II.1 Theoretical background

The purpose of this Chapter is to summarize the classical laminate theory, and to provide the information needed by the user of composite classes to understand a few conventions that have been assumed for the programming of Classical Laminate Analysis in FeResPost (axes, angles, numbering of layers,...).

The programmer will find a presentation of the classical laminate theory that follows closely what is programmed in C++ language in FeResPost. However, those who are interested in studying the theory, or who are not familiar with it, are referred to more extensive presentations of the classical laminate theory [Gay97, Pal99]. The presentation of the out-of-plane shear behavior of the laminate is original, even though inspired by information found in [Sof04a].

II.1.1 Conventions
II.1.2 Rotation in XY plane and algebraic notations
II.1.3 Materials and plies
II.1.3.1 Plies
II.1.3.2 Materials and constitutive equations
II.1.3.3 In-plane properties
II.1.3.4 Out-of-plane shear properties
II.1.4 Thickness and mass of laminate
II.1.5 In-plane and flexural laminate behavior
II.1.6 Out-of-plane shear of laminate
II.1.6.1 Out-of-plane shear equilibrium equations
II.1.6.2 Triangular distribution of in-plane stresses
II.1.6.3 Out-of-plane shear stress partial derivative equations
II.1.6.4 Integration of out-of-plane shear stress equation
II.1.6.5 Approximations with out-of-plane shear forces
II.1.6.6 Out-of-plane laminate shear stiffness
II.1.6.7 Calculation algorithm for shear stiffness
II.1.6.8 Ply out-of-plane shear stresses
II.1.7 CTE and CME calculations
II.1.7.1 In-plane and flexural thermo-elastic behavior
II.1.7.2 Out-of-plane shear thermo-elastic behavior
II.1.7.3 Hygrometric behavior of laminates
II.1.7.4 Full sets of equations
II.1.8 Calculation of load response
II.1.8.1 In-plane and flexural response
II.1.8.2 Out-of-plane shear response
II.1.8.3 Out-of-plane T/C deformation
II.1.9 Accelerating the calculation of load response
II.1.9.1 Calculation of laminate loads and strains
II.1.9.2 Calculation of plies stresses and strains
II.1.10 Failure theories
II.1.10.1 Tresca criterion (2D)
II.1.10.2 Von Mises criterion (2D)
II.1.10.3 Von Mises criterion (3D)
II.1.10.4 Maximum stress criterion
II.1.10.5 Maximum stress criterion (3D)
II.1.10.6 Maximum strain criteria (2D)
II.1.10.7 Maximum strain criterion (3D)
II.1.10.8 Combined strain criterion (2D)
II.1.10.9 Tsai-Hill criterion
II.1.10.10 Tsai-Hill criterion (version b)
II.1.10.11 Tsai-Hill criterion (version c)
II.1.10.12 Tsai-Hill criterion (3D)
II.1.10.13 Tsai-Hill criterion (3D version b)
II.1.10.14 Tsai-Wu criterion
II.1.10.15 Tsai-Wu criterion (3D)
II.1.10.16 Hoffman criterion
II.1.10.17 Puck criterion
II.1.10.18 Puck “b” criterion
II.1.10.19 Puck “c” criterion
II.1.10.20 Hashin criteria
II.1.10.21 Hashin criteria (3D)
II.1.10.22 Yamada-Sun criterion
II.1.10.23 Yamada-Sun criterion (version b)
II.1.10.24 3D honeycomb criterion
II.1.10.25 Honeycomb shear criterion
II.1.10.26 Honeycomb simplified shear criterion
II.1.10.27 Inter-laminar shear criterion
II.1.11 Temperature diffusion in laminates
II.1.11.1 Material thermal parameters
II.1.11.2 In-plane and out-of-plane components
II.1.11.3 In-plane rotations of vectorial and tensorial properties
II.1.11.4 Integration along the laminate thickness
II.1.12 Moisture diffusion in laminates
II.1.13 Units

Chapter II.1Theoretical background

Chapter II.1
Theoretical background