webinar_computationalanalysis

7/28/2019 webinar_ComputationalAnalysis

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www.welshcomposites.co.uk

Computational Analysis &

Design for CompositesProf. Johann Sienz & Dr. Mariela Luege

Swansea University


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OUTLINE

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Case studiesStringer design and rib design

Steps in the numerical analysis of compositestructures

Composite laminates definition and design

Stress strain relations for composite materialsfrom macroscopic and microscopic approaches

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

Laminates damage, failure criteria and buckling

Numerical simulation of a composite stiffenedpanel using the FE software HYPERWORKS

Preparation of input file and analysis of results

33 Hat stiffened panel


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OUTLINE

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Case studiesStringer design and rib design

Steps in the numerical analysis of composite

structures





Numerical simulation of a composite stiffenedpanel using the finite element softwareHYPERWORKS


33 Hat stiffened panel


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4

Underside of

Skin Panel

Stringers

Skin Panel

Rear Spar

Centre SparFront Spar

Ribs

Horizontal Stiffener

Skin

Vertical Stiffener

Packer

Stringer X-Section

Case studies:

Thin & thick composite stringer design

courtesy


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Case studies: Stringer X-section design

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InitialSuperply

layup

TraditionalBest Design

ShuffledOptimized

Design

Mass = 4.73kg

Buckling = 1.18

Mass = 11.64kg

Buckling = 3.14

Mass = 4.66kg

Buckling = 1.03

Skin

Vertical Stiffener

Horizontal Stiffener

Packer UD0

45-4590

courtesy

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GeometryExtraction

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 compositestructures




Laminates damage, failure criteria and bucklingNumerical simulation of a composite stiffenedpanel using the FE software HYPERWORKS



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Overview - Example

What do we know:

We have a plate

We know how it is supported

We know what compositematerial it is made of

We know what the loading is

What would we like to know?

Displacements

Strains

Stresses

Delamination

Buckling

Fracture

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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


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Computer-Aided Engineering

(CAE) toolsAvailable computer-aided engineering (CAE) toolscommonly 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 facilitiesfor the solution of large scale optimization problems11


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OUTLINE

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The topics that are covered include:

Case studies

Stringer design, rib design and some crush analysisSteps in the numerical analysis of compositestructures








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Material definition:

Composite laminateA fibre composite laminate consists of thin,parallel, unidirectional reinforced layers, whichare firmly bounded together

Each layer (called also lamina) is usuallyrepresented as an homogeneous orthotropicmaterial

Composite Laminates are typically defined using:

99 nr of layers,nr of layers,

99 thickness,thickness,

99 fibre orientation,fibre orientation,99 layer materiallayer material

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Design

A laminate may have between 4 and 400 layersand the fibre orientation changes from layer tolayer in a regular manner through the thicknessof the laminate, e.g. a 90/0/90 stackingsequence results in a cross-ply composite.

Layer thicknesses, fibre directions, type of fibres,and matrix should be chosen upon the conditionof optimizing an objective function, such asweight or price.

The design is an integrated process leading fromconstituents to structure in the sequence:

FIBRE + MATRIX UNIDIRECTIONAL COMPOSITE

LAMINATE COMPOSITE STRUCTURE

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Macro- vs. Micro-mechanics

Macromechanic analysis:Macromechanic analysis: no direct account of thefact that one is dealing with a composite material;one merely acknowledges this by modelling thematerial behaviour as isotropic, orthotropic or

anisotropic with the material model propertiesobtained experimentally.

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

Mixture theory

Homogenization theory

Studying performance on a micro-scale is essentialif one needs to understand fully what controls thestiffness and strength of the composites

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Stress analysis

If the thickness of the laminate is generally smallcompared to the planar dimensions

two dimensional analyses are used

Assumption concerning the variation ofdisplacements and/or stress through thethickness of the laminate:

Classical plate theory

First-order shear deformation theory

Further assumptions:

Layers are perfectly bounded together The material of each layer is linearly elastic and

orthotropic

Each layer is of uniform thickness

The strains are small16


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OUTLINE

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Stress strain relations for compositematerials from macroscopic and microscopicapproaches






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Effective material properties

Effective material properties define the relationbetween averages of field variables, such asstresses and strains, when their space variationis statistically homogeneous

11, 22, 33: normal stresses

12

, 13

, 23

: shear stresses

11, 22, 33: normal strains

12, 13, 23: shear strains

D: effective elastic coefficient reflecting materialsymmetry

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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,

Thermal expansion coefficient:

Strength value:

u

, u

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E,

x2 x3

x1


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Orthotropic composites

ExampleExample: unidirectional fibre composite layer

The fibres are oriented in two mutually

perpendicular directions

Effective propertiesEffective properties (plane stress):

Four material elastic constants: E1, E2, G12 , 12 Thermal expansion coefficient: 1, 2 Strength value: u

1, u

2, u

12

20

x2 x3

x1


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Anisotropic composites

Example:Example: short fibre composite layer

The fibres are oriented randomly or aligned in two non-

orthogonal directions

Effective propertiesEffective properties (plane stress): Six material elastic constants: D11,D22,D33,D12,D13,D23

Thermal expansion coefficient: 1,2 ,12

Strength value: u1,

u2,

u12

21

x2 x3

x1


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Mixture approach

Notion 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 thatboundary conditions at the surface of the composite do not affect its

effective properties

Model

t

1=Vf+Vm

t

Vf, Vm : fibre and matrixvolume fraction

Simplifiedmodel

t

Representative VolumeElement(RVE)

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RVE Longitudinal

Evaluation of the effective stiffness

Transversal

matrix fibre

fibrematrix

Ef

Em

P

EfEm P

=m+f

RVE Transverse

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Homogenization approach

Macro-micro approach applied to composites withperiodic micro-structure

The material properties of the equivalent

homogeneous continuum are called homogenizedor effective properties

The inhomogeneous material is substituted by anequivalent homogeneous one, by smearing the

microscopic features at the macroscopic level.

1D elastic bar problem:

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L

A A

Y=L

unitcell


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OUTLINE

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Laminates damage, failure criteria andbuckling




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Laminates damage

Laminate composite structure develop

Matrix cracks

Fibre-matrix debonding

Fibre fracture

Delamination

loss of stiffness andloss of stiffness and

of strength of the material!of strength of the material!

Once the mechanical properties of the layers are known, theinitial 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 areexceeded

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Composite (anisotropic)failure criterion

Layer failure index (F>1)

Maximum stress criterion

Maximum strain criterion

Tsai-Hill anisotropiccriterion:

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 loadis reached.

Compressed bar Compressed isotropic plate

Linear Buckling Analysis

Search for the smallest (denoted by cr ) with U 0 such that

(K-KG)U = 0

K: material sti ffness matrix , KG: geometric stiffness matrix

Pcr=crPref Critical or buckling loadCritical or buckling load

Buckling

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b c

=KE(h/b)2


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Delamination buckling local delamination can be seen as a crack in the bond

low velocity impacts and defects in manufacturing can lead tolocal delamination

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


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OUTLINE

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Numerical simulation of a compositestiffened panel using the FE softwareHYPERWORKS



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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

ts

tf

147mm

213mm

165mm

z

y

x

3.81m3.81m

A

BCD

E11= 6.4E4MPaE22= 3.2E4MPa

G12= 1.6E4MPa

12= 0.397

all =5.40*10-3all= 344.738MPa

all = 124.106

= 1.6E-7


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Hat stiffened plate

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Nx

q

Finite element mesh


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Thank you for your attention!

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