Advanced Mechanics of Materials and Applied Elasticity

Citation

Ugural, A. C., & Fenster, S. K. (2020). Advanced Mechanics of Materials and Applied Elasticity (6th ed.). Pearson.

Chapter Summary

The book has 13 chapters and five appendices, with about 720 pages before the index. Each chapter ends with references and problems, and several are divided into lettered parts. The preface says the chapters are largely self-contained, so the order can be changed to suit a course.

Chapter 1: Analysis of Stress

Opens with the relation between mechanics of materials and the theory of elasticity, the scope of the book and the role of analysis in design, then develops the components of stress, equilibrium, stresses on inclined sections and plane-stress transformation. It continues with principal stresses, Mohr's circles in two and three dimensions, octahedral stresses and boundary conditions, and ends with indicial notation.

Chapter 2: Strain and Material Properties

Covers strain, compatibility and the transformation of strain, then engineering materials and stress-strain diagrams. It derives Hooke's law in its generalized and orthotropic forms, discusses strain gages and rosettes, and introduces strain energy and Saint-Venant's principle.

Chapter 3: Problems in Elasticity

In three parts. Part A formulates plane strain and plane stress problems, Airy's stress function, polynomial solutions, thermal stresses and polar coordinates. Part B treats stresses due to concentrated loads and stress concentration factors. Part C treats contact stresses and deflections, including Hertz theory and spherical and cylindrical contacts.

Chapter 4: Failure Criteria

Part A treats static loading: failure by yielding and by fracture, the maximum shearing stress, distortion energy and octahedral shearing stress theories, the maximum principal stress, Mohr and Coulomb–Mohr theories, and an introduction to fracture mechanics with stress-intensity factors and fracture toughness. Part B treats repeated and dynamic loading: fatigue, fatigue life, impact and the ductile–brittle transition.

Chapter 5: Bending of Beams

Part A gives exact solutions for pure bending and for narrow cantilever and simply supported beams. Part B gives approximate solutions: the elementary theory, normal and shear stresses, composite beams, shear center and statically indeterminate systems. Part C treats curved beams by elasticity theory and by the curved beam formula, with a comparison of theories.

Chapter 6: Torsion of Prismatic Bars

Starts from circular bars and moves to the general torsion problem, Prandtl's stress function and the membrane analogy, narrow rectangular and thin-walled sections, restrained thin-walled members, torsion bar springs and curved circular bars.

Chapter 7: Numerical Methods

Part A covers finite difference analysis, including curved boundaries and boundary conditions. Part B introduces finite element analysis through bar, truss, beam and two-dimensional elements, a general formulation, the triangular element, plane-stress case studies and computational tools.

Chapters 8–9: Thick-Walled Cylinders and Rotating Disks; Beams on Elastic Foundations

Chapter 8 covers cylinders under pressure, compound cylinders and shrink fits, rotating disks of constant and variable thickness, thermal stresses and a finite element solution. Chapter 9 covers the general theory of beams on elastic foundations, infinite, semi-infinite and finite beams, and solution by finite differences.

Chapters 10–11: Applications of Energy Methods; Stability of Columns

Chapter 10 presents energy principles (Castigliano's theorem, the unit-load method, statically indeterminate systems) and variational methods (virtual work, minimum potential energy, trigonometric series, the Rayleigh–Ritz method). Chapter 11 treats the critical load, pin-ended and other columns, design formulas, imperfections, energy methods and finite difference solutions.

Chapters 12–13: Plastic Behavior of Materials; Stresses in Plates and Shells

Chapter 12 covers idealized stress–strain diagrams, plastic deflection of beams, limit design, plastic torsion and plastic stress–strain relations. Chapter 13 treats the bending of thin plates, with simply supported rectangular and circular plates and a finite element solution, and membrane stresses in thin shells of revolution and other shapes.

Appendices

The appendices cover problem formulation and solution, the solution of the stress cubic equation, moments of composite areas, tables and charts including stress concentration factors, and an introduction to MATLAB. Answers to selected problems follow.

Key Concepts

Chapters 1–3: Stress, strain and elasticity

• Stress transformation and Mohr's circle: finding principal and maximum shear stresses in two and three dimensions.
• Generalized Hooke's law: stress–strain relations for isotropic and orthotropic materials.
• Airy's stress function: the potential used for plane problems.
• Contact stresses: Hertz theory for spheres and cylinders.

Chapters 4–7: Failure, bending, torsion and numerical analysis

• Failure criteria: yielding and fracture theories for static loading, fatigue and fracture mechanics for repeated loading.
• Exact and approximate beam theories: elasticity solutions compared with elementary bending.
• Prandtl stress function and membrane analogy: the elasticity approach to torsion.
• Finite difference and finite element methods: numerical solution of problems without closed-form answers.

Chapters 8–13: Special structural problems

• Thick-walled cylinders and rotating disks: pressure, shrink fits and centrifugal loading.
• Energy and variational methods: Castigliano, virtual work and Rayleigh–Ritz.
• Column buckling and plastic collapse: stability and limit design.
• Plates and shells: plate bending and membrane theory.

Critical Analysis

Strengths

• Elasticity and mechanics of materials side by side. The preface says elasticity plays three roles: exact solutions for simple geometries, a check on the limits of the mechanics-of-materials approach, and the basis of numerical analysis. The beam chapter makes this visible by setting exact and approximate solutions beside each other.
• Classical and numerical methods balanced. The authors set out to give classical analysis a rather full treatment while emphasizing numerical techniques for problems that resist analytical solution, and Chapter 7 is devoted to finite differences and finite elements.
• Flexible structure. Most chapters are substantially self-contained, with lettered parts, so instructors can choose assignments for courses of different length.
• Practical supports. The preface mentions numerical examples throughout, problems in SI units with both SI and U.S. customary units defined, case studies in analysis and design, answers to selected problems and optional MATLAB solutions from the publisher; the book itself is independent of any software package.

Limitations

• Not a first course. The preface describes the book as for courses subsequent to an elementary treatment of the strength of materials, so readers need that background.
• Two-dimensional emphasis in elasticity. The preface singles out the two-dimensional treatment in Chapter 3 as the part whose weight an instructor may vary; there is no chapter devoted to three-dimensional solution methods.
• Narrow treatment of some materials. Orthotropic material appears in a section of Chapter 2 and one of Chapter 3, and the table of contents has no chapter on composites, anisotropic elasticity or wave propagation; readers needing those topics need a more specialised text.

Where It Fits in the Course

Ugural and Fenster is the bridge from elementary strength of materials to elasticity in this course list. Beer, Johnston, DeWolf and Mazurek's Mechanics of Materials and Hibbeler's Mechanics of Materials are the introductory courses it builds on; Gordon's The New Science of Strong Materials and Blockley's Structural Engineering: A Very Short Introduction are non-technical books for general readers that can come earlier still.

Sadd's Elasticity: Theory, Applications, and Numerics is the graduate-level next step. Its table of contents moves from mathematical preliminaries through two-dimensional problems to complex variable methods, anisotropic elasticity, thermoelasticity, nonhomogeneous elasticity and micromechanics. Ugural and Fenster stop short of that, and are the better choice for readers who want elasticity combined with energy methods, buckling, plasticity and plates and shells.

How to Use This Book

The preface describes the book as an outgrowth of classroom notes for advanced undergraduate and first-year graduate courses, useful also to practising engineers in aeronautical, civil and mechanical engineering and engineering mechanics.

A practical plan:

• Core: Chapters 1 and 2, which the preface recommends studying first, then Chapter 3 as far as the course requires.
• Choose by need: Chapter 4 for failure, Chapters 5–6 for beams and torsion, Chapter 7 for finite elements, Chapters 8–13 as topics demand (pressure vessels, disks, energy methods, buckling, plasticity, plates and shells).
• Practice: Work the examples with the problem formulation method of Appendix A, check answers against the selected solutions, and use Appendix E to repeat numerical problems in MATLAB.

Return to Chapter 1 for notation and sign conventions whenever a later chapter becomes opaque.