Computational Methods in Physics and Engineering pdf epub mobi txt 电子书 下载 2026

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出版者:World Scientific Publishing Company

作者:Samuel S. M. Wong

出品人:

页数:520

译者:

出版时间:1997-06

价格:USD 34.00

装帧:Paperback

isbn号码:9789810230432

丛书系列:

图书标签:

• 计算物理
• 计算工程
• 数值方法
• 科学计算
• 物理
• 工程
• 数学建模
• 算法
• 模拟
• 高等教育

好的，这是一份关于另一本名为《Advanced Solid Mechanics and Continuum Theory》的图书的详细简介，内容完全聚焦于该书本身，不涉及您提到的《Computational Methods in Physics and Engineering》。 Advanced Solid Mechanics and Continuum Theory A Comprehensive Exploration of Material Response Under Stress and Strain Preface to the Second Edition The field of solid mechanics, the cornerstone of mechanical and civil engineering, materials science, and increasingly, modern physics, continues to evolve at a rapid pace. The transition from classical elasticity, rooted in the work of Cauchy and Navier, to modern theories incorporating non-linearity, damage, and multi-scale phenomena demands a rigorous yet accessible exposition. This second edition of Advanced Solid Mechanics and Continuum Theory aims to serve as that definitive reference. We have retained the foundational rigor expected by graduate students and seasoned researchers while significantly expanding the coverage of contemporary topics, including finite deformation kinematics, anisotropic material models, and the treatment of modern composite structures. Our goal remains clear: to provide a unified mathematical framework for understanding how materials behave when subjected to mechanical loads, bridging the gap between abstract tensor analysis and tangible engineering prediction. --- Part I: Mathematical Foundations and Kinematics of Deformation This section establishes the essential mathematical language required for advanced continuum mechanics, moving beyond simple vector calculus into the realm of tensors and differential geometry relevant to describing complex spatial transformations. Chapter 1: Tensors, Coordinate Systems, and Transformations This chapter meticulously details the necessary algebraic toolkit. It begins with a refresher on vector spaces before diving into the rigorous definition of tensors—contravariant, covariant, and mixed types. Detailed treatment is given to tensor transformations under rigid body rotations, which forms the basis for defining material symmetry. We introduce the concept of the transformation of physical components versus coordinate components, a critical distinction often overlooked in introductory texts. Furthermore, the derivation and utility of the metric tensor in curvilinear coordinate systems (including cylindrical and spherical coordinates) are established, emphasizing its role in defining invariants and strain measures. Chapter 2: Kinematics of Continuous Bodies: Description of Motion Here, we shift focus to the geometric description of how a body deforms in space and time. The Lagrangian (material) description and the Eulerian (spatial) description are introduced and contrasted. The concepts of displacement, strain, and velocity fields are formalized using tensor notation. A deep dive into the finite deformation kinematics is undertaken, introducing the Deformation Gradient ($mathbf{F}$), the Jacobian determinant ($J$), and the rigorous derivation of the Green-Lagrange strain tensor and the Almansi strain tensor. This section critically analyzes the kinematics of infinitesimal strain theory as a first-order approximation of the finite strain measures, clearly delineating the conditions under which each is applicable. Special attention is paid to the decomposition theorems (e.g., polar decomposition) that separate local rotation from pure strain. --- Part II: Governing Equations and Linear Elasticity The core principles of conservation—mass, momentum, and energy—are translated into the language of continuum mechanics, leading directly to the field equations that govern mechanical response. Chapter 3: Conservation Laws in Continuum Mechanics This chapter formulates the fundamental balance equations. The balance of linear momentum yields Cauchy's equations of motion in both spatial and material representations. The Cauchy stress tensor, defined through the action of internal forces across an infinitesimal surface, is rigorously introduced. We then develop the balance of angular momentum, proving that the Cauchy stress tensor must be symmetric in the absence of body moments. Further attention is given to the concept of the Piola-Kirchhoff stress tensors ($mathbf{P}$ and $mathbf{S}$), essential for linking spatial observations back to the undeformed body configuration. The chapter concludes with a treatment of constitutive assumptions necessary to close the system of equations. Chapter 4: Linear Elastic Solids: Isotropic Materials This cornerstone chapter explores the simplest, yet most widely used, constitutive model: linear, homogeneous, isotropic elasticity. The derivation of Hooke's Law for isotropic materials is presented via symmetry arguments, resulting in the two-parameter formulation using Lamé constants ($lambda, mu$) or the engineering constants ($E, u$). Comprehensive coverage is given to the fundamental solutions of the equilibrium equations in the absence of body forces, including the classic plane stress and plane strain problems. The chapter culminates in the detailed analysis of the Navier-Lame equations and their application to problems like the Boussinesq problem (point load in a half-space) and the analysis of thick-walled cylinders under pressure. Chapter 5: Anisotropy and Heterogeneity in Elasticity Moving beyond the simplification of isotropy, this section addresses materials whose properties depend on direction, such as crystals, wood, and fiber-reinforced composites. The general form of the linear constitutive equation relating the generalized stress and strain tensors using the stiffness tensor ($mathbb{C}$) is established, emphasizing the requirement for material symmetry (e.g., transverse isotropy, orthotropy). Techniques for reducing the 4th-rank stiffness tensor to engineering constants in specific symmetry classes (Voigt notation) are provided, along with methods for calculating effective properties in laminated composites using rule-of-mixtures and basic lamination theory principles. --- Part III: Energy Methods and Stability This part transitions from direct solution of differential equations to the powerful alternative approach utilizing energy principles, which are often more amenable to complex geometries and variational formulations. Chapter 6: Strain Energy Density and Variational Principles The concept of strain energy density function ($W$) is formalized as the stored energy per unit undeformed volume. We distinguish between hyperelastic materials (where stress is derived from a potential) and non-hyperelastic materials. The Principle of Minimum Potential Energy (PMPE) is derived, establishing the variational foundation for structural analysis. The chapter then explores the complementary energy approach, leading to the Reissner-Hellinger principle and the Hertz-Love-Kirchhoff hypotheses used in plate theory, illustrating how these principles directly inform Finite Element Method formulations. Chapter 7: Buckling, Instability, and Bifurcation Phenomena This chapter tackles the nonlinear aspects of structural response beyond simple proportional loading. It focuses on the critical load phenomenon where a structure loses its stable equilibrium configuration. The classical Euler buckling load for columns is derived through energy methods and eigenvalue analysis of the linearized stability equations. The treatment extends to elastic stability in continuous media, introducing the concept of the Tangent Modulus Theory and the fundamental concepts of bifurcation analysis in the context of imperfect structures, providing a rigorous basis for understanding catastrophic failure modes in slender components. --- Part IV: Viscoelasticity and Damage Mechanics The final section addresses the time-dependent behavior and material degradation inherent in polymers, biological tissues, and engineering materials under long-term loading. Chapter 8: Linear Viscoelasticity: Time-Domain Responses This section recognizes that for many real materials, strain is not instantaneously proportional to stress. Viscoelasticity is introduced using the analogy between mechanical systems (springs and dashpots) and electrical circuits. The Boltzmann Superposition Principle is established, allowing constitutive relations to be written in terms of time-dependent relaxation or creep functions. Detailed analysis is performed on standard models—Maxwell, Kelvin-Voigt, and the Standard Linear Solid—examining their creep compliance and stress relaxation functions. The relationship between these time-domain functions and their frequency-domain counterparts (complex modulus) is explored using Laplace transforms. Chapter 9: Introduction to Damage and Fracture Mechanics The final chapter addresses the initiation and propagation of cracks. Fracture mechanics is introduced through the concepts of stress concentration around singularities. The chapter develops the Griffith Energy Release Rate Criterion and its relationship to the stress intensity factor ($K$). For materials exhibiting plasticity before fracture, the Dugdale-Barenblatt strip-yield model is presented as a transitional concept. Finally, the concept of continuum damage mechanics (CDM) is introduced, treating damage as a scalar internal variable that degrades the effective stiffness tensor of the material, providing a pathway to modeling progressive material failure beyond simple brittle fracture. --- Appendices Appendix A: Green’s Theorem and Divergence Theorem in Curvilinear Coordinates Appendix B: Matrix Representation of the Fourth-Rank Stiffness Tensor Appendix C: Fundamentals of Thermoelasticity (Coupled Theory) Advanced Solid Mechanics and Continuum Theory is designed not merely as a textbook but as a permanent reference, offering the depth and mathematical precision required to tackle the most challenging problems in contemporary materials science and structural engineering.

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这本书的封面设计非常吸引人，那种深邃的蓝色调和简洁的字体排版，一下子就让人感觉到这是一本严谨的学术著作。我是在寻找一本能够系统梳理经典物理学计算方法的书籍时发现它的。拿到手上才发现，它的内容深度远超我的预期。书中对数值积分和微分方程求解的介绍极为详尽，特别是作者对于不同方法的适用条件和收敛性分析，简直是一场思想的盛宴。例如，在处理薛定谔方程的数值解时，书里不仅仅罗列了算法，更是深入剖析了有限元法与有限差分法之间的哲学差异，以及如何在实际工程问题中权衡两者的优劣。我尤其欣赏作者在章节末尾设置的“挑战性思考”部分，这些问题往往需要读者跳出既有的框架去思考，真正锻炼了解决复杂问题的能力，而不是简单地套用公式。这本书的排版也十分精良，公式的推导过程清晰明了，即便是复杂的矩阵运算，也能被分解得井井有条，这对需要经常与数学工具打交道的科研工作者来说，无疑是一大福音。

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作为一名在流体力学领域工作的工程师，我一直苦于找不到一本能够将数学物理方法与实际工程模拟紧密结合的教材。这本书的出现，极大地弥补了我的遗憾。它对偏微分方程的数值解，特别是对 Navier-Stokes 方程求解时所涉及的稳定性和离散化误差的讨论，非常具有实战价值。作者在处理对流项带来的数值振荡问题时，引入了迎风格式（Upwind Schemes）并详细对比了其与中心差分法的差异，这种务实的态度在学术著作中是相当难得的。我尝试用书中介绍的方法去重现一些经典湍流模拟的简化模型，发现其代码的逻辑结构和变量命名都非常直观，极大地缩短了我从理论到实现的过渡时间。总的来说，这本书与其说是一本“方法”的书，不如说是一本“解决问题”的工具箱，里面的每一个工具都经过了精心的打磨和实战检验，拿起来就能用，而且用得放心。

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这本书的结构安排，体现了作者对学习者认知曲线的深刻理解。它并非按照传统的学科分类来组织内容，而是更侧重于从“问题类型”出发，逐步提升难度和抽象层次。一开始从最基础的插值和拟合入手，为后续的微分方程求解打下坚实的代数基础；随后自然过渡到积分和线性系统求解，这些都是现代计算物理的基石。最让我感到惊喜的是，作者在讲述优化算法时，没有仅仅停留在梯度下降法上，而是引入了更先进的拟牛顿法和全局优化策略，比如模拟退火。这种“步步为营，层层递进”的编写手法，使得即便是初次接触数值计算的读者，也能在清晰的逻辑引导下，逐步建立起完整的知识体系，而不会被突如其来的复杂概念所击倒。阅读体验非常流畅，仿佛有一位经验丰富、耐心十足的导师在身旁为你细致讲解每一个环节。

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初读此书时，我最大的感受是它在理论深度与实用性之间找到了一个近乎完美的平衡点。很多同类的书籍要么过于偏重理论的推导，导致读者在实际操作中无从下手；要么就是过于偏重软件实现，牺牲了对底层原理的理解。然而，这本书恰好避免了这些陷阱。它在讲解傅里叶变换和快速傅里叶变换（FFT）时，不仅详细解释了其背后的群论基础，还非常贴心地附上了关于如何在实际数据分析中处理噪声和周期性边界条件的具体指导。我印象最深的是关于蒙特卡洛方法的章节，作者没有停留在基础的随机数生成和采样上，而是深入探讨了马尔可夫链蒙特卡洛（MCMC）在复杂高维积分问题中的应用，特别是针对贝叶斯统计推断的例子，简直是教科书级别的范例。这本书的语言风格是那种沉稳而富有洞察力的，它引导你思考“为什么”而不是仅仅告诉你“怎么做”，这种深层次的教学方式，让学习过程充满了探索的乐趣。

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坦白说，这本书的厚度初看之下可能会让人望而却步，但一旦翻开，你就会发现时间过得飞快。作者在描述随机过程和误差分析时所展现出的严谨性，让我深感敬佩。例如，在讨论误差传播时，他不仅仅给出了标准差的公式，还结合了信息论的视角，探讨了有效有效信息量如何在数值计算中丢失，这一点在处理高精度实验数据还原时至关重要。书中的示例代码（虽然没有直接包含在正文中，但其描述的逻辑清晰到可以直接用任何语言重写）都紧密围绕着物理学中最核心的问题展开，比如量子隧穿效应的数值模拟，或者经典力学中的混沌动力学轨迹预测。这本书更像是一部里程碑式的参考书，它所涵盖的知识广度和深度，确保了它在未来很长一段时间内，都将是计算物理与工程领域不可或缺的经典读物。

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