Finite Element Concepts: A Closed-Form Algebraic Development

Finite Element Concepts: A Closed-Form Algebraic Development

by Gautam Dasgupta

Hardcover(1st ed. 2018)



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 continuedin the next chapter for truss analysis usingMathematicaprograms.The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed byfour-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-testsin all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed inclosed algebraic form.Appendices give a short introduction toMathematica, followed bytruss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. AllMathematicacodes for theoretical formulations and graphics are included with extensive numerical examples.

Product Details

ISBN-13: 9781493974214
Publisher: Springer New York
Publication date: 12/06/2017
Edition description: 1st ed. 2018
Pages: 333
Product dimensions: 6.10(w) x 9.25(h) x (d)

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 andcomputer mathematics including graphics and music. He constructed numerical forms of the viscoelasticcorrespondence principle,introduced the cloning algorithm to model frequency responses ofinfinite (unbounded) media with finite elements, derivedstochastic shape and Green's functions for finite and boundary element, and proved the Almansi Theorem for anisotropic continua.

Table of Contents

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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