Computation of Nonlinear Structures : Extremely Large Elements for Frames, Plates and Shells
Debabrata. Ray
Bok Engelsk 2015 · Electronic books.
| Utgitt | Somerset : : Wiley, , 2015.
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| Omfang | 1 online resource (1164 p.)
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| Opplysninger | Description based upon print version of record.. - Title page; Copyright; Dedication; Acknowledgements; 1 Introduction: Background and Motivation; 1.1 What This Book Is All About; 1.2 A Brief Historical Perspective; 1.3 Symbiotic Structural Analysis; 1.4 Linear Curved Beams and Arches; 1.5 Geometrically Nonlinear Curved Beams and Arches; 1.6 Geometrically Nonlinear Plates and Shells; 1.7 Symmetry of the Tangent Operator: Nonlinear Beams and Shells; 1.8 Road Map of the Book; References; Part I ESSENTIAL MATHEMATICS; 2 Mathematical Preliminaries; 2.1 Essential Preliminaries; 2.2 Affine Space, Vectors and Barycentric Combination. - 2.3 Generalization: Euclidean to Riemannian Space2.4 Where We Would Like to Go; 3 Tensors; 3.1 Introduction; 3.2 Tensors as Linear Transformation; 3.3 General Tensor Space; 3.4 Tensor by Component Transformation Property; 3.5 Special Tensors; 3.6 Second-order Tensors; 3.7 Calculus Tensor; 3.8 Partial Derivatives of Tensors; 3.9 Covariant or Absolute Derivative; 3.10 Riemann-Christoffel Tensor: Ordered Differentiation; 3.11 Partial (PD) and Covariant (C.D.) Derivatives of Tensors; 3.12 Partial Derivatives of Scalar Functions of Tensors; 3.13 Partial Derivatives of Tensor Functions of Tensors. - 3.14 Partial Derivatives of Parametric Functions of Tensors3.15 Differential Operators; 3.16 Gradient Operator: GRAD or ∇; 3.17 Divergence Operator: DIV or ∇; 3.18 Integral Transforms: Green-Gauss Theorems; 3.19 Where We Would Like to Go; 4 Rotation Tensor; 4.1 Introduction; 4.2 Cayley's Representation; 4.3 Rodrigues Parameters; 4.4 Euler - Rodrigues Parameters; 4.5 Hamilton's Quaternions; 4.6 Hamilton-Rodrigues Quaternion; 4.7 Derivatives, Angular Velocity and Variations; Part II ESSENTIAL MESH GENERATION; 5 Curves: Theory and Computation; 5.1 Introduction. - 5.2 Affine Transformation and Ratios5.3 Real Parametric Curves: Differential Geometry; 5.4 Frenet-Serret Derivatives; 5.5 Bernstein Polynomials; 5.6 Non-rational Curves Bezier-Bernstein-de Casteljau; 5.7 Composite Bezier-Bernstein Curves; 5.8 Splines: Schoenberg B-spline Curves; 5.9 Recursive Algorithm: de Boor-Cox Spline; 5.10 Rational Bezier Curves: Conics and Splines; 5.11 Composite Bezier Form: Quadratic and Cubic B-spline Curves; 5.12 Curve Fitting: Interpolations; 5.13 Where We Would Like to Go; 6 Surfaces: Theory and Computation; 6.1 Introduction. - 6.2 Real Parametric Surface: Differential Geometry6.3 Gauss-Weingarten Formulas: Optimal Coordinate System; 6.4 Cartesian Product Bernstein-Bezier surfaces; 6.5 Control Net Generation: Cartesian Product Surfaces; 6.6 Composite Bezier Form: Quadratic and Cubic B-splines; 6.7 Triangular Bezier-Bernstein Surfaces; Part III ESSENTIAL MECHANICS; 7 Nonlinear Mechanics: A Lagrangian Approach; 7.1 Introduction; 7.2 Deformation Geometry: Strain Tensors; 7.3 Balance Principles: Stress Tensors; 7.4 Constitutive Theory: Hyperelastic Stress-Strain Relation; Part IV A NEW FINITE ELEMENT METHOD. - 8 C-type Finite Element Method
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| ISBN | 9781118996959 (cloth)
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