computational analysis & design for composites€¦ · panel using the fe software hyperworks...

www.welshcomposites.co.uk

Computational Analysis & Design for Composites

Prof. Johann Sienz & Dr. Mariela Luege

Swansea University


OUTLINE

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Case studiesStringer design and rib design

Steps in the numerical analysis of composite structures

Composite laminates definition and design

Stress strain relations for composite materials from macroscopic and microscopic approaches

Effective properties for isotropic, orthotropic and anisotropic materials and overview of mixture and homogenization approaches

Laminates damage, failure criteria and buckling

Numerical simulation of a composite stiffened panel using the FE software HYPERWORKS

Preparation of input file and analysis of results

33 Hat stiffened panel


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Case studiesStringer design and rib design






Numerical simulation of a composite stiffened panel using the finite element software HYPERWORKS


33 Hat stiffened panel

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Underside ofSkin Panel

Stringers

Skin Panel

Rear Spar

Centre SparFront SparRibs

Horizontal Stiffener

Skin

Vertical Stiffener

Packer

Stringer X-Section

Case studies: Thin & thick composite stringer design

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Case studies: Stringer X-section design

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Initial Superply

layup

Traditional Best Design

Shuffled Optimized

Design

Mass = 4.73kgBuckling = 1.18



Skin

Vertical Stiffener

Horizontal Stiffener

Packer UD 0º

45º-45º90º

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Geometry Extraction

Initial design Topology OptimizationMaterial Layout

Size and Shape OptimizationBuckling and Stress

~ 10%

~ 35%

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Case studies: Leading edge droop nose rib design

Final design

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DYNAMIC ANALYSIS

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OUTLINE

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Case studiesStringer design, rib design and some crush analysis

Steps for the numerical analysis of composite structures








Overview - Example

What do we know:We have a plateWe know how it is supportedWe know what composite material it is made ofWe know what the loading is

What would we like to know?

DisplacementsStrainsStressesDelaminationBucklingFracture

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Steps in Finite Element software

Geometry definition: CAD, drawing facilities

FE mesh construction

Application of constraints and loads

Selection of the type of Material

Type of problem:Static, dynamic

Run the program

Analysis of results: Displacements, stresses, etc

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2D


Computer-Aided Engineering (CAE) tools

Available computer-aided engineering (CAE) tools commonly used in the industry :

ABAQUS, ALTAIR HYPERWORKS, ANSYS and NASTRAN

Common characteristics:

FE solvers for solids, fluids, thermal, acoustic, electromagnetic and/or multiphysics problems

Robust and reliable meshing tools

Several optimization methods:

topological, size and shape

Combination of performance data management, process automation and good data exchange facilities for the solution of large scale optimization problems11


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The topics that are covered include:










Material definition:Composite laminate

A fibre composite laminate consists of thin, parallel, unidirectional reinforced layers, which are firmly bounded together

Each layer (called also lamina) is usually represented as an homogeneous orthotropic material

Composite Laminates are typically defined using:

nr of layers, nr of layers,

thickness, thickness,

fibre orientation, fibre orientation,

layer materiallayer material

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DesignA laminate may have between 4 and 400 layers and the fibre orientation changes from layer to layer in a regular manner through the thickness of the laminate, e.g. a 90/0/90 stacking sequence results in a cross-ply composite.Layer thicknesses, fibre directions, type of fibres, and matrix should be chosen upon the condition of optimizing an objective function, such as weight or price.The design is an integrated process leading from constituents to structure in the sequence:

FIBRE + MATRIX ⇒ UNIDIRECTIONAL COMPOSITE ⇒LAMINATE ⇒ COMPOSITE STRUCTURE

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Macro- vs. Micro-mechanicsMacromechanic analysis: Macromechanic analysis: no direct account of the fact that one is dealing with a composite material; one merely acknowledges this by modelling the material behaviour as isotropic, orthotropic or anisotropic with the material model properties obtained experimentally.

Micromechanic analysis: Micromechanic analysis: the behavior of the composite is directly predicted from the knowledge of the properties of the constituents (fiber, matrix) by using mathematical tools, such as:

Mixture theoryHomogenization theory

Studying performance on a micro-scale is essential if one needs to understand fully what controls the stiffness and strength of the composites15


Stress analysisIf the thickness of the laminate is generally small compared to the planar dimensions

⇒ two dimensional analyses are used

Assumption concerning the variation of displacements and/or stress through the thickness of the laminate:

Classical plate theoryFirst-order shear deformation theory

Further assumptions:

Layers are perfectly bounded togetherThe material of each layer is linearly elastic and orthotropicEach layer is of uniform thicknessThe strains are small 16


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Effective material propertiesEffective material properties define the relation between averages of field variables, such as stresses and strains, when their space variation is statistically homogeneous

σ11, σ22, σ33 : normal stressesσ12, σ13, σ23 : shear stresses ε11, ε22, ε33 : normal strainsε12, ε13, ε23 : shear strains

D: effective elastic coefficient reflecting material symmetry

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Isotropic composites

Example: Example: particle composite layer

Characteristic: Characteristic: same material properties in all directions

Effective propertiesEffective properties:

Two material elastic constants: E, ν Thermal expansion coefficient: αStrength value: σu , τu

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E, ν

x2 x3

x1


Orthotropic composites

ExampleExample: unidirectional fibre composite layer

⇒ The fibres are oriented in two mutually perpendicular directions

Effective properties Effective properties (plane stress):Four material elastic constants: E1, E2, G12 , ν12

Thermal expansion coefficient: α1, α2

Strength value: σu1, σu

2, τu12

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x2 x3

x1


Anisotropic composites

Example: Example: short fibre composite layer

⇒ The fibres are oriented randomly or aligned in two non-orthogonal directions

Effective properties Effective properties (plane stress):

Six material elastic constants: D11, D22, D33, D12, D13, D23

Thermal expansion coefficient: α1, α2 , α12

Strength value: σu1, σu

2, τu12

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x2 x3

x1

Mixture approachNotion of representative volume element (RVE):

RVE main properties:1.Its structure is ‘entirely typical’ for the composite

2.It contains a ‘sufficient number’ of micro-structural elements so that boundary conditions at the surface of the composite do not affect its

effective properties

Model

t

≡

1=Vf + Vm

t

Vf , Vm : fibre and matrix volume fraction

Simplified model

t

Representative Volume Element (RVE)

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RVE Longitudinal

Evaluation of the effective stiffness

≡

Transversal

≡

matrix fibre

fibre matrix

Ef

Em ε

P

EfEm P

ε=εm+εf

RVE Transverse

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Homogenization approach

Macro-micro approach applied to composites with periodic micro-structure

The material properties of the equivalent homogeneous continuum are called homogenized or effective properties

The inhomogeneous material is substituted by an equivalent homogeneous one, by ‘smearing’ the microscopic features at the macroscopic level.

1D elastic bar problem:

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L

A A

Y=εL

unit cell


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Laminates damage

• Laminate composite structure develop

Matrix cracks Fibre-matrix debondingFibre fractureDelamination

loss of stiffness andloss of stiffness andof strength of the material!of strength of the material!

Once the mechanical properties of the layers are known, the initial failure of a layer within a laminate or structure can be

predicted by applying an appropriate failure criterion.Failure criterion is used only to check whether allowables are

exceeded

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Composite (anisotropic) failure criterion

• Layer failure index (F>1)

Maximum stress criterion

Maximum strain criterion

Tsai-Hill anisotropic criterion:

• Bonding failure index

• Global final failure index for composite elementMaximum of all computed layer and bonding failure indices

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Sudden large out-of-plane displacements when the critical value of the load is reached.

Compressed bar Compressed isotropic plate

Linear Buckling Analysis

Search for the smallest λ (denoted by λcr ) with U ≠ 0 such that

(K-λKG)U = 0

K: material stiffness matrix, KG: geometric stiffness matrix Pcr=λcr Pref Critical or buckling load Critical or buckling load

Buckling

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b σc=KE(h/b)2

Delamination buckling

• local delamination can be seen as a crack in the bond

• low velocity impacts and defects in manufacturing can lead to local delamination

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Delamination buckling can be analysed as a classical linear problem of buckling of a strip with fixed ends


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Hat stiffened panel

STATIC ANALYSIS: Definition of the Material properties

Single module design

Layer Material Properties Layer Stacking Sequence:

45/-45/0/90/0/-45/45

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351mm

109mm

tctw

tstf

147mm

213mm

165mm

z

y

x

3.81m3.81m

AB

CD

E11= 6.4E4MPa E22= 3.2E4MPaG12= 1.6E4MPa

ν12 = 0.397

εall =5.40*10-3

σall= 344.738MPaτall = 124.106

ρ = 1.6E-7

Hat stiffened plate

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Nx

q

Finite element mesh ⇒


Thank you for your attention!

computational analysis & design for composites€¦ · panel using the fe software hyperworks...

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