MSc thesis presentation - Aerospace Structures - July 2015

Static and free-vibration analysis of damagedmetallic and composite aerospace structures

through advanced beam models

Alessandro Rosati

POLITECNICO DI TORINOI Facoltà di Ingegneria

Tesi di laurea magistrale in Ingegneria Aerospaziale

Prof. Erasmo CarreraDott. Marco PetroloDott. Alfonso Pagani

Relatori:

22 luglio 2015

1D Beam models

Politecnico di TorinoTesi di laurea magistrale in Ingegneria Aerospaziale 2

Introduction

Low computational cost

Reliable results for slender, compact and homogeneous structures in bending

⊗ Strong assumptions/simplifications needed

⊗ Difficulties in handling with complex problems(composites, short and thin-walled structures)

Real wing 1D beam model

Carrera Unified Formulation (CUF)


Carrera Unified Formulation

i, j: shape function indexes (depending on the FE discretization)τ, s: expansion function indexes (depending on the model order)

Fundamental Nucleus:

Modelli CUF 1D Taylor e Lagrange



TE models:

LE models:

Timoshenko classical model, obtained as a particular case of N = 1

L9 isoparametric polynomial:

Component–Wise (CW)



Each component of the structure is modelled via beams only!

Present work outlines


Present work outlines

• development of a tool able to simulate, via TE and LE CUF models, the behavior of aeronautical multi-component structures subjected to increasing loads

Purpose: to understand the evolution of the stresses concerning to the main parts of the studied structures and to calculate the values of final loads

• evaluate the variation of natural frequencies of some structures, treated in previous works, as a result of the introduction of damages

Purpose: to understand the free-vibration behavior of structures in response to the introduction of damages and test CUFcapabilities to deal with non-destructive testing of structures

Damage Modelling


Damage Modelling

• modelled as percentage reductions or modifications of the elastic/shear modules of constitutive materials

• a proper factor has been introduced: it is defined as d* = 1 − d, in which d is the entity of damage (the damage percentage is given by 100 × d)

Ed*, m = d* × Em

Gd*, mn = d* × Gmn

Deteriorations in the mechanical characteristics of the structural components

(m, n are the involved directions in the adopted reference frame, m ≠ n)

Progressive Failure Analysis


Failure Analysis

Objectives: to evaluate the ultimate load of multi-component structures

the structure is subjected only to bending by means of a increasing transverse point load Fz

the evolution of stresses on eachcomponent of the structure has to bestudied

failure criteria have to be defined

The ultimate load is intended as the maximum external load at which the structurecollapse and it is no more able to perform its duties

Failure Criteria


Failure Analysis

The total failure of the multi-component structure is modelled as the loss of all constrained stringers.

Single failures on stringers:

• a ultimate stress value has to be chosen, as function of the material employed

• when a general stringer reaches its ultimate stress level, it is considered lost and a null elastic modulus has to be assigned to it (d* = 0)

Traction:Yield stress σ02

Compression:Euler buckling stress

Procedure and Assumptions


Failure Analysis

• there is a linear correspondence between external load Fz and internal tensions σ

• there is a linear correspondence between stresses σ and strains ε (elastic behaviour)

• isotropic materials are adopted

Assessment Phase:Comparison between results obtained by means of

EBBT CUF model and iterative analysis based on ideal-monocoque method

Isotropic material definition


Failure Analysis

An isotropic aluminium alloy material has been adopted for every componentof the studied structures:

E is the elastic modulus of the material, ν the Poisson ratio, ρ the density,Yield stress

E = 75 GPaν = 0.33

ρ = 2700 kg/m3

σ02 = 0.3 GPa

A rib has been located at the free-tip of every structure, where the external load is applied, and modelled with a elastic modulus ten times higher than the one adopted for other components

Ultimate load evaluation: 4-stringers wing-box


Failure Analysis: 4-stringers wing-box

b = 1 mh = 0.5 mt = 2 × 10−3 mL = 3 m As = 1.6 × 10−3 m2

• 10 B4 element mesh along the y−axis

• Clamped in y = 0

• Fz applied at [b/2, L, h/2]

• Resistant panels

Ultimate load evaluation: 6-stringers wing-box







b = 1 mh = 0.5 mt = 2 × 10−3 mL = 3 m As = 1.6 × 10−3 m2

Initial damages: 6-stringers wing-box



Ultimate Load × 10-5 N

Shear-instabilities: 6-stringers wing-box



• onset of instability phenomena on panels

• the instability condition modelled as a damage

Critical shear tension:

Multi wing-boxes


Failure Analysis: multi wing-boxes





b = 1 mh = 0.5 mt = 2 × 10−3 mL = 9 m ℓ = 3 mAs = 1.6 × 10−3 m2

Free-vibration analysis



• Isotropic, orthotropic and compositematerials have been investigated

• The Modal Assurance Criterion (MAC) has been adopted in order to yield a degree of consistency between mode shapes of undamaged and damagedstructure

Objectives: to understand the dynamic behaviour of structures

in response to the introduction of damages

Sandwich beam



• clamped-clamped

• face sheets (f) bonded to a core (c)


• isotropic material

L = 1 mhc = 0.16 mhf = 0.02 m

Ef = 68.9 GPaEc = 179.1 MPa

ρ f = 2687.3 kg/m3

ρ c = 119.69 kg/m3

ν f = ν c = 0.3

Sandwich beam



Component-Wise model is able to detect mode shapes involving the external layers only, because of the remarkable difference in the elastic modulus values

between the materials of faces and core respectively

Mode 5 - 796.021 Hz Mode 6 - 1070.623 Hz Mode 7 - 1081.442 Hz

Damages : bottom face-sheet



d* = 0.5

MAC evaluation



Undamaged - d* = 0.1Undamaged - d* = 0.5Undamaged - d* = 0.9

CW solutions, comparisons in mode shapesof undamaged and damaged structure

MAC evaluation



CW solutions, comparisons in mode shapes considring diferrent damage locations:the entire layer and a 20% of the total length zone at the free-tip and middle-span

Undamaged - d* = 0.1 Undamaged - d* = 0.1 Undamaged - d* = 0.1

Composite-type Longeron



• clamped-free

• 16 B4 along the y−axis

• total length: 1 m

UD and -45/45 layers:ORTHOTROPICEL = 40 GPaET = 4 GPaGLT = GTT = 1 GPaν LT = ν TT = 0.25

Foam:ISOTROPICE = 50 MPaν = 0.25

Damages: bottom UD layer



d* = 0.5

MAC evaluation, UD layer





MAC evaluation, UD layer



CW solutions, comparisons in mode shapes considring diferrent damage locations, on the bottom UD layer for 20% of the total length

Undamaged - d* = 0.5 Undamaged - d* = 0.5 Undamaged - d* = 0.5

Free-tip Middle-span Clamped-end

Damages: internal -45/45 thin layer



d* = 0.5

MAC evaluation, thin layer





Conclusions


Conclusions

• reliable ultimate loads in bending have been evaluated and significant structural behaviours have been pointed out at a low computational cost

• mode shapes and frequencies of undamaged and damaged structures calculated through solid FEM analyses have been almost duplicated by LE and high-order TE models

• MAC number evaluation has been in many cases a useful tool in order to point out discrepancies in the mode shapes of undamaged and damaged structures

Conclusions


Conclusions

Overcome the limitations imposed by the fundamental assumptions of classical beam theories

Some limitations in the approximation of some geometries can be found

TE models:

Is able to furnish reliable solutions and is not affected by limitations due to geometry/complexity of the structure to be analyzed.

Is able to correctly predict local shapes typical of sandwich or laminated structures

CW approach:

THANKS FOR YOUR ATTENTION!

Alessandro Rosati 22 luglio 2015

Any suggestions or questions are welcome

MSc thesis presentation - Aerospace Structures - July 2015

Engineering

Transcript of MSc thesis presentation - Aerospace Structures - July 2015