Shell like Structures Advanced Theories and Applications 1st Edition by Holm Altenbach, Victor Eremeyev 3319422770 9783319422770

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ISBN-10 :  3319422770 

ISBN-13 :  9783319422770

Author:  Holm Altenbachv, Victor Eremeyev  

The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems: • comprehensive review of the most popular theories of plates and shells, • relations between three-dimensional theories and two-dimensional ones, • presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories), • modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc., • applications in modeling of non-classical objects like, for example, nanostructures, • presentation of actual numerical tools based on the finite element approach.

Shell-like Structures: Advanced Theories and Applications 1st Table of contents:

Thin-Walled Structural Elements: Classification, Classical and Advanced Theories, New Applications
1 Introduction: Historical Remarks
2 Some Examples of New Applications
3 Main Directions in the Theory of Plates and Shells
3.1 Kirchhoff Theory
3.2 Mindlin Plate Theory
3.3 Reissner Plate Theory
3.4 Reddy Plate Theory
3.5 Föppl-von Kármán Plate Theory
4 Direct Approach to the Theory of Shells
5 Examples of Advanced Theories
5.1 Nanoeffects
5.2 Direct Approach to Viscoelastic Plates
References
Basics of Mechanics of Micropolar Shells
1 Introduction
2 On Rigid Body Dynamics
3 Kinematics of a Micropolar Shell
4 Euler’s Motion Laws of a Micropolar Shell
5 Strain Energy Density and Strain Measures
6 Constitutive Equations of an Elastic Isotropic Shell
7 The Virtual Work Principle and Formulation of Boundary Value Problems
8 Compatibility Conditions
9 Variational Statements
9.1 Lagrange-Type Principle
9.2 Hu-Washizu-Type Principle
9.3 Hamilton-Type Principle
10 Linear Theory of Micropolar Shells
11 Linearized Boundary-Value Problems
12 Eigen-Vibrations of Prestressed Micropolar Shells
12.1 Rayleigh Principle
12.2 Influence of Initial (Residual) Stresses
13 Constitutive Restrictions for Micropolar Shells
13.1 Linear Theory of Micropolar Shell
13.2 Coleman-Noll Inequality for Elastic Shells
13.3 Strong Ellipticity and Hadamard Inequality
13.4 Strong Ellipticity Condition and Acceleration Waves
13.5 Ordinary Ellipticity
14 Applications
14.1 Surface Stresses
14.2 Thin-Walled Structures Made of Micropolar Materials
14.3 Thin-Walled Structures Made of Viscoelastic Materials
14.4 Shells and Plates with Phase Transitions (PT)
14.5 Beams and Rods
15 Conclusions
References
The Bending-Gradient Theory for Laminates and In-Plane Periodic Plates
1 Introduction
2 The Asymptotic Expansion Framework
2.1 Notations
2.2 The 3D Problem
2.3 Scaling
2.4 Properties of the Non-Dimensional Solution
2.5 Expansion
3 Explicit or Cascade Resolution
3.1 Low Order Displacement Fields
3.2 Zeroth-Order Plate Model (Kirchhoff-Love)
3.3 Higher-Order Analysis
4 The Bending-Gradient Theory
5 Application of the Bending-Gradient Theory to Laminates
5.1 Voigt Notations
5.2 Closed-Form Solution for Pagano’s Configuration
5.3 Numerical Applications
6 Periodic Plates
References
Some Problems on Localized Vibrations and Waves in Thin Shells
1 Introduction
2 The Equivalent Single Layer Model for Thin Laminated Shells
2.1 Different Approaches in Modelling of Laminated Shells
2.2 Sandwich Structure
2.3 Basic Hypotheses
2.4 Governing Equations
3 Free Localized Vibrations of Thin Cylindrical Shells: Asymptotic Approach
3.1 Statement of a Problem
3.2 Asymptotic Method of Tovstik
3.3 Examples
4 On Localized Eigenmodes of Thin Laminated Shell Containing Magnetorheological Elastomer
4.1 Motivation
4.2 Setting a Problem
4.3 Asymptotic Solution
4.4 Circular Cylinder with Nonuniform Physical Properties of the MR Layer
5 Localized Eigenmodes of a Sandwich Cylindrical Shell Prestressed by Axial Forces
5.1 Setting a Problem
5.2 Asymptotic Solution
5.3 Reconstruction of Asymptotic Expansions
5.4 Examples
6 Eiegenmodes Localized Near Parallel in Long Axially Prestressed Cylindrical Shells
6.1 Setting a Problem
6.2 Asymptotic Solution
6.3 Examples
7 Wave Packets in Thin Cylindrical Shells
7.1 Localized Stationary and Quasi-Stationary Vibrations
7.2 Setting a Problem
7.3 Asymptotic Approach
7.4 Examples
8 Conclusions
References
Six Lectures in the Mechanics of Elastic Structures
1 Generalities on the Validation of Theories of Thin Elastic Structures
1.1 Prologue
1.2 Generalities on Theory Validation
1.3 Validation Methodologies
1.4 Computational Validation
1.5 Breaking a Lance for Simple Model Theories
2 Validation via Variational Convergence
2.1 Dimension-Reduction Methods
2.2 Standard Γ–Convergence, Stripped to the Bone
2.3 Standard Γ–Convergence Validation of an Approximate Problem
2.4 Improved Γ–Convergence Validation of an Approximate Problem
3 The Virtual Power Principle
3.1 The VPP is not a Variational Statement
3.2 The Standard VPP
3.3 A Strenghtened Version of the VPP
3.4 The PVP as a Dimension-Reduction Tool
4 A Modicum of Continuum Mechanics
4.1 Kinematics
4.2 Internal Constraints
5 Plate Buckling, à la von Kármán, But Not Quite
5.1 The 3D Buckling Problem
5.2 The 2D von Kármán Model
5.3 Back to the 3D Buckling Problem
5.4 Compatibility and v. K’s 1st Equation
5.5 Equilibrium and v. K’s 2nd Equation
6 Mechanical Scaling
6.1 The Scaling Procedure in Summary
6.2 Preparatory Scalings
6.3 The Scaled Load Potential
6.4 The Scaled Total-Energy Functional
6.5 A Mechanical Principle of Convergence in Energy
6.6 Taxonomy of Energy Functionals
6.7 Reissner-Mindlin’s Plates
Selected Topics on Mixed/Enhanced Four-Node Shell Elements with Drilling Rotation
1 Introduction
1.1 Drilling Rotation
1.2 Enhanced and Mixed/Enhanced Shell Elements
1.3 Algorithmic Treatment of Finite Rotations
2 Shell Kinematics and Drilling Rotation
2.1 Extended Configuration Space
2.2 Reissner-Mindlin Shell Kinematics
2.3 Drilling Rotation Constraint
3 Shell Hu-Washizu Functional with Rotations
3.1 3D HW Functional with Rotations
3.2 Complete (Pure) HW Functional for Shells
3.3 Incomplete (Partial) HW Functionals for Shells
4 Finite Rotations: Simple Algorithmic Treatment
4.1 Basic Definitions
4.2 Variations of Rotation Tensor
4.3 Operator T
4.4 Differential χT
4.5 First Variation of Rotation Tensor for Canonical Parametrization
4.6 Simple Algorithm for Treating Finite Rotations
5 Enhanced/Mixed HW Shell Elements
5.1 Skew Coordinates
5.2 Assumed Stress or Couple Resultants and Assumed Shell Strains
5.3 Enhanced Assumed Displacement Gradient (EADG) Method
5.4 Approximation of Drilling RC
6 Numerical Tests
6.1 Intersection of Two Perpendicular Elements
6.2 Cylindrical Shell Under Wind Load
6.3 Long C-Beam
7 Final Remarks

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Tags: Structures, Advanced Theories, Applications, Holm Altenbach, Victor Eremeyev