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2015 | Buch

The Theory of Elasticity in the 19th Century Kapitel lesen Erstes Kapitel lesen

Strength of Materials and Theory of Elasticity in 19th Century Italy

A Brief Account of the History of Mechanics of Solids and Structures

verfasst von: Danilo Capecchi, Giuseppe Ruta

Verlag: Springer International Publishing

Buchreihe : Advanced Structured Materials

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book examines the theoretical foundations underpinning the field of strength of materials/theory of elasticity, beginning from the origins of the modern theory of elasticity. While the focus is on the advances made within Italy during the nineteenth century, these achievements are framed within the overall European context. The vital contributions of Italian mathematicians, mathematical physicists and engineers in respect of the theory of elasticity, continuum mechanics, structural mechanics, the principle of least work and graphical methods in engineering are carefully explained and discussed. The book represents a work of historical research that primarily comprises original contributions and summaries of work published in journals. It is directed at those graduates in engineering, but also in architecture, who wish to achieve a more global and critical view of the discipline and will also be invaluable for all scholars of the history of mechanics.

Inhaltsverzeichnis

Frontmatter
Chapter 1. The Theory of Elasticity in the 19th Century
Abstract
Until 1820 there was a limited knowledge about the elastic behavior of materials: one had an inadequate theory of bending, a wrong theory of torsion, the definition of Young’s modulus. Studies were made on one-dimensional elements such as beams and bars, and two-dimensional, such as thin plates (see for instance the work of Marie Sophie Germain). These activities started the studies on three-dimensional elastic solids that led to the theory of elasticity of three-dimensional continua becoming one of the most studied theories of mathematical physics in the 19th century. In a few years most of the unresolved problems on beams and plates were placed in the archives. In this chapter we report briefly a summary on three-dimensional solids, focusing on the theory of constitutive relationships, which is the part of the theory of elasticity of greatest physical content and which has been the object of major debate. A comparison of studies in Italy and those in the rest of Europe is referenced.
Danilo Capecchi, Giuseppe Ruta
Chapter 2. An Aristocratic Scholar
Abstract
In the wake of the French scientists a significant number of Italian scholars of the early 19th century devoted themselves to continuum mechanics and theory of elasticity. The most significant results in this area of mathematical physics were those obtained by Gabrio Piola who, with Ottaviano Fabrizio Mossotti and Antonio Bordoni, was one of the most important mathematicians of the 1830s. In mechanics Piola was influenced by Cauchy, whom he met in his Italian stay in the years 1831–1833; the same cannot be said for mathematics for which Piola had as reference Lagrange. In his work of 1832, La meccanica de’ corpi naturalmente estesi trattata con il calcolo delle variazioni, Piola introduced the components of the stress tensor simply as undetermined multipliers appearing in the application of the principle of virtual work for the study of equilibrium within the continuum. Piola’s approach is now widely used in modern treatises on continuum mechanics.
Danilo Capecchi, Giuseppe Ruta
Chapter 3. The Mathematicians of the Risorgimento
Abstract
The constituting phase of the Kingdom of Italy was a time of recovery of mathematical studies. The political unity facilitated the inclusion of Italian mathematicians in the context of European research, in particular the German one. The internationalization of Italian mathematics is customarily associated with a trip taken in 1858 by some young mathematicians including Francesco Brioschi, Enrico Betti and Felice Casorati in Europe. In a few years we assist in the development of some schools that will maintain their role even in the 20th century. Among them, those promoted by Enrico Betti and Eugenio Beltrami were undoubtedly the most important. In this chapter we present briefly the contribution of two of the leading pioneers and their students.
Danilo Capecchi, Giuseppe Ruta
Chapter 4. Solving Statically Indeterminate Systems
Abstract
The most important event for the history of structural engineering in Italy in the second half of the 1800s was the approval of the law decree of 1859 of the Kingdom of Sardinia, known after its promoter Gabrio Casati, which took force from 1860 in the kingdom and was then extended to all Italy. This decree reformed the whole education system and established the schools for engineering. Among these schools, the most important one, at least at the beginning, was that in Turin. The key person of this school was Giovanni Curioni, heir of Menabrea, who had taught structural mechanics to the pupils of engineering schools before Casati’s reformation. Curioni inherited Menabrea’s researches on the way to solve redundant structures and supervised the graduation thesis that Alberto Castigliano and Valentino Cerruti presented in Turin in 1873, where the former extended Menabrea’s technique and the latter explored more traditional approaches to solve redundant trusses. In this chapter we focus on the contributions by Menabrea, Castigliano and Cerruti, trying to highlight strengths and weaknesses, and showing their connections.
Danilo Capecchi, Giuseppe Ruta
Chapter 5. Computations by Means of Drawings
Abstract
The second half of the 19th century saw a very quick diffusion of graphical statics. Lectures on graphical statics were given in Switzerland (Zurich); in Germany (Berlin, Munich, Darmstadt, Dresden); in the Baltic regions (Riga); in the Austrian-Hungarian empire (Vienna, Prague, Gratz, Brunn); in the United States; in Denmark. The author that mainly developed its techniques was the German scholar Carl Culmann, who placed graphical statics besides the newborn projective geometry. Culmann’s approach was enthusiastically followed in Italy, where, first in Milan at the Higher technical institute, then, after 1870, in many Schools of application for engineers, among which those of Padua, Naples, Turin, Bologna, Palermo, Rome, and, eventually, also in the universities of Pisa and Pavia, courses of graphical statics were activated. The Italian scholar who collected Culmann’s inheritance, and extended it, was Luigi Cremona.
Danilo Capecchi, Giuseppe Ruta
Backmatter
Metadaten
Titel
Strength of Materials and Theory of Elasticity in 19th Century Italy
verfasst von
Danilo Capecchi
Giuseppe Ruta
Copyright-Jahr
2015
Electronic ISBN
978-3-319-05524-4
Print ISBN
978-3-319-05523-7
DOI
https://doi.org/10.1007/978-3-319-05524-4

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