2010122 弹性力学(中英文)(2011).doc

天津大学弹性力学课程教学大纲课程编号：2010122课程名称：弹性力学学 时：96学 分：6学时分配：授课：96 上机：0 实验： 0 实践： 0 实践（周） 0授课学院：机械工程学院适用专业：工程力学先修课程：高等数学，材料力学，张量分析和场论一、课程的性质与目的弹性力学是固体力学学科的分支。该课程是研究和分析工程结构和材料强度和学习有限元法、塑性力学、断裂力学等后续课程的理论基础。课程的基本任务是研究弹性体在外载荷作用下，物体内部产生的位移、变形和应力分布规律，为解决工程结构和材料的强度、刚度和稳定性等问题提供解决思路和方法。二、教学基本要求要求学生对应力、应变等基本概念有较深入的理解，掌握弹性力学解决问题的思路和方法。能够系统地掌握弹性力学的基本理论、边值问题的提法和求解、弹性力学平面问题、柱形杆的扭转和能量原理，了解空间问题、复变函数解法、热应力和弹性波等。三、教学内容弹性力学I1绪论 11弹性力学的任务、内容和研究方法 12弹性力学的发展简史和工程应用 13弹性力学的基本假设和载荷分类 2应力理论 21内力和应力 22斜面应力公式 23应力分量转换公式 24主应力，应力不变量 25最大剪应力，八面体剪应力 26应力偏量 27应力平衡微分方程 28正交曲线坐标系中的平衡方程3应变理论 31位移和应变 32小应变张量 33刚体转动 34应变协调方程 35位移单值条件 36由应变求位移 37正交曲线坐标系中的几何方程4本构关系 41广义胡克定律 42应变能和应变余能 43热弹性本构关系 44应变能正定性5弹性理论的微分提法、解法及一般原理 51弹性力学问题的微分提法 52位移解法 53应力解法 54应力函数解法 55迭加原理 56解的唯一性原理 57圣维南原理6柱形杆问题 61问题的提法，单拉和纯弯情况 62柱形杆的自由扭转 63反逆法与半逆法，扭转问题解例 64薄膜比拟 65较复杂的扭转问题 66柱形杆的一般弯曲7平面问题 71平面问题及其分类 72平面问题的基本解法 73应力函数的性质 74直角坐标解例 75极坐标中的平面问题 76轴对称问题 77非轴对称问题 78关于解和解法的讨论弹性力学II8复变函数解法 81平面问题的复格式 82单连域中复势的确定程度 83多连域中复势的多值性 84级数解法 85保角变换解法 86柯西积分公式的应用9空间问题 91齐次拉梅纳维方程的一般解 92非齐次拉梅纳维方程的解 93位移的势函数分解 94空间轴对称问题 95半空间问题 96接触问题10能量原理 101基本概念和术语 102可能功原理，功的互等定理 103虚功原理和余虚功原理 104最小势能原理和最小余能原理 105弹性力学变分问题的欧拉方程 106弹性力学变分问题的直接解法（一） 107可变边界条件，卡氏定理 108广义变分原理 109弹性力学变分问题的直接解法（二）11热应力 111热传导基本概念 112热弹性基本方程 113热应力问题简例及不产生热应力的条件 114基本方程的求解 115平面热应力问题12弹性波的传播 121杆中的弹性波 122无限介质中的弹性波 123球面波 124平面波 125平面波的发射与折射 126平面波在自由界面处的反射，瑞利波 127勒夫波四、学时分配教学内容授课上机实验实践实践(周)1绪论（包括张量简介）42应力理论123应变理论104本构关系85弹性理论的微分提法、解法及一般原理86柱形杆问题107平面问题 128复变函数解法89空间问题610能量原理1011热应力412弹性波的传播4总计：96五、评价与考核方式平时成绩（出勤、作业等）20%，期末考试成绩80%。六、教材与主要参考资料教 材: 弹性力学，陆明万、罗学富著，清华大学出版社，2001主要参考资料：弹性理论，王龙甫，科学出版社， 1978年；弹性力学教程，王敏中，王炜， 武际可，北京大学出版社， 2002年；TU Syllabus for Elasticity Theory Code:2010122Title:Elasticity TheorySemester Hours:96Credits:6Semester Hour StructureLecture：96 Computer Lab：0 Experiment：0 Practice：0 Practice (Week)：0Offered by:Mechanical Engineering Schoolfor:Engineering MechanicsPrerequisite:Higher mathematics, Material mechanics, Tensor analysis and field theory1. Objective Students should proficiently master of the basic concepts such as stress and strain and the basic theory of elasticity. They should master the presenting and solving of the elastic mechanics problems, plane problem, prismatic bar problems, plane problems and energy principles. In addition, they should know the theories about the space problems, thermal stress and elastic wave. 2. Course Description Elasticity Theory is one of branches of solid mechanics. This course is a theoretical foundation to study and analyze the strength of engineering structures and materials and study the courses such as Finite Element Method, Plasticity Mechanics and Fracture Mechanics. This course mainly study the deformation and stress distribution in the elastic body under loadings. It provides the solving method for the strength, stiffness and stability problems for engineering materials and structures.3. TopicsElasticity I1Introduction 11 Object, contents and study method of theory of elasticity 12 Development history and applications in engineering areas 13 Basic assumptions and classifying of loadings2Stress theory 21 Internal forces and stress 22 Surface tractions on a inclined section 23 Transformation of stress components 24 Principal stresses and stress invariant 25 The maximal shearing stress, octahedral shear stress 26 The stress deviation tensor 27 Differential equations of equilibrium 28 Differential equations of equilibrium in the orthogonal curvilinear coordinates 3Strain theory 31 Displacement and strain 32 Infinitesimal strain tensor 33 Rotation of rigid body 34 Compatibility equation of strain 35 Single-value condition of displacement fields 36 To get the displacement from strain 37 Geometrical equations in orthogonal curvilinear coordinates 4Constitutive relations 41 Generalized Hook law 42 Strain energy and strain complementary energy 43 Thermo-elastic constitutive relations 44 The positive definiteness of the strain energy function5Differential presentation of the elastic mechanics problems 51 Differential presentation of the elastic mechanics problems 52 Displacement solving method 53 Stress solving method 54 Stress functions solving method 55 Superposition principle 56 The uniqueness of solution 57 Saint-Venants Principle6Prismatic bar problems 61 Problems presentation in the case of uniaxial tension and pure bending 62 Free twist of a prismatic bar 63 Inverse method and semi-inverse method, examples of twisting problems 64 Membrane analogy 65 Complicated twisting problem 66 General bending of the prismatic bar7Plane problems 71 Plane problems and classification 72 Basic solving method for plane problems 73 properties of the stress functions 74 Examples in rectangular coordinates 75 Plane problems in polar coordinates 76 Axisymmetric problems 77 Non axisymmetric problems 78 Discussions on the solutions and the solving methodsElasticity II8Complex function method 81 complex forms of plane problems 82 complex potential in single connected domain 83 multi-value of complex potential in multi-connected domain 84 series method 85 conformal transformation method 86 applications of Cauchy integral formulations9Three dimensional problems 91 General solutions of L-N equations 92 Solutions of the non-homogeneous L-N equations 93 Decomposition of displacement potential function 94 Three dimensional symmetrical problems 95 Half space problems 96 Contact problems10Energy principle 101 Basic concepts and terminology 102 Possible work principle, reciprocal theorem 103 Principle of virtual work and Principle of complementary virtual work 10 4 Principle of minimum potential energy and principle of minimum complementary energy 105 Euler equations for the variational problems in elastic mechanics 106 Direction solving method for the variational problems in elastic mechanics: I 107 Moving boundary condition，Castiglianos theorem 108 Generalized variational problems 109 Direction solving method for the variational problems in elastic mechanics: II11Thermal stress 111Concept of heat conduct 112Basic equations of thermo-elasticity 113Examples of thermal stress and condition of zero thermal stress 114Solving of basic equations 115Plane thermal stress problems12Propagation of elastic wave 121Elastic wave in bar 122Elastic wave in infinite medium 123Spherical wave 124Plane wave 125Reflection and refraction of elastic wave 126Reflection of elastic wave at free interface and Rayleigh wave 127Love wave4. Semester