Strength of Materials and Theory of Elasticity in 19th Century Italy: A Brief Account of the History of Mechanics of Solids and Structures (Advanced Structured Materials, 52)

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 Preface 6 Editorial Considerations 8 Contents 9 1 The Theory of Elasticity in the 19th Century 14 1.1 Theory of Elasticity and Continuum Mechanics 14 1.1.1 The Classical Molecular Model 16 1.1.2 Internal Criticisms Toward the Classical Molecular Model 26 1.1.3 Substitutes for the Classical Molecular Model 30 1.1.4 The Perspective of Crystallography 38 1.1.5 Continuum Mechanics in the Second Half of the 19th Century 44 1.2 Theory of Structures 48 1.2.1 Statically Indeterminate Systems 50 1.2.2 The Method of Forces 52 1.2.3 The Method of Displacements 55 1.2.4 Variational Methods 60 1.2.5 Applications of Variational Methods 63 1.2.6 Perfecting of the Method of Forces 69 1.3 The Italian Contribution 79 1.3.1 First Studies in the Theory of Elasticity 83 1.3.2 Continuum Mechanics 84 1.3.3 Mechanics of Structures 86 References 89 2 An Aristocratic Scholar 95 2.1 Introduction 95 2.2 The Principles of Piola's Mechanics 98 2.3 Papers on Continuum Mechanics 101 2.3.1 1832. La meccanica de' corpi naturalmente estesi trattata col calcolo delle variazioni 105 2.3.2 1836. Nuova analisi per tutte le questioni della meccanica molecolare 112 2.3.3 1848. Intorno alle equazioni fondamentali del movimento di corpi qualsivogliono 116 2.3.4 1856. Di un principio controverso della meccanica analitica di lagrange e delle sue molteplici applicazioni 121 2.3.5 Solidification Principle and Generalised Forces 121 2.4 Piola's Stress Tensors and Theorem 125 2.4.1 A Modern Interpretation of Piola's Contributions 126 2.4.2 The Piola-Kirchhoff Stress Tensors 128 References 131 3 The Mathematicians of the Risorgimento 134 3.1 Enrico Betti 134 3.1.1 The Principles of the Theory of Elasticity 138 3.1.2 The Reciprocal Work Theorem 143 3.1.3 Calculation of Displacements 146 3.1.4 The Saint Venant Problem 149 3.2 Eugenio Beltrami 152 3.2.1 Non-Euclidean Geometry 155 3.2.2 Sulle equazioni generali della elasticità 157 3.2.3 Papers on Maxwell's Electro-Magnetic Theory 160 3.2.4 Compatibility Equations 164 3.2.5 Beltrami-Michell's Equations 166 3.2.6 Papers on Structural Mechanics 167 3.3 The Pupils 171 3.3.1 The School of Pisa 171 3.3.2 Beltrami's Pupils 179 References 185 4 Solving Statically Indeterminate Systems 189 4.1 Scuole d'applicazione per gl'ingegneri 189 4.1.1 The First Schools of Application for Engineers 192 4.2 The Teaching 198 4.3 Luigi Federico Menabrea 201 4.3.1 1858. Nouveau principe sur la distribution des tensions 204 4.3.2 1868. Étude de statique physique 214 4.3.3 1875. Sulla determinazione delle tensioni e delle pressioni ne' sistemi elastici 218 4.3.4 Rombaux' Application of the Principle of Elasticity 220 4.4 Carlo Alberto Castigliano 224 4.4.1 1873. Intorno ai sistemi elastici 227 4.4.2 1875. Intorno all'equilibrio dei sistemi elastici 237 4.4.3 1875. Nuova teoria intorno all'equilibrio dei sistemi elastici 239 4.4.4 1879. Théorie de l'équilibre des systémes élastiques et ses Applications 243 4.4.5 A Missing Concept: The Complementary Elastic Energy 252 4.5 Valentino Cerruti 256 4.5.1 Sistemi elastici articolati. A Summary 257 4.5.2 Trusses with Uniform Resistance 262 4.5.3 Statically Indeterminate Trusses 265 References 271 5 Computations by Means of Drawings 276 5.1 Graphical Statics 276 5.2 Graphical Statics and Vector Calculus 280 5.3 The Contributions of Maxwell and Culmann 282 5.3.1 Reciprocal Figures According to Maxwell 282 5.3.2 Culmann's Graphische Statik 287 5.4 The Contribution of Luigi Cremona 296 5.4.1 The Funicular Polygon and the Polygon of Forces as Reciprocal Figures 298 5.4.2 The Lectures on Graphical Statics 311 5.4.3 Cremona's Inheritance 314 References 323 Appendix A Quotations 326 Index 398 Front Matter....Pages i-xiii The Theory of Elasticity in the 19th Century....Pages 1-81 An Aristocratic Scholar....Pages 83-121 The Mathematicians of the Risorgimento....Pages 123-177 Solving Statically Indeterminate Systems....Pages 179-265 Computations by Means of Drawings....Pages 267-316 Back Matter....Pages 317-393