Coverart for item
The Resource Mathematical Modelling in Solid Mechanics

Mathematical Modelling in Solid Mechanics

Label
Mathematical Modelling in Solid Mechanics
Title
Mathematical Modelling in Solid Mechanics
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Advanced Structured Materials Ser.
Series volume
v.69
Mathematical Modelling in Solid Mechanics
Label
Mathematical Modelling in Solid Mechanics
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4822061
Publication
Copyright
Related Contributor
Related Location
Related Agents
Related Authorities
Related Subjects
Related Items
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Emerging Trends in Applied Mathematics and Mechanics (ETAMM 2016) -- Organizing Committee -- International Scientific Committee -- Plenary Lectures -- Keynotes Lectures -- Contents -- Contributors -- Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof -- 1 Introduction -- 2 Convergence of Measure Functionals -- 3 Micro-Model for Non-Linear Beams -- 3.1 Discrete Configurations and Operators -- 3.2 Left Hand Side Clamped Inextensible Beam -- 3.3 Deformation Energy Associated with Three Points Interactions -- 4 From Micro to Macro Model: D-Convergence Result -- 4.1 Functionals Associated to the Micro Model -- 4.2 Functional Associated to the Macro Model -- 4.3 D-Convergence result -- 5 Proof of the Main Result -- 5.1 Approximation of a Sequence with Bounded Energy -- 5.2 The Proof of Theorem 4.1 -- 6 Conclusions -- References -- Analysis of the Deformation of Cosserat Elastic Shells Using the Dislocation Density Tensor -- 1 Introduction -- 2 Strain and Curvature Measures in the Cosserat (6-Parameter) Shell Model -- 2.1 Kinematics -- 2.2 Differential Geometry -- 2.3 The Dislocation Density Tensor -- 3 Governing Equations for the Equilibrium of Cosserat Shells -- 4 Variational Formulation and Existence of Minimizers -- 5 Application: Isotropic Cosserat Shells -- 6 Open Problems -- References -- Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity -- 1 Introduction -- 2 Governing Equations and Inequalities -- 3 Weak Form of Equilibrium and the Elastic--Plastic Initial-Boundary Value Problem -- 4 The Fully Discrete Problem -- 5 Concluding Remarks -- References -- Finite Elasto-Plastic Models for Lattice Defects in Crystalline Materials -- 1 Introduction -- 2 Geometry and Kinematics of Elasto-Plastic Body -- 3 Energetic Assumptions
  • 3.1 Micro Balance Equations -- 3.2 Free Energy Density Function -- 4 The Postulate of the Free Energy Imbalance -- 5 Viscoplastic Type Evolution Equations -- 6 Concluding Remarks -- References -- Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution -- 1 Introduction -- 1.1 Motivation and Basic Ideas -- 1.2 A Summary of the Algorithm and of the Formalism Employed -- 1.3 Short Summary of Preliminary Numerical Results -- 1.4 Further Comparison with Finite Element Simulations -- 2 Spontaneous Evolution and Discrete Energy Equivalent -- 3 Fracture and Crack Formation and Evolution -- 3.1 Introduction of the Fracture -- 3.2 Basic Fracture and Crack Evolution -- 3.3 Uniaxial External Action -- 3.4 Almost-Steady State -- 4 Conclusion and Further Objectives -- References -- A Review on Wave Propagation Modeling in Band-Gap Metamaterials via Enriched Continuum Models -- 1 Introduction -- 1.1 Notations -- 1.2 The Fundamental Role of Micro-Inertia in Enriched Continuum Mechanics -- 2 The Classical Relaxed Micromorphic Model -- 3 The Micromorphic Model with Curvature 86422285 DivP69645069 2+86422285 CurlP69645069 2 -- 4 The Micromorphic Model with Curvature 86422285 DivP69645069 2 -- 5 The Standard Mindlin-Eringen Model -- 6 The Internal Variable Model -- 7 Conclusions -- References -- A Continuous Model for the Wave Scattering by a Bounded Defective Domain -- 1 Introduction -- 2 Differential Tools on Riemann--Cartan Geometry -- 3 Elastic Wave in a Riemann--Cartan Manifold -- 3.1 Constitutive Model -- 3.2 Navier Equation -- 4 Screw-Type Torsion in Cylindrical Coordinate System -- 4.1 Stress Tensor -- 4.2 Configurational Force -- 5 General Time-Harmonic Solutions -- 5.1 Solution in a Perfect Medium -- 5.2 Solution in a Defective Medium -- 6 Scattering Problem -- 6.1 Boundary Conditions
  • 6.2 Displacement and Stress -- 7 Asymptotics -- 7.1 Low Defect's Density -- 7.2 Higher Defect Density -- 7.3 Discussion -- 8 Conclusion -- References -- A History-Dependent Variational-Hemivariational Inequality in Contact Mechanics -- 1 Introduction -- 2 The Contact Model -- 3 Variational Analysis -- 4 An Abstract Existence and Uniqueness Result -- 5 Proof of Theorem 8.1 -- References -- Monolithic Algorithm for Dynamic Fluid-Structure Interaction Problem -- 1 Introduction -- 2 Setting the Fluid-Structure Interaction Problem -- 3 Total Lagrangian Framework for the Structure Approximation -- 4 Updated Lagrangian Framework for the Structure Approximation -- 5 Monolithic Algorithm for the Fluid-Structure Equations -- 6 Numerical Test. Flow Around a Flexible Thin Structure Attached to a Fixed Cylinder -- 7 Conclusions -- References -- Elastic-Plastic Rolling Contact Problems with Graded Materials and Heat Exchange -- 1 Introduction -- 2 General Contact Problem -- 3 Rolling Contact Problem -- 3.1 Thermo-Elastoplastic Model -- 3.2 Numerical Results -- References -- New Thoughts in Nonlinear Elasticity Theory via Hencky's Logarithmic Strain Tensor -- 1 Strain and Strain Measures in Nonlinear Elasticity -- 2 Euclidean Strain Measures -- 2.1 The Euclidean Strain Measure in Linear Isotropic Elasticity -- 2.2 The Euclidean Strain Measure in Nonlinear Isotropic Elasticity -- 3 The Riemannian Strain Measure in Nonlinear Isotropic Elasticity -- 3.1 3̀94̀2"̀613A4̀̀54̀7"̀603AGL+(n) as a Riemannian Manifold -- 3.2 The Geodesic Distance to 3̀94̀2"̀613A4̀̀54̀7"̀603ASO(n) -- References -- Continuum Physics with Violations of the Second Law of Thermodynamics -- 1 Violations of the Second Law of Thermodynamics in Heat Conduction and Viscous Flow -- 2 Random Fields -- 3 Thermoviscous Fluid with a Thermal Relaxation Time -- 4 Thermoelasticity with Two Relaxation Times
  • 5 Violations of Second Law in Poromechanics -- 6 Conclusions -- References -- An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations -- 1 Introduction -- 2 Formulation of the Problem -- 2.1 Definition of the Deformation Energy Functional -- 2.2 Formulation of the Variational Principle -- 2.3 Balance of Forces and Moments -- 2.4 The Deformation Energy Functional for 2D Isotropic and for D4 Anisotropic Linear Second Gradient Elasticity -- 3 The Case of a Rectangle -- 3.1 The General Framework of Straight Lines -- 3.2 Characterization of Vertices -- 4 Analytical Solutions -- 4.1 Analytical Solutions for the Isotropic Case -- 4.2 Analytical Solutions for the D4 anisotropic case -- 4.3 D4 Anisotropic Trapezoidal Case -- 5 Conclusion -- References -- Identification of Two-Dimensional Pantographic Structures with a Linear D4 Orthotropic Second Gradient Elastic Model Accounting for External Bulk Double Forces -- 1 Introduction -- 2 Outline of the Model -- 3 Analytical Solutions -- 3.1 Heavy Sheet -- 3.2 Non-conventional Bending -- 3.3 Trapezoidal Case -- 4 Pantographic Case -- 4.1 Heavy Sheet -- 4.2 Non-conventional Bending -- 4.3 Trapezoidal Case -- 4.4 Summary -- 4.5 About the Redundancy of Equations Coming from gedanken experiments -- 5 Some Remarks on the Internal Energy -- 6 Conclusion -- References -- Models of Debonding Caused by Vibrations, Heat and Humidity -- 1 Introduction -- 2 The 3D Model -- 2.1 Comments and Open Issues for Model 1 -- 3 1D Two Rod-Beams Model -- 3.1 Comments and Open Issues for Model 2 -- 4 The 1D Two Rods Model -- 4.1 Two Comments on Model 3 -- References -- A Variational-Hemivariational Inequality in Contact Mechanics -- 1 Introduction -- 2 The Contact Model -- 3 Variational Analysis -- 4 Numerical Analysis -- 5 Numerical Simulations -- References
  • Truncation and Indirect Incremental Methods in Hencky's Perfect Plasticity -- 1 Introduction -- 2 Generalized Hencky Plasticity Problem -- 2.1 Basic Definitions and Properties -- 2.2 The Von Mises Yield Criterion -- 2.3 The Drucker--Prager Yield Criterion -- 3 Truncation Method -- 3.1 Limit Analysis for Bounded B -- 3.2 Truncation Method for Unbounded B -- 4 Indirect Incremental Method -- 5 Finite Element Approximation -- 6 Computable Bounds of n* and Numerical Experiments -- 6.1 Computable Bounds of n* and Numerical Methods -- 6.2 Numerical Example with the Von Mises Criterion -- 6.3 Numerical Example with the Drucker--Prager Criterion -- 7 Conclusion -- References -- Can a Hencky-Type Model Predict the Mechanical Behaviour of Pantographic Lattices? -- 1 Introduction -- 2 Discrete Model for Pantographic Sheets -- 3 Comparison with Experiments -- 3.1 Fiber Push-Out Test -- 3.2 Pantograph with Non-orthogonal Fibers: Ü1=s/6 -- 3.3 Pantograph with Non-orthogonal Fibers: Ü1=s/3 -- 4 Concluding Remarks -- References -- Index
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9789811037641&userID=ebsco-test&password=ebsco-test
Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4393451'}
Extent
1 online resource (327 pages)
Form of item
online
Isbn
9789811037641
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

Library Locations

    • Folsom LibraryBorrow it
      110 8th St, Troy, NY, 12180, US
      42.729766 -73.682577
Processing Feedback ...