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Support for Decision Making in Design of Composite Laminated Structures. Part 1: Parametric Knowledge Model

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Abstract

The design process of laminated composites faces two challenges: the engineer designs the product and its morphology, but also, simultaneously, the material. The number of design solutions can be huge since the solution space is very large. Standard CAE systems (CAD, Finite Element Simulation) do not offer to the designer an approach to explore design spaces easily handling design parameters that are intrinsic to the laminate structures: number of plies, layers’ constitutive laws, viscoelastic capacity of the matrix and volume fraction of fibers. This paper provides a new model of behavior making explicit these design parameters. This Parametric and reduced Behavior Model (PRBM) allows engineers to make rapid simulations of the product they are creating. Integrated in a meta-model of Knowledge, it is combined to usual specific knowledge that are typically the domain of composite experts and manufacturing experts. Our PRBM is made from a separated numerical method, next enabling (1) a multiscale approach: the engineer can implement reasoning either at the scale of the fiber, or at the scale of the ply, at the scale of the plies interfaces, at the scale of the lamination or at the scale of the structure, or, (2) a multiphysical approach: the engineer can independently manage the mechanical effect of each ply and each interface, either in static or dynamic cases; in the latter, the creeping behavior can be considered. Two simple cases are presented to illustrate the relevance of the PRBM when simulating composite structures: one under a static load and the having a dynamic behavior.

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Abbreviations

E :

Young’s modulus (MPa)

E f :

Fiber Young’s modulus (MPa)

E m :

Matrix Young’s modulus (MPa)

E l :

Young’s modulus of the ply in the direction of the fibers (MPa)

E t :

Young’s modulus of the ply in a direction transversal to the fiber direction (MPa)

F y , F z :

External forces (N)

F(ω):

Force as a function of frequency (N)

B :

Body force

G :

Shear modulus (MPa)

v :

Poisson’s ratio

l :

Length (mm)

h :

Height (mm)

w :

Width (mm)

u:

Displacement in direction x

v:

Displacement in direction y

w:

Displacement in direction z

ε :

Strain tensor

σ :

Stress Tensor (Pa)

σ ij :

Stress tensor element (Pa)

F 0 :

Objective function

ς, ξ, ψ :

(Weights)

\( {\mathbf{\mathcal{L}}}_{\boldsymbol{max}} \) :

Maximum deformation to the direction y

\( {\boldsymbol{U}}_{\boldsymbol{x},\boldsymbol{y},\boldsymbol{z},{\boldsymbol{p}}_{\mathbf{1}},{\boldsymbol{p}}_{\mathbf{2}},\bullet \bullet \bullet, {\boldsymbol{p}}_{\boldsymbol{d}}} \) :

Approximation of displacement field (mm)

U(x, y, z, p 1, p 1, ⋯, p d):

Displacement field as a function of given parameters (mm)

C :

Tensor of material properties in local coordinates

n :

Number of enrichment modes in PGD sense

\( \overline{\boldsymbol{C}} \) :

Tensor of material properties in global coordinates

\( \overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{1}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{2}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{3}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{4}}\right) \) :

Tensor of material properties at plies 1, 2, 3, 4 in global coordinates

C int :

Tensor of material properties at the interfaces

D :

Transformation matrix

ρ :

Density (kg/m3)

ρ f :

Fiber density

ρ m :

Resin density

Ω :

Geometric domain

θ i :

Fiber orientation of ply i (degrees)

V f :

Fiber volume fraction (%)

G 0 :

Short term shear modulus (GPa)

G ∞ :

Long-term shear modulus (GPa)

α :

Fractional derivative order

τ :

Decay time (s)

X, Y, Z, P1, P2, P3, P4, P5, P6, P7:

PGD functions

x,y,z,p 1 ,p 2 ,p 3 ,p 4 ,p 5 ,p 6 ,p 7 :

PGD domains

T max :

Maximum twist

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Authors and Affiliations

  1. I2M CNRS UMR 5295, Université de Bordeaux, ENSAM, Esplanade des Arts et Métiers, 33400, Talence, France

    Gilberto Fontecha Dulcey, Xavier Fischer & Pierre Joyot

  2. École Supérieure des Technologies Industrielles Avancées – ESTIA, Université de Bordeaux, technopole izarbel, 64210, Bidart, Aquitaine, France

    Gilberto Fontecha Dulcey, Xavier Fischer & Pierre Joyot

  3. Universidad Pontificia Bolivariana, Km 7, Autopista Piedecuesta, Bucaramanga, Colombia

    Gilberto Fontecha Dulcey

  4. Department of Mechanical Engineering, Clemson University, Fluor Daniel Building, Clemson, SC, 29634, USA

    Georges Fadel

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  1. Gilberto Fontecha Dulcey
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Correspondence to Gilberto Fontecha Dulcey.

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Fontecha Dulcey, G., Fischer, X., Joyot, P. et al. Support for Decision Making in Design of Composite Laminated Structures. Part 1: Parametric Knowledge Model. Appl Compos Mater 26, 643–662 (2019). https://doi.org/10.1007/s10443-018-9741-x

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