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Finite element concepts : a closed-form algebraic development / Gautam Dasgupta.

Dasgupta, Gautam, author.
2018
TA347.F5
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Title
Finite element concepts : a closed-form algebraic development / Gautam Dasgupta.
Author
Dasgupta, Gautam, author.
ISBN
9781493974238 (electronic book)
1493974238 (electronic book)
9781493974214
1493974211
9781493974214
DOI
https://doi.org/10.1007/978-1-4939-7423-8
Published
New York, NY : Springer, 2018.
Language
English
Description
1 online resource (xxxvi, 333 pages) : illustrations
Item Number
10.1007/978-1-4939-7423-8 doi
Call Number
TA347.F5
Dewey Decimal Classification
518/.25
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 14, 2017).
Available in Other Form
Print version: 9781493974214
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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.

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