ElasticityA Brief Lecture Note(Incomplete)Guidelines(1) The lectures will be given in Chinese, but the Lecture Notes will be written in English (well, rather informal English). The bilingual approach is anticipated to offer surprising advantages such as lowering the language barrier and getting familiar with English vocabularies that will be in desperate use in the years to come. I also foresee the potential to expand the lecture notes to a formally writing textbook.(2) The contents are selected to highlight the physical insights of elasticity, to promote the readability by frequently citing the historic events and perspectives, enumerating the new applications of elasticity, and addressing the new research thrusts of elasticity in the past 50 years. (3) The lectures will be given mainly in a traditional way of chalks plus blackboard. For a course with a perfect logic system such as Elasticity, I cannot find a better way other than the old tradition. Let the imaginative minds of the students follow the trace of a chalk tip on blackboard.(4) Beside lectures, the course should be complemented through intensive readings. Twelve references are appointed. Discussions among students about their contents are encouraged.(5) The homework will take 20% of the overall score, the mid-term exam another 20%, while the final exam (open book) will take the rest 60%.(6) For those students who are eager to explore more challenging issues of elasticity, a total of 10 to 15 advanced problems will be proposed. A student may solve any one of these problems, write in the form of a report, and submit it to the instructor. These reports will be graded by the instructor, and those scored higher than 90/100 can be used as substitutes for their final exams. Only the reports that solve the problem earliest among the entire class or solve the problem in a unique approach are qualified as the substitutes of the final exams.Who Cares?Elasticity is the most important course in the field of solid mechanics, and also tops the list for the key courses in a broader area of engineering mechanics. Elasticity goes a long way in its applications, spanning length scales from nanometers for a carbon nanotube to kilometers of a geological formation. Without the mastery of elasticity, you are incompetent in doing any serious works as a professional in engineering mechanics, even not ranked as a capable engineer.Beside its contents, elasticity is a course that exemplifies the beauty of mathematical physics. Many concepts and methods in modern science and engineering are originated from elasticity. However, elasticity is also a quite difficult course to learn, please be prepared for it. You definitely need to spend 5 times as the lecture hours to grasp the materials. Without competitors, it will be The Course that burdens you the most in this semester. As one of the elite courses in Tsinghua University, we are planning a feast of materials that would be unparallel in the most universities in the world (the exceptions are MIT and Ecole Polytechnique). Some of the contents prepared in this lecture note will surpass the coverage of the textbook by Mingwan LU and Xuefu LUO.Pre-requestThe students are required to have first courses on Calculus, Mathematical Physics (including the introduction on Complex Analysis, Operational Calculus, and PDE) and Strength of Materials. We also assume you have a preliminary knowledge on Continuum Mechanics, familiar with the concepts of stress, strain and balance laws. The knowledge on the indicial notation of tensors is also assumed. For those students who are lack of this preliminary knowledge, we suggest them to read the first four chapters and the relevant appendices in the textbook by Lu and Luo.Contents1 Introduction1.1 History of Elasticity1.2Applications of Elasticity2Elasticity of Solids2.1Definition of Elasticity2.2Two Physical Origins of Elasticity2.3Tensor Description of Elasticity2.4Physical Foundation of Elastic Symmetry3Field Equations of Elasticity - Differential Formulation3.1 Balance Equations of Momentum and Moment3.2Compatibility Equation3.3Field Equations of Dynamic Elasticity3.4Quasi-static Field Equations3.5Constraints3.6Boundary Conditions3.7Formulation of Elasticity4.Prismatic Rods4.1Formulation for Prismatic Rods4.2Uniaxial Tension and Pure Bending4.3Corrective Solution (Saint Venant Decay)4.4Free Torsion of Prismatic Rods4.5Inverse and Semi-inverse Solutions4.6Formulation of Anti-plane Problems5Plane Problems Theory and Methods5.1Plane Strain and Plane Stress5.2Planar Anisotropic Case5.3Planar Isotropic Case Biharmonic Equation5.4Solution in Cartesian Coordinates5.5Solution in Polar Coordinates5.6Kolosov-Muskhelishvilli Method6Plane Problems Applications6.1Stress Concentration6.2Curved Beams6.3Wedges6.4Po