Statics and influence functions : from a modern perspective / Friedel Hartmann, Peter Jahn.
Hartmann, F. (Friedel), 1945- author.; Jahn, Peter, author.
2021
TA648 .H37 2021
Available Online

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Title Statics and influence functions : from a modern perspective / Friedel Hartmann, Peter Jahn.
Author Hartmann, F. (Friedel), 1945- author.
Edition Second edition.
ISBN 9783030558895 (electronic book)
3030558894 (electronic book)
9783030558888
3030558886
DOI https://doi.org/10.1007/978-3-030-55889-5
Published Cham, Switzerland : Springer, [2021]
Language English
Description 1 online resource
Other Standard Identifiers 10.1007/978-3-030-55889-5 doi
Call Number TA648 .H37 2021
Dewey Decimal Classification 624.171
531
Summary This extended and revised second edition is intended for engineering students and researchers working with finite element methods in structural and mechanical analysis. Discussing numerical structural analysis from first mechanical and mathematical principles, it establishes the central role of influence functions (Green's functions) in linear computational mechanics. The main features of the book are mentioned below. · Introducing Green's first and second identity as the core theorems of statics and mechanics. Formulation of the variational and energy principles of mechanics with an emphasis on the computational aspects and on the qualitative features of variational solutions. · Derivation of influence functions from duality principles, the distinction between weak and strong influence functions, the difference between monopoles and dipoles and how amputated dipoles lead to singularities, and how singularities on the boundary pollute the solution inside the domain - an unavoidable effect in 2-D and 3-D. · A detailed discussion of the various features of the finite element method and the key role of the notion of "shake-equivalence" as originally introduced by Turner et alt. Establishing that in linear finite element analysis the accuracy depends on the accuracy of the influence functions. Introducing Betti extended as a core theorem of finite element analysis. · A systematic treatment of the role which Green's functions play in reanalysis, sensitivity analysis, parameter identification and in optimization. Explaining why averaging material parameters succeeds and how local stiffness changes can be identified with the action of equilibrium forces f+. · Presenting a new technique, one-click reanalysis, which allows to make modifications to a structure by clicking on single elements and seeing directly the new shape, bypassing the need to solve the modified system. · Four programs for the solution of the Poisson equation, 2-D elasticity, plate-bending problems and planar frames are offered for download in this second edition. These are all-purpose programs but with a particular emphasis on influence functions. The frame program also demonstrates one-click reanalysis
Note First edition: 2017.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from digital title page (viewed on February 01, 2021).
Added Author Jahn, Peter, author.
Series Springer series in solid and structural mechanics ; 13. 2195-3511
Available in Other Form Print version: 9783030558888
Print version: 9783030558901
Print version: 9783030558918
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Foundation
Betti's Theorem
Finite Elements
Betti Extended
Stiffness Changes and Reanalysis
Singularities
Mixed formulations
Nonlinear Problems.

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