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.