Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge Texts in Applied Mathematics
Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge Texts in Applied Mathematics
复制标题
DOI：
10.1115/1.1579456
复制
发表时间：
2003-07
影响因子：
14.3
通讯作者：
JC Robinson;Christophe Pierre
中科院分区：
文献类型：
--
作者：
JC Robinson;Christophe Pierre
这是一本正式的介绍连续介质力学的书，主要是为应用数学家和理论工程师写的，保持了理性连续介质力学的风格，由七个章节组成。前言对其内容作了简要的描述。第一章介绍了在中间水平上使用符号和笛卡尔张量符号的张量。讨论了对称张量的谱性质及其极分解、简单各向同性张量函数以及微分和积分规律。本章最后介绍了群中正交群在单模群中的极大性的推导。第二章是运动学；介绍了运动函数及其空间和时间导数，以及欧拉和拉格朗日描述中建议的应变和应变率的各种度量。第3章有一个模糊的标题，“控制方程”，但致力于质量守恒定律，线性和角动量，以及能量和熵平衡。它还涵盖了柯西应力张量的性质的介绍，并引入了力学方程的变分公式。第四章讨论本构关系。讨论了坐标系无差异在观察者变化下的不变性和在刚体运动叠加下的不变性。
This is a formal book on introductory continuum mechanics, written primarily for applied mathematicians and theoretical engineers kept in the style of rational continuum mechanics and consisting of seven chapters. The preface provides a brief descriptive coverage of its content. Chapter 1 gives an introduction into tensors at an intermediate level using symbolic and Cartesian tensor notation interchangingly. The spectral properties of symmetric tensors and their polar decomposition, simple isotropic tensor functions as well as differentiation and integral laws are discussed. The chapter ends with an introduction to groups where the maximality of the orthogonal group in the unimodular group is derived. Chapter 2 is devoted to kinematics; the motion function and its spatial and time derivatives are introduced as are various measures of strain and rates of strain as suggested in the Eulerian and Lagrangian description.Chapter 3 carries the vague title,‘‘Governing Equations,’’but is devoted to the conservation laws of mass, linear and angular momenta, and the energy and entropy balances. It also covers a presentation of the properties of the Cauchy stress tensor and introduces into a variational formulation of the mechanical equations. Constitutive relations are dealt with in Chapter 4. Frame indifference is discussed both as invariance under a change of observer as well as one under a superimposed rigid body motion.