{"product_id":"computation-of-nonlinear-structures-9781118996959","title":"Computation of Nonlinear Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eComprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method\u003cb\u003e\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eTakes a self-contained approach of including all the essential background materials such as differential geometry, mesh generation, tensor analysis with particular elaboration on rotation tensor, finite element methodology and numerical analysis for a thorough understanding of the topics\u003c\/li\u003e \u003cli\u003ePresents for the first time in closed form the \u003ci\u003egeometric stiffness\u003c\/i\u003e, the \u003ci\u003emass\u003c\/i\u003e, the \u003ci\u003egyroscopic damping\u003c\/i\u003e and the \u003ci\u003ecentrifugal stiffness\u003c\/i\u003e matrices for beams, plates and shells\u003c\/li\u003e \u003cli\u003eIncludes numerous examples and exercises\u003c\/li\u003e \u003cli\u003ePresents solutions for locking problems\u003c\/li\u003e \u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Comprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method.\" (Zentralblatt MATH 2016)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAcknowledgements xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction: Background and Motivation 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 What This Book Is All About 1\u003c\/p\u003e \u003cp\u003e1.2 A Brief Historical Perspective 2\u003c\/p\u003e \u003cp\u003e1.3 Symbiotic Structural Analysis 9\u003c\/p\u003e \u003cp\u003e1.4 Linear Curved Beams and Arches 9\u003c\/p\u003e \u003cp\u003e1.5 Geometrically Nonlinear Curved Beams and Arches 10\u003c\/p\u003e \u003cp\u003e1.6 Geometrically Nonlinear Plates and Shells 11\u003c\/p\u003e \u003cp\u003e1.7 Symmetry of the Tangent Operator: Nonlinear Beams and Shells 12\u003c\/p\u003e \u003cp\u003e1.8 Road Map of the Book 14\u003c\/p\u003e \u003cp\u003eReferences 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I ESSENTIAL MATHEMATICS 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Mathematical Preliminaries 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Essential Preliminaries 21\u003c\/p\u003e \u003cp\u003e2.2 Affine Space, Vectors and Barycentric Combination 33\u003c\/p\u003e \u003cp\u003e2.3 Generalization: Euclidean to Riemannian Space 36\u003c\/p\u003e \u003cp\u003e2.4 Where We Would Like to Go 40\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Tensors 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 41\u003c\/p\u003e \u003cp\u003e3.2 Tensors as Linear Transformation 44\u003c\/p\u003e \u003cp\u003e3.3 General Tensor Space 46\u003c\/p\u003e \u003cp\u003e3.4 Tensor by Component Transformation Property 50\u003c\/p\u003e \u003cp\u003e3.5 Special Tensors 57\u003c\/p\u003e \u003cp\u003e3.6 Second-order Tensors 62\u003c\/p\u003e \u003cp\u003e3.7 Calculus Tensor 74\u003c\/p\u003e \u003cp\u003e3.8 Partial Derivatives of Tensors 74\u003c\/p\u003e \u003cp\u003e3.9 Covariant or Absolute Derivative 75\u003c\/p\u003e \u003cp\u003e3.10 Riemann–Christoffel Tensor: Ordered Differentiation 78\u003c\/p\u003e \u003cp\u003e3.11 Partial (PD) and Covariant (C.D.) Derivatives of Tensors 79\u003c\/p\u003e \u003cp\u003e3.12 Partial Derivatives of Scalar Functions of Tensors 80\u003c\/p\u003e \u003cp\u003e3.13 Partial Derivatives of Tensor Functions of Tensors 81\u003c\/p\u003e \u003cp\u003e3.14 Partial Derivatives of Parametric Functions of Tensors 81\u003c\/p\u003e \u003cp\u003e3.15 Differential Operators 82\u003c\/p\u003e \u003cp\u003e3.16 Gradient Operator: GRAD(∙) or ∇(∙) 82\u003c\/p\u003e \u003cp\u003e3.17 Divergence Operator: DIV or ∇∙ 84\u003c\/p\u003e \u003cp\u003e3.18 Integral Transforms: Green–Gauss Theorems 87\u003c\/p\u003e \u003cp\u003e3.19 Where We Would Like to Go 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Rotation Tensor 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 91\u003c\/p\u003e \u003cp\u003e4.2 Cayley’s Representation 100\u003c\/p\u003e \u003cp\u003e4.3 Rodrigues Parameters 107\u003c\/p\u003e \u003cp\u003e4.4 Euler – Rodrigues Parameters 112\u003c\/p\u003e \u003cp\u003e4.5 Hamilton’s Quaternions 115\u003c\/p\u003e \u003cp\u003e4.6 Hamilton–Rodrigues Quaternion 119\u003c\/p\u003e \u003cp\u003e4.7 Derivatives, Angular Velocity and Variations 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II ESSENTIAL MESH GENERATION 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Curves: Theory and Computation 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 135\u003c\/p\u003e \u003cp\u003e5.2 Affine Transformation and Ratios 136\u003c\/p\u003e \u003cp\u003e5.3 Real Parametric Curves: Differential Geometry 139\u003c\/p\u003e \u003cp\u003e5.4 Frenet–Serret Derivatives 145\u003c\/p\u003e \u003cp\u003e5.5 Bernstein Polynomials 148\u003c\/p\u003e \u003cp\u003e5.6 Non-rational Curves Bezier–Bernstein–de Casteljau 154\u003c\/p\u003e \u003cp\u003e5.7 Composite Bezier–Bernstein Curves 181\u003c\/p\u003e \u003cp\u003e5.8 Splines: Schoenberg B-spline Curves 185\u003c\/p\u003e \u003cp\u003e5.9 Recursive Algorithm: de Boor–Cox Spline 195\u003c\/p\u003e \u003cp\u003e5.10 Rational Bezier Curves: Conics and Splines 198\u003c\/p\u003e \u003cp\u003e5.11 Composite Bezier Form: Quadratic and Cubic B-spline Curves 215\u003c\/p\u003e \u003cp\u003e5.12 Curve Fitting: Interpolations 229\u003c\/p\u003e \u003cp\u003e5.13 Where We Would Like to Go 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Surfaces: Theory and Computation 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 247\u003c\/p\u003e \u003cp\u003e6.2 Real Parametric Surface: Differential Geometry 248\u003c\/p\u003e \u003cp\u003e6.3 Gauss–Weingarten Formulas: Optimal Coordinate System 272\u003c\/p\u003e \u003cp\u003e6.4 Cartesian Product Bernstein–Bezier Surfaces 280\u003c\/p\u003e \u003cp\u003e6.5 Control Net Generation: Cartesian Product Surfaces 296\u003c\/p\u003e \u003cp\u003e6.6 Composite Bezier Form: Quadratic and Cubic B-splines 300\u003c\/p\u003e \u003cp\u003e6.7 Triangular Bezier–Bernstein Surfaces 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III ESSENTIAL MECHANICS 323\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Nonlinear Mechanics: A Lagrangian Approach 325\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 325\u003c\/p\u003e \u003cp\u003e7.2 Deformation Geometry: Strain Tensors 326\u003c\/p\u003e \u003cp\u003e7.3 Balance Principles: Stress Tensors 337\u003c\/p\u003e \u003cp\u003e7.4 Constitutive Theory: Hyperelastic Stress–Strain Relation 351\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV A NEW FINITE ELEMENT METHOD 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 C-type Finite Element Method 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 367\u003c\/p\u003e \u003cp\u003e8.2 Variational Formulations 369\u003c\/p\u003e \u003cp\u003e8.3 Energy Precursor to Finite Element Method 386\u003c\/p\u003e \u003cp\u003e8.4 c-type FEM: Linear Elasticity and Heat Conduction 402\u003c\/p\u003e \u003cp\u003e8.5 Newton Iteration and Arc Length Constraint 438\u003c\/p\u003e \u003cp\u003e8.6 Gauss–Legendre Quadrature Formulas 446\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V APPLICATIONS: LINEAR AND NONLINEAR 457\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Application to Linear Problems and Locking Solutions 459\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 459\u003c\/p\u003e \u003cp\u003e9.2 c-type Truss and Bar Element 460\u003c\/p\u003e \u003cp\u003e9.3 c-type Straight Beam Element 465\u003c\/p\u003e \u003cp\u003e9.4 c-type Curved Beam Element 484\u003c\/p\u003e \u003cp\u003e9.5 c-type Deep Beam: Plane Stress Element 498\u003c\/p\u003e \u003cp\u003e9.6 c-type Solutions: Locking Problems 509\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Nonlinear Beams 523\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 523\u003c\/p\u003e \u003cp\u003e10.2 Beam Geometry: Definition and Assumptions 530\u003c\/p\u003e \u003cp\u003e10.3 Static and Dynamic Equations: Engineering Approach 534\u003c\/p\u003e \u003cp\u003e10.4 Static and Dynamic Equations: Continuum Approach – 3D to 1D 539\u003c\/p\u003e \u003cp\u003e10.5 Weak Form: Kinematic and Configuration Space 555\u003c\/p\u003e \u003cp\u003e10.6 Admissible Virtual Space: Curvature, Velocity and Variation 560\u003c\/p\u003e \u003cp\u003e10.7 Real Strain and Strain Rates from Weak Form 570\u003c\/p\u003e \u003cp\u003e10.8 Component or Operational Vector Form 580\u003c\/p\u003e \u003cp\u003e10.9 Covariant Derivatives of Component Vectors 587\u003c\/p\u003e \u003cp\u003e10.10 Computational Equations of Motion: Component Vector Form 590\u003c\/p\u003e \u003cp\u003e10.11 Computational Derivatives and Variations 596\u003c\/p\u003e \u003cp\u003e10.12 Computational Virtual Work Equations 607\u003c\/p\u003e \u003cp\u003e10.13 Computational Virtual Work Equations and Virtual Strains: Revisited 614\u003c\/p\u003e \u003cp\u003e10.14 Computational Real Strains 627\u003c\/p\u003e \u003cp\u003e10.15 Hyperelastic Material Property 630\u003c\/p\u003e \u003cp\u003e10.16 Covariant Linearization of Virtual Work 639\u003c\/p\u003e \u003cp\u003e10.17 Material Stiffness Matrix and Symmetry 655\u003c\/p\u003e \u003cp\u003e10.18 Geometric Stiffness Matrix and Symmetry 658\u003c\/p\u003e \u003cp\u003e10.19 c-type FE Formulation: Dynamic Loading 673\u003c\/p\u003e \u003cp\u003e10.20 c-type FE Implementation and Examples: Quasi-static Loading 685\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Nonlinear Shell 721\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 721\u003c\/p\u003e \u003cp\u003e11.2 Shell Geometry: Definition and Assumptions 727\u003c\/p\u003e \u003cp\u003e11.3 Static and Dynamic Equations: Continuum Approach – 3D to 2D 746\u003c\/p\u003e \u003cp\u003e11.4 Static and Dynamic Equations: Continuum Approach – Revisited 763\u003c\/p\u003e \u003cp\u003e11.5 Static and Dynamic Equations: Engineering Approach 771\u003c\/p\u003e \u003cp\u003e11.6 Weak Form: Kinematic and Configuration Space 783\u003c\/p\u003e \u003cp\u003e11.7 Admissible Virtual Space: Curvature, Velocity and Variation 788\u003c\/p\u003e \u003cp\u003e11.8 Real Strain and Strain Rates from Weak Form 799\u003c\/p\u003e \u003cp\u003e11.9 Component or Operational Vector Form 810\u003c\/p\u003e \u003cp\u003e11.10 Covariant Derivatives of Component Vectors 817\u003c\/p\u003e \u003cp\u003e11.11 Computational Equations of Motion: Component Vector Form 820\u003c\/p\u003e \u003cp\u003e11.12 Computational Derivatives and Variations 830\u003c\/p\u003e \u003cp\u003e11.13 Computational Virtual Work Equations 841\u003c\/p\u003e \u003cp\u003e11.14 Computational Virtual Work Equations and Virtual Strains: Revisited 851\u003c\/p\u003e \u003cp\u003e11.15 Computational Real Strains 861\u003c\/p\u003e \u003cp\u003e11.16 Hyperelastic Material Property 864\u003c\/p\u003e \u003cp\u003e11.17 Covariant Linearization of Virtual Work 877\u003c\/p\u003e \u003cp\u003e11.18 c-type FE Formulation: Dynamic Loading 891\u003c\/p\u003e \u003cp\u003e11.19 c-type FE Formulation: Quasi-static Loading 914\u003c\/p\u003e \u003cp\u003e11.20 c-type FE Implementation and Examples: Quasi-static Loading 930\u003c\/p\u003e \u003cp\u003eIndex 967\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528843698519,"sku":"9781118996959","price":117.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118996959.jpg?v=1731873243","url":"https:\/\/bookcurl.com\/products\/computation-of-nonlinear-structures-9781118996959","provider":"Book Curl","version":"1.0","type":"link"}