Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

1998 | Buch

Nonconvexity in Engineering Applications Kapitel lesen Erstes Kapitel lesen

Nonconvex Optimization in Mechanics

Algorithms, Heuristics and Engineering Applications by the F.E.M.

verfasst von: E. S. Mistakidis, G. E. Stavroulakis

Verlag: Springer US

Buchreihe : Nonconvex Optimization and Its Applications

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

Nonconvexity and nonsmoothness arise in a large class of engineering applica­ tions. In many cases of practical importance the possibilities offered by opti­ mization with its algorithms and heuristics can substantially improve the per­ formance and the range of applicability of classical computational mechanics algorithms. For a class of problems this approach is the only one that really works. The present book presents in a comprehensive way the application of opti­ mization algorithms and heuristics in smooth and nonsmooth mechanics. The necessity of this approach is presented to the reader through simple, represen­ tative examples. As things become more complex, the necessary material from convex and nonconvex optimization and from mechanics are introduced in a self-contained way. Unilateral contact and friction problems, adhesive contact and delamination problems, nonconvex elastoplasticity, fractal friction laws, frames with semi­ rigid connections, are among the applications which are treated in details here. Working algorithms are given for each application and are demonstrated by means of representative examples. The interested reader will find helpful references to up-to-date scientific and technical literature so that to be able to work on research or engineering topics which are not directly covered here.

Inhaltsverzeichnis

Frontmatter

Nonconvexity in Engineering Applications

Frontmatter
1. Nonconvexity in Engineering Applications
Abstract
Elements involving nonconvex and/or nonsmooth energy potentials appear in several mechanical problems. The nonconvexity of the energy potential appears as a result of the introduction of a nonmonotone, possibly multivalued stress-strain or reaction-displacement law. Consider for example the nonmonotone reaction (S i ) — displacement (u i ) diagram of Fig. 1.1a which leads to the nonconvex energy potential of Fig. 1.1b. Similar is the situation with the sawtooth stress-strain law of Fig. 1.1c which appears in reinforced concrete under tension (Scanlon’s diagram) and leads to the potential energy function of Fig. 1.1d. The same effects may appear also in other problems of structural mechanics.
E. S. Mistakidis, G. E. Stavroulakis

Applied Nonconvex Optimization Background

Frontmatter
2. Applied Nonconvex Optimization Background
Abstract
The problem of finding an extremum of a given function over the space where the function is defined or over a subset of it, is called an optimization problem. In mechanics several “principles” which govern physical phenomena in general and the response of mechanical systems in particular are written in the form of an optimization problem. The principles of minimum potential energy in statics, the maximum dissipation principle in dissipative media and the least action principle in dynamics are some examples (see, among others, Hamel, 1949, Lippmann, 1972, Cohn and Maier, 1979, de Freitas, 1984, de Freitas and Smith, 1985, Panagiotopoulos, 1985, Hartmann, 1985, Sewell, 1987, Bazant and Cedolin, 1991). More general optimization problems which are not always based on physical considerations arise in several engineering problems, for instance problems of optimal design of structures, control, identification and reliability analysis of structures and mechanical systems.
E. S. Mistakidis, G. E. Stavroulakis

Superpotential Modelling and Optimization in Mechanics with and without Convexity and Smoothness

Frontmatter
3. Convex Superpotential Problems. Variational Equalities and Inequalities
Abstract
A systematic way for the derivation of variational principles in mechanics goes through the consideration of a potential energy or a complementary energy function. The classical set of possibly nonlinear equations of mechanics from the one side, i.e., the compatibility equations, the equilibrium equations and the material laws, and, from the other side, the optimality conditions of the mathematical optimization theory are integrated in this approach. In fact, the governing relations of the problem either are taken into account in the derivation of the problem or they are produced from the optimality conditions of the associated energy optimization problem.
E. S. Mistakidis, G. E. Stavroulakis
4. Nonconvex Superpotential Problems. Variational and Hemivariational Inequalities
Abstract
Linearity of the kinematics and of the constitutive relations combined with fairly general material stability assumptions guarantee the convexity of a structural analysis problem in either a potential energy or in a complementary energy formulation, as it has been discussed in details in the previous Chapter. In real life applications some of these assumptions may be violated: kinematic nonlinearity which is indispensable for the description of buckling effects, decohesion, damage and fracture problems which introduce material or interface instabilities and softening behaviour in elastoplasticity are some of the applications which lead to nonconvex problems in mechanics. This is due to the fact that most of the materials used are composite, e.g., concrete with steel, fibre reinforced materials etc. Moreover, the composite nature of the materials may appear also at the micromechanical level, e.g., concrete itself is a composition of stone aggregates and cement paste, etc.
E. S. Mistakidis, G. E. Stavroulakis
5. Optimal Design Problems
Abstract
In this Section related problems which arise in the optimal design of structures are formulated as two level optimization problems and are numerically treated by multilevel iterative techniques. Certain classes of optimal material design problems and topology optimization problems formulated by means of the homogenization approach can be treated with this method. This approach can also be used for the rigourous formulation of optimality criteria methods for optimal design of structures. These methods are popular in engineering applications because, roughly speaking, they decompose the difficult optimal design problem into a number of classical structural analysis problems with appropriate, decentralized (at the finite element level) modification rules.
E. S. Mistakidis, G. E. Stavroulakis

Computational Mechanics. Computer Implementation, Applications and Examples

Frontmatter
6. Computational Mechanics Algorithms
Abstract
As it has already been discussed in previous Chapters of this book, a large number of the nonlinear structural analysis problems can be written in a form of a potential or complementary energy optimization problem. Moreover, unilateral effects, friction, plasticity and damage effects introduce inequality restrictions in the optimization problem or require the consideration of more complicated potentials and dissipation functions.
E. S. Mistakidis, G. E. Stavroulakis
7. Applications
Abstract
The aim of this Section is to investigate the properties and the behaviour of the algorithms presented in the previous Chapters. For this reason, several one- and two- dimensional examples are considered involving very few unknowns only. Although these examples are really very simple and can be solved without a computer, they give a good idea of the results that can be expected in the real engineering examples presented later in this Chapter. Indeed, the results of the algorithms can be followed up and certain conclusions are derived.
E. S. Mistakidis, G. E. Stavroulakis
Backmatter
Metadaten
Titel
Nonconvex Optimization in Mechanics
verfasst von
E. S. Mistakidis
G. E. Stavroulakis
Copyright-Jahr
1998
Verlag
Springer US
Electronic ISBN
978-1-4615-5829-3
Print ISBN
978-1-4613-7672-9
DOI
https://doi.org/10.1007/978-1-4615-5829-3