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In recent years, the Finite Element Methods FEM were more and more
employed in development and design departments as very fast working
tools in order to determine stresses, deformations,
eigenfrequencies etc. for all kinds of constructions under complex
loading conditions. Meanwhile. very effective software systems have
been developed by various research teams although some mathematical
problems (e. g. convergence) have not been solved satisfac torily
yet. In order to make further advances and to find a common
language between mathe maticians and mechanicians the "Society for
Applied Mathematics and Mechanics" (GAMM) agreed on the foundation
of a special Committee: "Discretization Methods in Solid Mechanics"
focussing on the following problems: - Structuring of various
methods (displacement functions, hybrid and mixed approaches, etc.
>, - Survey of approach functions
(Lagrange-/Hermite-polynominals, Spline-functions), - Description
of singularities, - Convergence and stability, - Practical and
theoretical optimality to all mentioned issues (single and
interacting). One of the basic aims of the GAMM-Committee is the
interdisciplinary cooperation between mechanicians, mathematicians,
and users which shall be intensified. Thus, on September 22, 1985
the committee decided to hold a seminar on "Structural
Optimization" in order to allow an exchange of experiences and
thoughts between the experts of finite element methods and those of
structural optimization. A GAMM-seminar entitled "Discretization
Methods and Structural Optimization - Procedures and Applications"
was hold on October 5-7, 1988 at the Unversity of Siegen."
Stiffened steel plates have been used for many years especially in
the fields of bridges, ships and towers. They are very efficient
components of a structure, having both a high strength - to -weight
ratio and a pleasing appearance. However, in some cases they have a
tendency to buckle in one mode or even two simultaneous modes. In
existing codes of practice designers have been supplied with many
comprehensive rules so that they can calculate failure loads
(collapse conditions) and the loads at which first yield occurs
(serviceability conditions). A key calculation in each of these
determinations is that which gives the critical stress. However,
the critical stress depends upon many features such as the boundary
conditions along the sides and at the ends and the geometry of the
cross-section. A short stiffened plate may buckle locally whereas a
longer panel with the same cross-section may buckle as a wide Euler
column. The labour involved in checking individual trial designs is
often formidable. It is the aim of this book to try to ease this
burden for designers. They will find that it is a simple matter to
use this book as if it were a catalogue of sectional properties.
Indeed the tables contained herein present the usual section
properties but they also indicate the stresses at which local
buckling occurs and the panel length beyond which global (i.e.
Euler type) buckling governs.
6 stehen. Soweit mtfglich, wurden far alle hehandelten Rerechnungs-
methoden ei nfache Rei spi el e aufgenommen: di ese Rei spi el e
werden, wie in Teil 1, Mit dem Programmsystem SMIS geltfst. nie
Verfasser mtfchten sich hei Frau II. Lechtenhtfhmer fUr die sorgf
ltige Erledigung der umfangreichen Schreibarhei- ten auf einer
Textverarbeitungsanl age und hei Frau II. Hein- ze fUr die
Anfertigung der Zeichnungen hedanken. nie Rerechnung der meisten
Reispiele erfolgte auf den Rechenanlagen der lIniversit t r.
esamthochschule Essen, die Reispiele 6. 3,8. 2 und 8. 4 wurden auf
der Rechenanlage der Firma Rilfinger ft Rerger in Mannheim
herechnet. 7 Inhaltsverzeichnis Vorwort 5 Inhalt 7 Rezeichnungen 10
1 EinfUhrung 12 1. 1 Statische, quasistatische und dynamische
Relastung 12 1. 2 Zur Entwicklung der Raudynamik 13 1. 3
Erfahrungswerte und Abschatzungen 20 1. 4 Rerechnungsvorschriften
22 2 Schwingungen mit einem Freiheitsgrad 24 2. 1 Grundbegriffe 24
2. 2 Die nifferentialgleichung der Rewegung 28 2. 3 Freie
Schwingungen 34 2. 4 Harmonische Relastung 40 2. 5 Periodische
Relastung - Fourierreihe 45 2. 6 Nichtperiodische Relastung -
Fourierintegral 48 2. 7 Das Duhamel - Integral 52 2. 8 NumerisC:
'he Integration der Rewegungsgleichung 56 2. 9 Antwortspektfen 60
('7 3 ElementMatrizen 3. 1 Dynamische Elementsteifigkeitsmatrix 67
3. 2 Die konsistente Elementmassenmatrix 78 3. 3 Die konzentrierte
Elementmassenmatrix 84 4 Freie ungedampfte Schwingungen von
Stabwerken R5 4. 1 Aufstellung der Rewegungsgleichungen 85 4. 2
Freie Schwingungen 88 8 Inhaltsverzeichnis 5 Erzwungene ungedSmpfte
Schwingungen von Stabwerken 112 5.
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