Structural analysis : with applications to aerospace structures

- Bauchau, Olivier Andre
- Craig, J. I. (James I.)

関連文献: 1件

著者

- Bauchau, Olivier Andre
- Craig, J. I. (James I.)

書誌事項

Structural analysis : with applications to aerospace structures

O.A. Bauchau, J.I. Craig

（Solid mechanics and its applications, 163）

Springer, c2009

大学図書館所蔵件 / 全3件

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Includes bibliographical references and index

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内容説明

The authors and their colleagues developed this text over many years, teaching undergraduate and graduate courses in structural analysis courses at the Daniel Guggenheim School of Aerospace Engineering of the Georgia Institute of Technology. The emphasis is on clarity and unity in the presentation of basic structural analysis concepts and methods. The equations of linear elasticity and basic constitutive behaviour of isotropic and composite materials are reviewed. The text focuses on the analysis of practical structural components including bars, beams and plates. Particular attention is devoted to the analysis of thin-walled beams under bending shearing and torsion. Advanced topics such as warping, non-uniform torsion, shear deformations, thermal effect and plastic deformations are addressed. A unified treatment of work and energy principles is provided that naturally leads to an examination of approximate analysis methods including an introduction to matrix and finite element methods. This teaching tool based on practical situations and thorough methodology should prove valuable to both lecturers and students of structural analysis in engineering worldwide. This is a textbook for teaching structural analysis of aerospace structures. It can be used for 3rd and 4th year students in aerospace engineering, as well as for 1st and 2nd year graduate students in aerospace and mechanical engineering.

Part I Basic tools and concepts
1 Basic Equations of Linear Elasticity .1.1 The concept of stress
1.1.1 The state of stress at a point
1.1.2 Volume equilibrium equations
1.1.3 Surface equilibrium equations
1.2 Analysis of the state of stress at a point
1.2.1 Stress components acting on an arbitrary face
1.2.2 Principal stresses
1.2.3 Rotation of stresses
1.2.4 Problems
1.3 The state of plane stress
1.3.1 Equilibrium equations
1.3.2 Stresses acting on an arbitrary face within the sheet
1.3.3 Principal stresses
1.3.4 Rotation of stresses
1.3.5 Special states of stress
1.3.6 Mohr's circle for plane stress
1.3.7 Lame's ellipse
1.3.8 Problems
1.4 The concept of strain
1.4.1 The state of strain at a point
1.4.2 The volumetric strain
1.5 Analysis of the state of strain at a point
1.5.1 Rotation of strains 1.5.2 Principal strains
1.6 The state of plane strain
1.6.1 Strain-displacement relations for plane strain
1.6.2 Rotation of strains
1.6.3 Principal strains
1.6.4 Mohr's circle for plane strain
1.7 Measurement of strains
1.7.1 Problems
1.8 Strain compatibility equations
2 Constitutive Behavior of Materials
2.1 Constitutive laws for isotropic materials
2.1.1 Homogeneous, isotropic, linear elastic materials
2.1.2 Thermal effects
2.1.3 Problems
2.1.4 Ductile materials
2.1.5 Brittle materials
2.2 Allowable stress
2.3 Yielding under combined loading
2.3.1 Tresca's criterion
2.3.2 Von Mises' criterion
2.3.3 Comparing Tresca's and von Mises' criteria
2.3.4 Problems
2.4 Material selection for structural performance
2.4.1 Strength design
2.4.2 Stiffness design 2.4.3 Buckling design
2.5 Composite materials
2.5.1 Basic characteristics
2.5.2 Stress diffusion in a composite
2.6 Constitutive laws for anisotropic materials
2.6.1 Constitutive laws for a lamina in the fiber aligned triad
2.6.2 Constitutive laws for a lamina in an arbitrary triad
2.7 Strength of a transversely isotropic lamina
2.7.1 Strength of a lamina under simple loading conditions
2.7.2 The Tsai-Wu failure criterion
2.7.3 The reserve factor
3 Linear Elasticity Solutions
3.1 Solution procedures
3.1.1 Displacement formulation
3.1.2 Stress formulation
3.1.3 Solutions to elasticity problems
3.2 Plane strain problems
3.3 Plane stress problems
3.4 Plane strain and plane stress in polar coordinates
3.5 Problem featuring cylindrical symmetry
3.5.1 Problems
4 Engineering Structural Analysis
4.1 Solution approaches
4.2 Bar under constant axial force
4.3 Hyperstatic systems
4.3.1 Solution procedures
4.3.2 The displacement or stiffness method
4.3.3 The force or flexibility method
4.3.4 Problems
4.3.5 Thermal effects in hyperstatic system
4.3.6 Manufacturing imperfection effects in hyperstatic system
4.3.7 Problems
4.4 Pressure vessels
4.4.1 Rings under internal pressure
4.4.2 Cylindrical pressure vessels
4.4.3 Spherical pressure vessels
4.4.4 Problems
4.5 Saint-Venant's principle
Part II Beams and thin-wall structures5 Euler-Bernoulli Beam Theory
5.1 The Euler-Bernoulli Assumptions
5.2 Implications of the Euler-Bernoulli assumptions
5.3 Stress resultants
5.4 Beams subjected to axial loads
5.4.1 Kinematic description
5.4.2 Sectional constitutive law
5.4.3 Equilibrium equations
5.4.4 Governing equations
5.4.5 The sectional axial stiffness
5.4.6 The axial stress distribution
5.4.7 Problems
5.5 Beams subjected to transverse loads
5.5.1 Kinematic description
5.5.2 Sectional constitutive law
5.5.3 Equilibrium equations
5.5.4 Governing equations
5.5.5 The sectional bending stiffness
5.5.6 The axial stress distribution
5.5.7 Rational design of beams under bending
5.5.8 Problems
5.6 Beams subjected to axial and transverse loads
5.6.1 Kinematic description
5.6.2 Sectional constitutive law
5.6.3 Equilibrium equations
5.6.4 Governing equations
6 Three-Dimensional Beam Theory
6.1 Kinematic description
6.2 Sectional constitutive law
6.3 Sectional equilibrium equations
6.4 Governing equations
6.5 Decoupling the three-dimensional problem
6.5.1 Definition of the principal axes of bending
6.5.2 Decoupled governing equations
6.6 The principal centroidal axes of bending
6.6.1 The bending stiffness ellipse
6.7 Definition of the neutral axis
6.8 Evaluation of sectional stiffnesses
6.8.1 The parallel axis theorem
6.8.2 Thin-walled sections
6.8.3 Triangular area equivalence method
6.8.4 Useful results
6.8.5 Problems
6.9 Summary of three-dimensional beam theory
6.9.1 Examples
6.9.2 Discussion of the results
6.10 Problems
7 Torsion
7.1 Torsion of circular cylinders
7.1.1 Kinematic description
7.1.2 The stress field
7.1.3 Sectional constitutive law
7.1.4 Equilibrium equations
7.1.5 Governing equations
7.1.6 The torsional stiffness
7.1.7 Measuring the torsional stiffness
7.1.8 The shear stress distribution
7.1.9 Rational design of cylinders under torsion
7.1.10 Problems
7.2 Torsion combined with axial force or bending
7.2.1 Problems
7.3 Torsion of bars with arbitrary cross-sections
7.3.1 Introduction
7.3.2 Saint-Venant's solution
7.3.3 Saint-Venant's solution for a rectangular cross-section
7.3.4 Problems
7.4 Torsion of a thin rectangular cross-section
7.5 Torsion of thin-walled open sections
7.5.1 Problems
8 Thin-Walled Beams
8.1 Basic equations for thin-walled beams
8.1.1 The thin wall assumption
8.1.2 Stress flows
8.1.3 Stress resultants
8.1.4 Local equilibrium equation
8.2 Bending of thin-walled beams
8.2.1 Problems
8.3 Shearing of thin-walled beams
8.3.1 Shearing of open sections
8.3.2 Evaluation of stiffness static moments
8.3.3 Shear flow distributions in open sections
8.3.4 Problems
8.3.5 Shear center for open sections
8.3.6 Problems
8.3.7 Shearing of closed sections
8.3.8 Shearing of multi-cellular sections
8.3.9 Problems
8.4 The shear center
8.4.1 Calculation of the shear center location
8.4.2 Problems
8.5 Torsion of thin-walled beams
8.5.1 Torsion of open sections
8.5.2 Torsion of closed section
8.5.3 Comparison of open and closed sections
8.5.4 Torsion of combined open and closed sections
8.5.5 Torsion of multi-cellular sections
8.5.6 Problems
8.6 Coupled bending-torsion problems
8.6.1 Problems
8.7 Warping of thin-walled beams under torsion
8.7.1 Kinematic description
8.7.2 Stress-strain relations
8.7.3 Warping of open sections
8.7.4 Problems
8.7.5 Warping of closed sections
8.7.6 Warping of multi-cellular sections
8.8 Equivalence of the shear and twist centers
8.9 Non-uniform torsion
8.9.1 Non-uniform torsion: a classical approach
8.9.2 Problems
8.10 Structural idealization
8.10.1 Lumping the thin-walled section into sheet and stringer components 8.10.2 Axial stress in the stringers
8.10.3 Shear flow in the sheet components
8.10.4 Torsion of sheet-stringer sections
8.10.5 Problems
Part III Energy and variational methods9 Virtual Work Principles
9.1 Introduction
9.2 Equilibrium and work fundamentals
9.2.1 Static equilibrium conditions
9.2.2 Concept of mechanical work
9.3 Principle of virtual work
9.3.1 Principle of virtual work for a single particle
9.3.2 Kinematically admissible virtual displacements
9.3.3 Use of infinitesimals as virtual displacements
9.3.4 Principle of virtual work for a system of particles
9.3.5 Application of the principle of virtual work to mechanical systems
9.3.6 Application of the principle of virtual work to trusses
9.3.7 Generalized coordinates and forces
9.3.8 Problems
9.4 Principle of complementary virtual work
9.4.1 Compatibility equations for a planar truss
9.4.2 Principle of complementary virtual work for trusses
9.4.3 Complementary virtual work
9.4.4 Problems
9.5 Unit load method for trusses
9.5.1 Statement of the unit load method for trusses
9.5.2 Application to trusses
9.5.3 Problems .
9.6 Unit load method for beams
9.6.1 Beam deflection due to bending
9.6.2 Beam deflection due to torsion
9.6.3 Application to beam problems
9.6.4 Deflections of beams with unsymmetric cross sections
9.6.5 Problems
9.7 Application of the unit load method to hyperstatic problems
9.7.1 Force method for trusses
9.7.2 Force method for beams
9.7.3 Combined truss and beam problems
9.7.4 Multiple redundancies
9.7.5 Problems
10 Energy Methods
10.1 Conservative forces
10.1.1 Potential for internal and external forces
10.1.2 Calculation of the potential functions
10.2 Principle of minimum total potential energy
10.2.1 Nonconservative external forces
10.3 Strain energy in springs
10.3.1 Rectilinear springs
10.3.2 Torsional springs
10.4 Problems
10.5 Strain energy in beams
10.5.1 Beam under axial loads
10.5.2 Beam under transverse loads
10.5.3 Beam under torsional loads
10.6 Strain energy in solids
10.6.1 General three-dimensional stress state
10.6.2 Beams under multi-axis bending and axial load
10.7 Applications to trusses
10.7.1 Problems
10.7.2 Development of a finite element formulation for trusses
10.7.3 Problems
10.7.4 Applications to beams
10.8 Principle of minimum complementary energy
10.8.1 The potential of the prescribed displacements
10.8.2 Constitutive laws for elastic materials
10.8.3 The principle of minimum complementary energy
10.8.4 The principle of least work
10.8.5 Examples using the PMCP/LWP
10.8.6 Problems
10.9 Energy theorems
10.9.1 Clapeyron's theorem
10.9.2 Castigliano's first theorem
10.9.3 Crotti-Engesser theorem
10.9.4 Castigliano's second theorem
10.9.5 Applications of energy theorems
10.9.6 The dummy load method
10.9.7 Unit load method revisited
10.9.8 Conclusions
10.9.9 Problems
10.10Reciprocity theorems
10.10.1Betti's theorem
10.10.2Maxwell's theorem
10.10.3Problems
11 Variational and Approximate Solutions
11.1 Approach
11.2 Approximations based on the principle of minimum total potential energy
11.2.1 Application to a bending of a beam
11.2.2 Examples
11.2.3 Problems
11.3 The strong and weak statements of equilibrium
11.3.1 The weak form for beams under axial loads
11.3.2 Approximate solutions for beams under axial loads
11.3.3 Problems
11.3.4 The weak form for beams under transverse loads
11.3.5 Approximate solutions for beams under transverse loads
11.3.6 Problems 11.3.7 Equivalence with energy principles
11.3.8 The principle of minimum total potential energy
11.3.9 Treatment of the boundary conditions
11.4 Formal procedures for the derivation of approximate solutions
11.4.1 Basic approximations
11.4.2 Principle of virtual work
11.4.3 The principle of minimum total potential energy
11.4.4 Examples
11.4.5 Problems
11.5 A Finite Element formulation for beams
11.5.1 Formulation of an Euler-Bernoulli beam element
11.5.2 Examples
11.5.3 Summary
11.5.4 Problems
12 Variational and Energy Principles
12.1 Variational formulation of beam problems
12.2 Mathematical Preliminaries
12.2.1 Stationary point of a function
12.2.2 Lagrange multiplier method
12.2.3 Stationary point of a definite integral
12.3 Variational and Energy Principles
12.3.1 Review of the equations of linear elasticity
12.3.2 The principle of virtual work
12.3.3 The principle of complementary virtual work
12.3.4 The strain energy density function
12.3.5 The stress energy density function
12.3.6 The principle of minimum total potential energy
12.3.7 The principle of minimum complementary energy
12.3.8 Examples
12.3.9 The principle of least work
12.3.10Hu-Washizu's principle
12.3.11Hellinger-Reissner's principle
12.3.12Problems
12.4 Applications of Variational and Energy Principles
12.4.1 The shear lag problem
12.4.2 The non-uniform torsion problem
12.4.3 The non-uniform torsion problem (closed sections)
12.4.4 The non-uniform torsion problem (open sections)
12.4.5 Problems
Part IV Advanced topics
13 Introduction to Plasticity and Thermal Stresses
13.1 Yielding under combined loading
13.1.1 Introduction to yield criteria
13.1.2 Tresca's criterion
13.1.3 Von Mises' criterion
13.1.4 Problems
13.2 Applications of yield criteria to structural problems
13.2.1 Problems
13.2.2 Plastic bending
13.2.3 Problems
13.2.4 Plastic torsion
13.2.5 Examples
13.3 Thermal stresses in structures
13.3.1 The direct method
13.3.2 Examples
13.3.3 Problems
13.3.4 The constraint method
13.4 Application to bars and trusses
13.4.1 Examples
13.4.2 Problems
13.4.3 Application to beams
13.4.4 Examples
13.4.5 Problems
14 Buckling of Beams
14.1 Rigid bar with root torsional spring
14.1.1 Analysis of a perfect system
14.1.2 Analysis of an imperfect system
14.2 Buckling of beams
14.2.1 Equilibrium equations
14.2.2 Buckling of a pinned-pinned beam (Equilibrium approach)
14.2.3 Buckling of a pinned-pinned beam (Imperfection approach)
14.2.4 Work done by the axial force
14.2.5 Buckling of a pinned-pinned beam (Energy approach)
14.2.6 Examples
14.2.7 Buckling of beams with various end conditions
14.2.8 Problems
14.3 Buckling of sandwich beams
15 Shearing Deformations in Beams
15.1 Introduction
15.1.1 A simplified approach
15.1.2 An equilibrium approach
15.1.3 Examples
15.1.4 Problems
15.2 Shear deformable beams: an energy approach
15.2.1 Shearing effects on static deflections
15.2.2 Examples
15.2.3 Shearing effects on buckling
15.2.4 Shearing and rotary inertia effects on vibration
15.2.5 Problems
16 Kirchhoff Plate Theory
16.1 Governing equations of Kirchhoff plate theory
16.1.1 Kirchhoff assumptions
16.1.2 Stress resultant
16.1.3 Equilibrium equations
16.1.4 Constitutive laws
16.1.5 Summary of Kirchhoff plate theory
16.2 The bending problem
16.2.1 Typical boundary conditions
16.2.2 Simple plate bending solutions
16.2.3 Problems
16.3 Anisotropic plates
16.3.1 Laminated composite plates
16.3.2 Constitutive laws for laminated composite plates
16.3.3 The in-plane stiffness matrix
16.3.4 Problems
16.3.5 The bending stiffness matrix
16.3.6 The coupling stiffness matrix
16.3.7 Problems
16.3.8 Directionally stiffened plates
16.3.9 Governing equations for anisotropic plates
16.4 Solution techniques for rectangular plates
16.4.1 Navier's solution for simply supported plates
16.4.2 Examples
16.4.3 Problems
16.4.4 Levy's solution
16.4.5 Problems
16.5 Circular plates
16.5.1 Governing equations for the bending of circular plates
16.5.2 Circular plates subjected to loading presenting circular symmetry
16.5.3 Examples
16.5.4 Problems
16.5.5 Circular plates subjected to arbitrary loading
16.5.6 Examples
16.5.7 Problems 16.6 Energy formulation of Kirchhoff plate theory
16.6.1 The virtual work done by internal forces and moments
16.6.2 The virtual work done by the applied loads
16.6.3 The principle of virtual work for Kirchhoff plates
16.6.4 The principle of minimum total potential energy for Kirchhoff plates
16.6.5 Energy based approximate solutions for Kirchhoff plates
16.6.6 Examples
16.6.7 Problems
16.7 Shear deformable plates
16.7.1 Problems
16.8 Buckling of plates
16.8.1 Problems
17 Appendix: Mathematical Tools
17.1 Coordinate systems and transformations
17.1.1 The rotation matrix
17.1.2 Rotation of vector components
17.1.3 The rotation matrix in two dimensions
17.1.4 Rotation of vector components in two dimensions
17.2 Least-square solution of linear systems with redundant equations
17.3 Arrays and matrices
17.3.1 Partial derivatives of a linear form
17.3.2 Partial derivatives of a quadratic form
17.4 Orthogonality properties of trigonometric functions
References
Index

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Structural analysis : with applications to aerospace structures

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Structural analysis : with applications to aerospace structures

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