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Computation of Nonlinear Structures: Extremely Large Elements for Frames, Plates and Shells [Kõva köide]

  • Formaat: Hardback, 992 pages, kõrgus x laius x paksus: 262x188x51 mm, kaal: 1774 g
  • Ilmumisaeg: 11-Dec-2015
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111899695X
  • ISBN-13: 9781118996959
Teised raamatud teemal:
Computation of Nonlinear Structures: Extremely Large Elements for Frames, Plates and ShellsSuurem pilt
  • Formaat: Hardback, 992 pages, kõrgus x laius x paksus: 262x188x51 mm, kaal: 1774 g
  • Ilmumisaeg: 11-Dec-2015
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111899695X
  • ISBN-13: 9781118996959
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781118996959.html
Märksõnad:

Extremely Large Elements For Nonlinear Analysis of StructuralFrames, Plates and Shells comprehensivelyintroduces linear andnonlinear structural analysis through mesh generation, solidmechanics and a new numerical methodology called c-type finiteelement method.

Comprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method

  • Takes 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
  • Presents for the first time in closed form the geometric stiffness, themass, the gyroscopic damping and the centrifugal stiffness matrices for beams, plates and shells
  • Includes numerous examples and exercises
  • Presents solutions for locking problems

Arvustused

"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)

Acknowledgements xi
1 Introduction: Background and Motivation
1(18)
1.1 What This Book Is All About
1(1)
1.2 A Brief Historical Perspective
2(7)
1.3 Symbiotic Structural Analysis
9(1)
1.4 Linear Curved Beams and Arches
9(1)
1.5 Geometrically Nonlinear Curved Beams and Arches
10(1)
1.6 Geometrically Nonlinear Plates and Shells
11(1)
1.7 Symmetry of the Tangent Operator: Nonlinear Beams and Shells
12(2)
1.8 Road Map of the Book
14(5)
References
15(4)
Part I ESSENTIAL MATHEMATICS
19(114)
2 Mathematical Preliminaries
21(20)
2.1 Essential Preliminaries
21(12)
2.2 Affine Space, Vectors and Barycentric Combination
33(3)
2.3 Generalization: Euclidean to Riemannian Space
36(4)
2.4 Where We Would Like to Go
40(1)
3 Tensors
41(50)
3.1 Introduction
41(3)
3.2 Tensors as Linear Transformation
44(2)
3.3 General Tensor Space
46(4)
3.4 Tensor by Component Transformation Property
50(7)
3.5 Special Tensors
57(5)
3.6 Second-order Tensors
62(12)
3.7 Calculus Tensor
74(1)
3.8 Partial Derivatives of Tensors
74(1)
3.9 Covariant or Absolute Derivative
75(3)
3.10 Riemann--Christoffel Tensor: Ordered Differentiation
78(1)
3.11 Partial (PD) and Covariant (C.D.) Derivatives of Tensors
79(1)
3.12 Partial Derivatives of Scalar Functions of Tensors
80(1)
3.13 Partial Derivatives of Tensor Functions of Tensors
81(1)
3.14 Partial Derivatives of Parametric Functions of Tensors
81(1)
3.15 Differential Operators
82(1)
3.16 Gradient Operator: GRAD(·) or (·)
82(2)
3.17 Divergence Operator: DIV or (·)
84(3)
3.18 Integral Transforms: Green--Gauss Theorems
87(3)
3.19 Where We Would Like to Go
90(1)
4 Rotation Tensor
91(42)
4.1 Introduction
91(9)
4.2 Cayley's Representation
100(7)
4.3 Rodrigues Parameters
107(5)
4.4 Euler -- Rodrigues Parameters
112(3)
4.5 Hamilton's Quaternions
115(4)
4.6 Hamilton--Rodrigues Quaternion
119(6)
4.7 Derivatives, Angular Velocity and Variations
125(8)
Part II ESSENTIAL MESH GENERATION
133(190)
5 Curves: Theory and Computation
135(112)
5.1 Introduction
135(1)
5.2 Affine Transformation and Ratios
136(3)
5.3 Real Parametric Curves: Differential Geometry
139(6)
5.4 Frenet--Serret Derivatives
145(3)
5.5 Bernstein Polynomials
148(6)
5.6 Non-rational Curves Bezier--Bernstein--de Casteljau
154(27)
5.7 Composite Bezier--Bernstein Curves
181(4)
5.8 Splines: Schoenberg B-spline Curves
185(10)
5.9 Recursive Algorithm: de Boor--Cox Spline
195(3)
5.10 Rational Bezier Curves: Conies and Splines
198(17)
5.11 Composite Bezier Form: Quadratic and Cubic B-spline Curves
215(14)
5.12 Curve Fitting: Interpolations
229(16)
5.13 Where We Would Like to Go
245(2)
6 Surfaces: Theory and Computation
247(76)
6.1 Introduction
247(1)
6.2 Real Parametric Surface: Differential Geometry
248(24)
6.3 Gauss--Weingarten Formulas: Optimal Coordinate System
272(8)
6.4 Cartesian Product Bernstein--Bezier Surfaces
280(16)
6.5 Control Net Generation: Cartesian Product Surfaces
296(4)
6.6 Composite Bezier Form: Quadratic and Cubic B-splines
300(6)
6.7 Triangular Bezier--Bernstein Surfaces
306(17)
Part III ESSENTIAL MECHANICS
323(42)
7 Nonlinear Mechanics: A Lagrangian Approach
325(40)
7.1 Introduction
325(1)
7.2 Deformation Geometry: Strain Tensors
326(11)
7.3 Balance Principles: Stress Tensors
337(14)
7.4 Constitutive Theory: Hyperelastic Stress--Strain Relation
351(14)
Part IV A NEW FINITE ELEMENT METHOD
365(92)
8 C-type Finite Element Method
367(90)
8.1 Introduction
367(2)
8.2 Variational Formulations
369(17)
8.3 Energy Precursor to Finite Element Method
386(16)
8.4 c-type FEM: Linear Elasticity and Heat Conduction
402(36)
8.5 Newton Iteration and Arc Length Constraint
438(8)
8.6 Gauss--Legendre Quadrature Formulas
446(11)
Part V APPLICATIONS: LINEAR AND NONLINEAR
457(510)
9 Application to Linear Problems and Locking Solutions
459(64)
9.1 Introduction
459(1)
9.2 c-type Truss and Bar Element
460(5)
9.3 c-type Straight Beam Element
465(19)
9.4 c-type Curved Beam Element
484(14)
9.5 c-type Deep Beam: Plane Stress Element
498(11)
9.6 c-type Solutions: Locking Problems
509(14)
10 Nonlinear Beams
523(198)
10.1 Introduction
523(7)
10.2 Beam Geometry: Definition and Assumptions
530(4)
10.3 Static and Dynamic Equations: Engineering Approach
534(5)
10.4 Static and Dynamic Equations: Continuum Approach -- 3D to 1D
539(16)
10.5 Weak Form: Kinematic and Configuration Space
555(5)
10.6 Admissible Virtual Space: Curvature, Velocity and Variation
560(10)
10.7 Real Strain and Strain Rates from Weak Form
570(10)
10.8 Component or Operational Vector Form
580(7)
10.9 Covariant Derivatives of Component Vectors
587(3)
10.10 Computational Equations of Motion: Component Vector Form
590(6)
10.11 Computational Derivatives and Variations
596(11)
10.12 Computational Virtual Work Equations
607(7)
10.13 Computational Virtual Work Equations and Virtual Strains: Revisited
614(13)
10.14 Computational Real Strains
627(3)
10.15 Hyperelastic Material Property
630(9)
10.16 Covariant Linearization of Virtual Work
639(16)
10.17 Material Stiffness Matrix and Symmetry
655(3)
10.18 Geometric Stiffness Matrix and Symmetry
658(15)
10.19 c-type FE Formulation: Dynamic Loading
673(12)
10.20 c-type FE Implementation and Examples: Quasi-static Loading
685(36)
11 Nonlinear Shell
721(246)
11.1 Introduction
721(6)
11.2 Shell Geometry: Definition and Assumptions
727(19)
11.3 Static and Dynamic Equations: Continuum Approach -- 3D to 2D
746(17)
11.4 Static and Dynamic Equations: Continuum Approach -- Revisited
763(8)
11.5 Static and Dynamic Equations: Engineering Approach
771(12)
11.6 Weak Form: Kinematic and Configuration Space
783(5)
11.7 Admissible Virtual Space: Curvature, Velocity and Variation
788(11)
11.8 Real Strain and Strain Rates from Weak Form
799(11)
11.9 Component or Operational Vector Form
810(7)
11.10 Covariant Derivatives of Component Vectors
817(3)
11.11 Computational Equations of Motion: Component Vector Form
820(10)
11.12 Computational Derivatives and Variations
830(11)
11.13 Computational Virtual Work Equations
841(10)
11.14 Computational Virtual Work Equations and Virtual Strains: Revisited
851(10)
11.15 Computational Real Strains
861(3)
11.16 Hyperelastic Material Property
864(13)
11.17 Covariant Linearization of Virtual Work
877(14)
11.18 c-type FE Formulation: Dynamic Loading
891(23)
11.19 c-type FE Formulation: Quasi-static Loading
914(16)
11.20 c-type FE Implementation and Examples: Quasi-static Loading
930(37)
Index 967
Debabrata Ray, Institute for Dynamic Response, Inc, USA For more than thirty years, Dr. Ray has been a consultant working on structural issues including the finite element method, mesh generation, computer -aided geometric design, soil-structure interaction for earthquake resistance, fluid-structure interaction, continuum-finite element synthesis for Nuclear Power Plant structures. His clients include General Electric and the Electric Power and Research Institute. He was previously the Vice President at the URS Corporation and is the Ex-Principal of the Institute for Dynamic Response, Inc.