The present study provides an overview of modeling and discretization aspects in finite element analysis of thin-walled structures. Shell formulations based upon derivation from three-dimensional continuum mechanics, the direct approach, and the degenerated solid concept are compared, highlighting conditions for their equivalence. Rather than individually describing the innumerable contributions to theories and finite element formulations for plates and shells, the essential decisions in modeling and discretization, along with their consequences, are discussed. It is hoped that this approach comprises a good amount of the existing literature by including most concepts in a generic format. The contribution focuses on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics. Although application to dynamics and problems involving material nonlinearities is straightforward, these subjects are not taken into account explicitly.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470091355.ecm026

Szabó, I., Geschichte der mechanischen Prinzipien und ihrer wichtigsten Anwendungen. Basel‐Stuttgart. Birkhäuser Verlag. 1977. XV, 491 S., Fr. 48,–

Models and finite elements for thin-walled structures

In a period of a few decades, the formulation known as the principle of virtual power (PVP) has gained a prominent place among the most efficient tools in the thermomechanics of continua. Strongly marked by a “continental” (French-Italian) influence, it has successfully incorporated the basic invariances of modern continuum mechanics while capturing the spirit of twentieth-century analysis (generalized functions or distributions) in which it became synonymous of weak formulation. It proved to provide the surest and safest way to formulate complex theories of continua (so-called “generalized continuum mechanics”, theory of coupled fields, etc) and approximate or generalized theories of structural members and the associated natural boundary conditions while preparing the way for the full thermomechanical formulation, providing the best setting for the proof of various mathematical theorems, and paving the way for modern numerical methods. The present contribution, illustrated by many examples of varying complexity, emphasizes the role of Paul Germain (1920–2009) in this formulation. The author, himself an active contributor and a never tired propagandist of the method, has participated in these developments during four decades and presents here his witness but critical viewpoint, highlighting the difficult points and also the esthetically pleasing ones where necessary.

The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool

Fluid flow and mixing in secondary metallurgy

Analytical calculation of in-plane response of plates with concentrated masses to impact and application to pyroshock simulation

Die Kontrolltheorie beschaftigt sich mit der Steuerungdynamischer Systeme im Hinblick auf die Erreichung gewunschter Ziele. Das Problem der Optimierung dynamischer Systeme besteht darin, Funktionen zu finden, welche ein gegebenes Zielfunktional unter gewissen Nebenbedingungen optimieren. Zweck des vorliegenden Beitrages ist es, einen elementaren Zugang zumMaximumprinzip sowie dessen okonomischer Interpretation zu bieten. Die Ermittlung optimaler Kontrolltrajektorien wird anhand einiger einfacher Beispiele illustriert (Kassenhaltung, Produktionsund Investitionsplanung, Werbe- und Preispolitik, Wissenschafts-Management). Ohne Vollstandigkeit anzustreben, wird daneben eine Reihe weiterer Anwendungen desdeterministischen Maximumprinzips im Operations Research skizziert. Einen wesentlichen Vorteil, den das Maximumprinzip etwa im Vergleich zur dynamischen Programmierung aufweist, stellt die Moglichkeitqualitativer Einsichten in die Struktur der Losungspfade dar, die haufig schon ohne komplette Losung des Kontrollproblems zur Aufdeckung interessanter okonomischer Zusammenhange fuhren.

Szabó, I., Geschichte der mechanischen Prinzipien und ihrer wichtigsten Anwendungen. Basel‐Stuttgart. Birkhäuser Verlag. 1977. XV, 491 S., Fr. 48,–

Citations

Models and finite elements for thin-walled structures

The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool

Fluid flow and mixing in secondary metallurgy

Analytical calculation of in-plane response of plates with concentrated masses to impact and application to pyroshock simulation

Anwendungen des Maximumprinzips im Operations Research, Teil 1

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