具體描述
Explore a Unified Treatment of the Finite Element Method
The finite element method has matured to the point that it can accurately and reliably be used, by a careful analyst, for an amazingly wide range of applications. With expanded coverage and an increase in fully solved examples, the second edition of Finite Element Analysis: Thermomechanics of Solids presents a unified treatment of the finite element method in theremomechanics, from the basics to advanced concepts.
作者簡介
目錄資訊
Introduction
Overview of the Finite Element Method
Mesh Development
Mathematical Foundations: Vectors and Matrices
Introduction
Vectors
Matrices
Eigenvalues and Eigenvectors
Coordinate Transformations
Orthogonal Curvilinear Coordinates
Gradient Operator in Orthogonal Coordinates
Divergence and Curl of Vectors in Orthogonal Coordinates
Appendix: Divergence and Curl of Vectors in Orthogonal Curvilinear Coordinates
Mathematical Foundations: Tensors
Tensors
Divergence of a Tensor
Invariants
Positive Definiteness
Polar Decomposition Theorem
Kronecker Products of Tensors
Examples
Introduction to Variational Methods
Introductory Notions
Properties of the Variational Operator
Example: Variational Equation for a Cantilevered Elastic Rod
Higher Order Variations
Examples
Fundamental Notions of Linear Solid Mechanics
The Displacement Vector
The Linear Strain and Rotation Tensors
Examples of Linear Strain and Rotation Tensors
Traction and Stress
Equilibrium
Stress and Strain Transformations
Principal Stresses and Strains
Stress Strain Relations
Principle of Virtual Work in Linear Elasticity
Thermal and Thermomechanical Response
Balance of Energy and Production of Entropy
Classical Coupled Linear Thermoelasticity
Thermal and Thermomechanical Analogs of the Principle of Virtual Work and Associated Finite Element Equations
One-Dimensional Elastic Elements
Interpolation Models for One Dimensional Elements
Strain-Displacement Relations in One Dimensional Elements
Stress-Strain Relations in One Dimensional Elements
Element Mass and Stiffness Matrices from the Principle of Virtual Work
Integral Evaluation by Gaussian Quadrature: Natural Coordinates
Unconstrained Rod Elements
Unconstrainted Elements for Beams and Beam-Columns
Assemblage and Imposition of Constraints
Damping in Rods and Beams
General Discussion of Assemblage
General Discussion of the Imposition of Constraints
Inverse Variational Method
Two- and Three-Dimensional Elements in Linear Elasticity and Linear Conductive Heat Transfer
Two Dimensions
Interpolation Models in Three Dimensions
Strain Displacement Relations and Thermal Analogs
Stress-Strain Relations
Stiffness and Mass Matrices and Their Thermal Analogs
Thermal Counterpart of the Principle of Virtual Work
Conversion to Natural Coordinates in Two and Three Dimensions
Assembly of Two and Three Dimensional Elements
Solution Methods for Linear Problems - I
Numerical Methods in FEA
Time Integration: Stability and Accuracy
Properties of the Trapezoidal Rule
Integral Evaluation by Gaussian Quadrature
Modal Analysis by FEA
Solution Methods for Linear Problems -II
Introduction
Solution Method for an Inverse Problem
Accelerated Eigenstructure Computation in FEA
Fourth Order Time Integration
Additional Topics in Linear Thermoelastic Systems
Transient Conductive Heat Transfer in Linear Media
Coupled Linear Thermoelasticity
Incompressible Elastic Media
Torsion of Prismatic Bars
Buckling of Elastic Beams and Plates
Introduction to Contact Problems
Rotating and Unrestrained Elastic Bodies
Finite Elements in Rotation
Critical Speeds in Shaft-Rotor Shaft
Finite Element Analysis for Unconstrained Elastic Bodies
Appendix: Angular Velocity Vector in Spherical Coordinates
Aspects on Nonlinear Continuum Thermomechanics
Introduction
Nonlinear Kinematics of Deformation
Mechanical Equilibrium and the Principle of Virtual Work
Principle of Virtual Work Under Large Deformation
Nonlinear Stress-Strain-Temperature Relations: The Isothermal Tangent Modulus Tensor
Introduction to Nonlinear FEA
Introduction
Types of Nonlinearlity
Newton Iteration
Combined Incremental and Iterative Methods: A Simple Example
Finite Stretching of a Rubber Rod Under Gravity
Newton Iteration Near a Critical Point
Introduction to the Arc Length Method
Incremental Principle of Virtual Work
Incremental Kinematics
Stress Increments
Incremental Equation of Balance of Linear Momentum
Incremental Principle of Virtual Work
Incremental Finite Element Equation
Contributions From Nonlinear Boundary Conditions
Effect of Variable Contact
Interpretation as Newton Iteration
Buckling
Tangent Modulus Tensors for Thermomechanical Response of Elastomers
Introduction
Compressible Elastomers
Incompressible and Near-Incompressible Elastomers
Stretch-Ration Based Models: Isothermal Conditions
Extension to Thermohyperelastic Materials
Thermomechanics of Damped Elastomers
Constitutive Model in Thermoviscohyperelasticity
Variational Principles and Finite Element Equations for A Thermoviscohyperelastic Material
Tangent Modulus Tensors for Inelastic and Thermoinelastic Materials
Plasticity
Tangent Modulus Tensor in Small Strain Isothermal Plasticity
Plasticity Under Finite Strain
Thermoplasticity
Tangent Modulus Tensor in Viscoplasticity
Continuum Damage Mechanics
Selected Advanced Numerical Methods in FEA
Iterative Triangularization of Perturbed Matrices
Stiff Arc Length Constraint in Nonlinear FEA
Non-Iterative Solution of Finite Element Equations in Incompressible Solids
References
Index
· · · · · · (收起)
讀後感
用戶評價
這部著作，在我手頭的這本，赫然印著《**FINITE ELEMENT ANALYSIS**》這個名字，但它給我的感受，卻完全不像一本嚴肅的工程力學教材。初翻之下，我被其中那股奔放不羈的敘事風格給吸引住瞭。它更像是一部探討“**時間悖論與量子糾纏**”的哲學小說，裏麵充斥著對“**觀察者效應**”的深入剖析，用一種近乎詩意的語言描繪瞭微觀粒子在不同維度間跳躍的景象。作者似乎對傳統的物理學框架抱有一種挑戰的姿態，試圖用一種全新的、高度抽象化的數學模型來解釋宇宙的運行規律，這讓閱讀過程充滿瞭智力上的探險欲。書中對於“**多重宇宙的邊界條件**”的討論尤其令人拍案叫絕，它並非聚焦於具體的數值計算，而是探討瞭當係統無限趨近於混沌時，信息熵如何重新定義“**有限**”的含義。我甚至懷疑，書名或許是一種故意的反諷，引導讀者跳齣對“有限元”的固有認知，轉而探索更廣闊的理論疆域。對於那些期待看到網格劃分、剛度矩陣求解的讀者來說，這本書無疑會帶來巨大的認知落差，但對於尋求跨學科思維碰撞的探索者而言，它提供瞭一片充滿未解謎題的廣闊心智空間，讓人不禁在深夜裏點亮颱燈，對著書頁沉思良久，試圖捕捉那些稍縱即逝的哲學靈光。
评分老實說，我原本是想找一本關於結構動力學分析的參考書，結果拿到瞭這本，內容簡直讓人哭笑不得。這本書的主體內容，竟然是一部關於“**維多利亞時代蒸汽朋剋偵探小說**”的連載草稿，而且還是那種情節極其麯摺、人物關係錯綜復雜的版本。每一章都以一個懸而未決的謎題開始，涉及復雜的機械裝置、塗有毒藥的黃銅齒輪，以及一群穿著燕尾服、抽著煙鬥的貴族嫌疑人。書中對於“**如何用精確到毫秒的時差來布局不在場證明**”的描述，其邏輯縝密程度，簡直可以媲美最頂級的邏輯謎題大師的作品。作者在描述那些精密的機械結構時，用詞極其華麗，比如“**虹彩光澤的鋼材**”、“**在月光下發齣低沉嗡鳴的自動報時器**”，完全沒有提及任何關於應力集中或材料疲勞的詞匯。我甚至在其中發現瞭一張手繪的倫敦下水道地圖，標注著秘密集會地點，這與任何工程計算都毫無關係。讀到一半，我差點忘瞭自己當初想學習有限元方法的初衷，完全被捲入瞭福爾摩斯式的推理漩渦之中。這本書，與其說是技術手冊，不如說是一部充滿奇思妙想的文學作品，隻不過它的“技術”是虛構的，服務於劇情需要。
评分當我拿起這本書時，我感覺自己仿佛穿越到瞭一個高度理想化的未來社會，這本書是一本關於“**城市規劃中的人性化空間設計規範**”的內部指導手冊。它關注的核心是如何通過調整建築的朝嚮、材料的反射率以及公共空間的幾何布局，來最大化居民的“**幸福指數**”和“**社區親密度**”。書中詳細規定瞭例如“**咖啡館窗戶的最佳垂直夾角**”是多少度纔能最大限度地捕捉午後陽光而不産生眩光，以及“**人行道材質的粗糙度對步行速度與心情的關聯係數**”。所有的“計算”都圍繞著社會學和心理學的參數展開，例如，它用復雜的圖錶展示瞭“**鄰裏互動頻率與樓梯間休息平颱數量的綫性關係**”。其中有一章專門討論瞭“**噪音的審美管理**”，提議用精心編排的環境音樂來覆蓋掉不和諧的交通噪音，而不是簡單地進行隔音處理。這本書完全摒棄瞭傳統的承重、荷載或應力分析，轉而探討的是一種基於“**社會流體力學**”的城市設計哲學，充滿瞭對理想生活圖景的烏托邦式描繪，讀起來讓人既嚮往又覺得有些不切實際。
评分這本書的風格極其鮮明，它幾乎完全由一係列關於“**深度海洋生態係統中的生物聲學交流**”的田野調查筆記構成。文字的排版和結構都模仿瞭早期科學探險傢的日誌，充滿瞭手寫的注釋和粗略的素描圖。內容聚焦於對特定深海生物群落發齣的復雜聲波模式的解碼工作，作者似乎堅信這些聲音並非隨機的生物信號，而是一種高度結構化的、類似於“**水下語言的語法體係**”。書中詳細記錄瞭不同水壓和溫度下，某些未知生物體發齣的脈衝信號的頻率漂移情況，並試圖用一種基於“**非綫性聲學散射理論**”的框架來解釋這些現象。令人費神的是，作者似乎極度推崇一種“**情感共振預測模型**”來輔助翻譯，這使得整個科學記錄帶上瞭一種濃厚的主觀色彩。例如，某段記錄寫道：“14:30，觀察到‘幽靈水母’發齣四次極低頻的共振，我斷定那是它們在錶達對捕食者逼近的‘深層憂慮’。”這本書對數據采集的執著令人欽佩，但其理論基石卻完全建立在一種高度擬人化的生物學猜想之上，與結構分析的嚴謹性相去甚遠。
评分打開這本書，我立刻感覺到一種來自上世紀八十年代科幻美學的懷舊氣息，盡管它的封麵設計極其現代且簡潔。內容上，它似乎完全沉浸在對“**失落的亞特蘭蒂斯文明的能源係統**”的考古式重建中。作者用極其詳盡的筆墨，描繪瞭一套基於地熱能和潮汐力構建的復雜循環係統，這些描述完全脫離瞭我們當代已知的任何工程學範疇。書中反復齣現一種奇特的“**共振頻率調諧**”技術，據說這是亞特蘭蒂斯人控製物質形態的關鍵。我花瞭數小時試圖理解其中描繪的那些迴路圖，它們看起來像是融閤瞭電路圖、古代象形文字和某種復雜的星象圖。更令人費解的是，作者在描述能源輸齣效率時，總是引用一些晦澀難懂的“**精神能級”**數據，這使得整個敘述籠罩在一層神秘的宗教色彩之下。我猜測，這本書的真正目的可能不是傳授技術，而是通過構建一個宏大而自洽的“**失敗文明的藍圖**”，來反思我們當代科技發展的路徑是否也存在著某種根本性的缺陷。它更像是一部精美的技術神話集，每一個章節都像是一個被塵封的古代工程秘典，需要用想象力而非計算器去“解讀”。
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