彈性力學

譚建國

國立成功大學土木工程學系

滄海書局

2019

ISBN 978-986-363-090-6

中文介紹

彈性力學為固體力學的基礎科目，坊間不乏經典的外文書籍，但少有完備的中文教材。本書旨在提供一本適合大學部高年級生與研究生研習彈性力學簡明嚴謹而深入淺出的中文課本。

全書共十一章，包括: 1. 數學預備知識。2. 應力分析。3. 應變分析。4. 彈性材料與彈性力學問題的架構。5. 若干基本問題。6. 二維問題。7. 柱體之扭轉與撓曲。8. 複變函數解法。9. 三維問題。10. 彈性力學的變分原理與應用。11. 狀態空間法與異向性彈性力學。本書兼顧理論與應用，著重基本概念與理論架構，以及解析問題的思路與數學方法，必要的數學知識適時闡明或以附錄補充。各章習題多為輔助讀者理解內文而設計的問題與註解。

最後一章闡述基於哈米頓力學發展的狀態空間解析模式及其在異向性彈性力學的應用，主要內容是依據作者研究相關課題所發表的論著綜理成章，期能有助讀者研究其他課題。

Elasticity

Tarn, Jiann-Quo

Abstract

     Elasticity is a classical subject of long standing, and there is no lack of good monographs on its theory and applications. However, textbooks which are concise yet provide the reader with sufficient details and mathematical rigor are in short supply. This book is intended to provide a self-contained and easy-to-understand text in Chinese for advanced undergraduates and graduate students in the field of engineering mechanics and related disciplines.

     The book consists of eleven chapters: 1. Mathematical Prerequisites. 2. Analysis of Stress. 3. Analysis of Strain. 4. Linear Elastic Materials, Framework of Problems of Elasticity. 5. Some Elementary Problems. 6. Two-Dimensional Problems. 7. Torsion and Flexure of Prismatic Bars. 8. Complex Variable Methods. 9. Three-Dimensional Problems. 10. Variational Principles of Elasticity and Applications. 11. State Space Approach to Anisotropic Elasticity. Throughout the book, the basic ideas and analytic approaches are emphasized, with many examples of theoretical interest and practical importance to illustrate the underlying theory and solution methods. A set of problems which complement the subject of each chapter is included. For easy understanding of the contents, background knowledge is provided wherever appropriate and essential prerequisites are supplemented in the appendices.

    The final chapter delineates the Hamiltonian state space formalism of anisotropic elasticity and its applications. The materials are essentially derived from our publications on the relevant subjects. We believe an introduction to this versatile approach is useful for the interested reader to explore other research areas.