 2017
Edition Number: 1
Number of Pages: XXXVI, 333
Number of Illustrations: 45 b/w illustrations
Topics: Mathematical and Computational Engineering, Partial Differential Equations, Computational Science and Engineering, Mechanical Engineering, Civil Engineering