Statics and Influence Functions From a Modern Perspective

· 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-ben...

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Bibliographic Details
Main Authors: Hartmann, Friedel, Jahn, Peter (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2021, 2021
Edition:2nd ed. 2021
Series:Springer Series in Solid and Structural Mechanics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Description
Summary:· 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
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 leadto 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+.
Physical Description:XV, 464 p. 289 illus., 272 illus. in color online resource
ISBN:9783030558895