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Engineering Mechanics of Deformable Solids A Presentation with Exercises

ISBN-10: 0199651647
ISBN-13: 9780199651641
Edition: 2012
Authors: Sanjay Govindjee
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Book details

List price: $49.99
Copyright year: 2012
Publisher: Oxford University Press
Publication date: 10/25/2012
Binding: Hardcover
Pages: 360
Size: 7.50" wide x 10.00" long x 0.75" tall
Weight: 2.266
Language: English

Dietmar Grossreceived his Engineering Diploma in Applied Mechanics and his Doctor of Engineering degree at the University of Rostock. He was Research Associate at the University of Stuttgart and since 1976 he is Professor of Mechanics at the University of Darmstadt. His research interests are mainly focused on modern solid mechanics on the macro and micro scale, including advanced materials. Werner Haugerstudied Applied Mathematics and Mechanics at the University of Karlsruhe and received his Ph.D. in Theoretical and Applied Mechanics from Northwestern University in Evanston. He worked in industry for several years, was a Professor at the Helmut-Schmidt-University in Hamburg and went to the University of Darmstadt in 1978. His research interests are, among others, theory of stability, dynamic plasticity and biomechanics. Jörg Schröderstudied Civil Engineering, received his doctoral degree at the University of Hannover and habilitated at the University of Stuttgart. He was Professor of Mechanics at the University of Darmstadt and went to the University of Duisburg-Essen in 2001. His fields of research are theoretical and computer-oriented continuum mechanics, modeling of functional materials as well as the further development of the finite element method.Wolfgang A. Wallstudied Civil Engineering at Innsbruck University and received his doctoral degree from the University of Stuttgart. Since 2003 he is Professor of Mechanics at the TU München and Head of the Institute for Computational Mechanics. His research interests cover broad fields in computational mechanics, including both solid and fluid mechanics. His recent focus is on multiphysics and multiscale problems as well as computational biomechanics.Sanjay Govindjeereceived his SB from MIT and an MS and PhD from Stanford University in mechanical engineering.He was an engineering analyst at the Lawrence Livermore National Laboratory (1991-93) and Professor of Mechanics at ETH Zurich (2006-08). Currently he is a Chancellor�s Professor and Professor of Civil Engineering at the University of California Berkeley (1993-2006, 2008-present). His expertise lies in computational mechanics and the modeling of materials based upon molecular and atomic structure with a particular emphasis upon polymeric based materials, large deformations, and inelastic phenomena.

Introduction
Force systems
Units
Characterization of force systems
Distributed forces
Equivalent forces systems
Work and power
Conservative forces
Conservative systems
Static equilibrium
Equilibrium of a body
Virtual work and virtual power
Equilibrium of subsets: Free-body diagrams
Internal force diagram
Dimensional homogeneity
Exercises
Tension-Compression Bars: The One-Dimensional Case
Displacement field and strain
Units
Strain at a point
Stress
Units
Pointwise equilibrium
Constitutive relations
One-dimensional Hooke's Law
Additional constitutive behaviors
A one-dimensional theory of mechanical response
Axial deformation of bars: Examples
Differential equation approach
Energy methods
Stress-based design
Chapter summary
Exercises
Stress
Average normal and shear- stress
Average stresses for a bar under axial load
Design with average stresses
Stress at a point
Nomenclature
Internal reactions in terms of stresses
Equilibrium in terms of stresses
Polar and spherical coordinates
Cylindrical/polar stresses
Spherical stresses
Chapter summary
Exercises
Strain
Shear strain
Pointwise strain
Normal strain at a point
Shear strain at a point
Two-dimensional strains
Three-dimensional strain
Polar/cylindrical and spherical strain
Number of unknowns and equations
Chapter summary
Exercises
Constitutive Response
Three-dimensional Hooke's Law
Pressure
Strain energy in three dimensions
Two-dimensional Hooke's Law
Two-dimensional plane stress
Two-dimensional plane strain
One-dimensional Hooke's Law: Uniaxial state of stress
Polar/cylindrical and spherical coordinates
Chapter summary
Exercises
Basic Techniques of Strength of Materials
One-dimensional axially loaded rod revisited
Thinness
Cylindrical thin-walled pressure vessels
Spherical thin-walled pressure vessels
Saint-Venant's principle
Chapter summary
Exercises
Circular and Thin-Wall Torsion
Circular bars: Kinematic assumption
Circular bars: Equilibrium
Internal torque-stress relation
Circular bars: Elastic response
Elastic examples
Differential equation approach
Energy methods
Torsional failure: Brittle materials
Torsional failure: Ductile materials
Twist-rate at and beyond yield
Stresses beyond yield
Torque beyond yield
Unloading after yield
Thin-walled tubes
Equilibrium
Shear flow
Internal torque-stress relation
Kinematics of thin-walled tubes
Chapter summary
Exercises
Bending of Beams
Symmetric bending: Kinematics
Symmetric bending: Equilibrium
Internal resultant definitions
Symmetric bending: Elastic response
Neutral axis
Elastic examples: Symmetric bending stresses
Symmetric bending: Elastic deflections by differential equations
Symmetric multi-axis bending
Symmetric multi-axis bending: Kinematics
Symmetric multi-axis bending: Equilibrium
Symmetric multi-axis bending: Elastic
Shear stresses
Equilibrium construction for shear stresses
Energy methods: Shear deformation of beams
Plastic bending
Limit cases
Bending at and beyond yield: Rectangular cross-section
Stresses beyond yield: Rectangular cross-section
Moment beyond yield: Rectangular cross-section
Unloading after yield: Rectangular cross-section
Chapter summary
Exercises
Analysis of Multi-Axial Stress and Strain
Transformation of vectors
Transformation of stress
Traction vector method
Maximum normal and shear stresses
Eigenvalues and eigenvectors
Mohr's circle of stress
Three-dimensional Mohr's circles of stress
Transformation of strains
Maximum normal and shear strains
Multi-axial failure criteria
Tresca's yield condition
Henky-von Mises condition
Chapter summary
Exercises
Virtual Work Methods: Virtual Forces
The virtual work theorem: Virtual force version
Virtual work expressions
Determination of displacements
Determination of rotations
Axial rods
Torsion rods
Bending of beams
Direct shear in beams (elastic only)
Principle of virtual forces: Proof
Axial bar: Proof
Beam bending: Proof
Applications: Method of virtual forces
Chapter summary
Exercises
Potential-Energy Methods
Potential energy: Spring-mass system
Stored elastic energy: Continuous systems
Castigliano's first theorem
Stationary complementary potential energy
Stored complementary energy: Continuous systems
Castigliano's second theorem
Stationary potential energy: Approximate methods
Ritz's method
Approximation errors
Types of error
Estimating error in Ritz's method
Selecting functions for Ritz's method
Chapter summary
Exercises
Geometric Instability
Point-mass pendulum: Stability
Instability: Rigid links
Potential energy: Stability
Small deformation assumption
Euler buckling of beam-columns
Equilibrium
Applications
Limitations to the buckling formulae
Eccentric loads
Rigid links
Euler columns
Approximate solutions
Buckling with distributed loads
Deflection behavior for beam-columns with combined axial and transverse loads
Chapter summary
Exercises
Virtual Work Methods: Virtual Displacements
The virtual work theorem: Virtual displacement version
The virtual work expressions
External work expressions
Axial rods
Torsion rods
Bending of beams
Principle of virtual displacements: Proof
Axial bar: Proof
Beam bending: Proof
Approximate methods
Chapter summary
Exercises
Additional Reading
Units, Constants, and Symbols
Representative Material Properties
Parallel-Axis Theorem
Integration Facts
Integration is addition in the limit
Additivity
Fundamental theorem of calculus
Mean value
The product rule and integration by parts
Integral theorems
Mean value theorem
Localization theorem
Divergence theorem
Bending without Twisting: Shear Center
Shear center
Index

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