Thermal Stress Analysis of Composite Beams, Plates and Shells

Thermal Stress Analysis of Composite Beams, Plates and Shells

by Erasmo Carrera, Fiorenzo A. Fazzolari, Maria Cinefra
Released November 2016
Publisher(s): Academic Press
ISBN: 9780124200937

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Book description

Thermal Stress Analysis of Composite Beams, Plates and Shells: Computational Modelling and Applications presents classic and advanced thermal stress topics in a cutting-edge review of this critical area, tackling subjects that have little coverage in existing resources. It includes discussions of complex problems, such as multi-layered cases using modern advanced computational and vibrational methods.

Authors Carrera and Fazzolari begin with a review of the fundamentals of thermoelasticity and thermal stress analysis relating to advanced structures and the basic mechanics of beams, plates, and shells, making the book a self-contained reference. More challenging topics are then addressed, including anisotropic thermal stress structures, static and dynamic responses of coupled and uncoupled thermoelastic problems, thermal buckling, and post-buckling behavior of thermally loaded structures, and thermal effects on panel flutter phenomena, amongst others.



  • Provides an overview of critical thermal stress theory and its relation to beams, plates, and shells, from classical concepts to the latest advanced theories
  • Appeals to those studying thermoelasticity, thermoelastics, stress analysis, multilayered structures, computational methods, buckling, static response, and dynamic response
  • Includes the authors' unified formulation (UF) theory, along with cutting-edge topics that receive little coverage in other references
  • Covers metallic and composite structures, including a complete analysis and sample problems of layered structures, considering both mesh and meshless methods
  • Presents a valuable resource for those working on thermal stress problems in mechanical, civil, and aerospace engineering settings

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. About the Authors
  6. Preface
    1. References
  7. Introduction
    1. Thermal structures and their applications
    2. Advanced structural theories in the modelling of thermal stress problems
    3. Classification of thermoelastic problems
    4. Book's content
    5. References
  8. Part I: Thermoelasticity
    1. Chapter 1: Fundamentals of thermoelasticity
      1. Abstract
      2. 1.1. Stress tensor
      3. 1.2. Displacement and strain tensor
      4. 1.3. Conservation laws
      5. 1.4. Three-dimensional thermoelasticity
      6. 1.5. Two-dimensional thermoelasticity
      7. References
    2. Chapter 2: Solution of sample problems in classical thermoelasticity
      1. Abstract
      2. 2.1. Sample problems in thermoelasticity
      3. 2.2. Heat conductions problems
      4. References
    3. Chapter 3: Coupled and uncoupled variational formulations
      1. Abstract
      2. 3.1. Classical variational principles
      3. 3.2. Thermoelastic variational formulations
      4. References
  9. Part II: Classical and Advanced Modelling of Thermal Structures
    1. Chapter 4: Fundamental of mechanics of beams, plates and shells
      1. Abstract
      2. 4.1. Typical structures
      3. 4.2. Axiomatic method
      4. 4.3. Asymptotic method
      5. 4.4. Beam
      6. 4.5. Classical models and the complete linear expansion case
      7. 4.6. Plate
      8. 4.7. Classical models and the complete linear expansion
      9. 4.8. 2D shell models with N-order displacement field, the Taylor expansion class
      10. 4.9. Geometry description
      11. 4.10. Classical models and unified formulation
      12. References
    2. Chapter 5: Advanced theories for composite beams, plates and shells
      1. Abstract
      2. 5.1. Introduction to the unified formulation
      3. 5.2. Stiffness matrix of a bar and the related fundamental nucleus
      4. 5.3. Fundamental nucleus for the case of a bar element with internal nodes
      5. 5.4. FEM and the theory of structure: a four indices fundamental nucleus
      6. 5.5. The assembly procedure
      7. 5.6. A unified approach for one-, two- and three-dimensional structures
      8. 5.7. Beam
      9. 5.8. DEBBT, TBT and N=1 in unified form
      10. 5.9. Higher-order models
      11. 5.10. 1D models with a physical volume/surface-based geometry and pure displacement variables, the Lagrange Expansion class (LE)
      12. 5.11. Physical volume/surface approach
      13. 5.12. Lagrange polynomials and isoparametric formulation
      14. 5.13. LE displacement fields and cross-section elements
      15. 5.14. Cross-section multi-elements and locally refined models
      16. 5.15. Plate
      17. 5.16. CPT, FSDT and N=1 model in unified form
      18. 5.17. Unified formulation of N-order
      19. 5.18. 2D models with physical volume/surface-based geometry and pure displacement variables, the Lagrange expansion class (LE)
      20. 5.19. Physical volume/surface approach
      21. 5.20. Lagrange expansion model
      22. 5.21. Extension to multilayered structures
      23. 5.22. Multilayered structures
      24. 5.23. Theories on multilayered structures
      25. 5.24. Unified formulation for multilayered structures
      26. 5.25. UF in terms of 1×1 secondary nuclei
      27. 5.26. Discussion on possible best beam, plate and shell diagrams
      28. 5.27. The mixed axiomatic/asymptotic method
      29. 5.28. Static analysis of beams
      30. 5.29. Modal analysis of beams
      31. 5.30. Static analysis of plates and shells
      32. 5.31. The best theory diagram
      33. References
    3. Chapter 6: Multilayered, anisotropic thermal stress structures
      1. Abstract
      2. 6.1. Equations of anisotropic elasticity
      3. 6.2. Functionally graded materials constitutive law
      4. 6.3. RMVT constitutive law
      5. 6.4. Constitutive equations for thermoelastic problems
      6. References
    4. Chapter 7: Computational methods for thermal stress analysis
      1. Abstract
      2. 7.1. Approximate solution methods
      3. 7.2. Ritz method
      4. 7.3. Ritz method and Reissner's mixed variational theorem
      5. 7.4. Galerkin and generalized Galerkin methods
      6. 7.5. Governing differential equations
      7. 7.6. Coupled and uncoupled thermoelastic equations
      8. References
  10. Part III: Thermal Stress Analysis: Results and Applications
    1. Chapter 8: Through-the-thickness thermal fields in one-layer and multilayered structures
      1. Abstract
      2. 8.1. Introduction
      3. 8.2. Description of the four sample problems
      4. 8.3. Numerical illustrations for temperature profiles
      5. 8.4. Results on plate response
      6. References
    2. Chapter 9: Static response of uncoupled thermoelastic problems
      1. Abstract
      2. 9.1. Introduction
      3. 9.2. Thermal stress analysis of laminated composites by a variable kinematic MITC9 shell element
      4. References
    3. Chapter 10: Free vibration response of uncoupled thermoelastic problems
      1. Abstract
      2. 10.1. Introduction
      3. 10.2. Sandwich plate with cross-ply face sheets
      4. 10.3. Sandwich plate with angle-ply face sheets
      5. 10.4. Effect of the thermal environment on the free vibration response
      6. References
    4. Chapter 11: Static and dynamic responses of coupled thermoelastic problems
      1. Abstract
      2. 11.1. Introduction
      3. 11.2. Mechanical loading: static instantaneous thermo-mechanical analysis
      4. 11.3. Thermal loading: higher-order effects on displacements and stress results
      5. 11.4. Thermal loading: assessment of temperature profile, steady-state solution
      6. 11.5. Thermo-mechanical dynamic analysis of aluminum plate
      7. References
    5. Chapter 12: Thermal buckling
      1. Abstract
      2. 12.1. Introduction
      3. 12.2. Thermal buckling analysis of laminated composite and sandwich structures
      4. 12.3. Influence of thermal-mechanical interaction loadings on the circular frequency parameters
      5. References
    6. Chapter 13: Thermal stresses in functionally graded materials
      1. Abstract
      2. 13.1. Introduction
      3. 13.2. Natural frequencies of FGM isotropic and sandwich plates
      4. 13.3. Critical temperature of FGM isotropic and sandwich plates
      5. 13.4. Free vibration characteristics of FGM sandwich plates in thermal environment
      6. References
    7. Chapter 14: Thermal effect on flutter of panels
      1. Abstract
      2. 14.1. Introduction
      3. 14.2. Flutter behaviour of flat panels in supersonic flow
      4. 14.3. Aeroelastic instabilities of FGM panels under thermo-mechanical loads
      5. References
  11. Index

Product information

  • Title: Thermal Stress Analysis of Composite Beams, Plates and Shells
  • Author(s): Erasmo Carrera, Fiorenzo A. Fazzolari, Maria Cinefra
  • Release date: November 2016
  • Publisher(s): Academic Press
  • ISBN: 9780124200937