This document summarizes Alessandro Rosati's master's thesis on analyzing damaged aerospace structures using advanced beam models. The thesis develops Carrera Unified Formulation (CUF) beam models to simulate the static and free vibration behavior of multi-component structures subjected to increasing loads or damage. It evaluates ultimate loads and natural frequencies of wings and composite beams with initial damage or shear instabilities modeled. The CUF models provide reliable results comparable to solid finite element analyses at lower computational cost. The thesis demonstrates the CUF approach's ability to handle complex composite and sandwich geometries, as well as predict local mode shapes.
Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'...Franco Bontempi
Lezione su applicazioni dell'ottimizzazione strutturale a casi reali di strutture per l'ingegneria civile tenuta nell'ambito del corso di dottorato sull'ottimizzazione strutturale, Roma 21 maggio 2015.
Bike Share Webinar Presentation July 2015 Dr Elliot FishmanDr. Elliot Fishman
This presentation acts as the foundation for a webinar on international bike share. It covers the history of bike share, impact analysis, as well as barriers and facilitators to use.
Advice is provided for cities looking to establish bike share, as well as for those looking to boost the performance of existing ones.
Fire Resistance of Materials & Structures - Analysing the Steel StructureArshia Mousavi
A library room, whose structural steel members are to be checked in fire conditions (in terms of bearing capacity, R criterion).
The aims of this project are as follows:
1. Design of the beam and the column at room temperature
a) design the beam capacity at the ULS and the check the deflection at the SLS (d ≤ L1/250 in the rare combination) b) design the column for its buckling resistance.
2. Design the beam fire protection (boards) for the required fire resistance under the quasi-permanent load
the combination and assuming a three-sided exposure (concrete deck on top)
suggested steps: design load under fire
ultimate load of the beam at time = 0
ductility class
global failure or just a critical section?
increased capacity of the critical sections by the adaptation factors degree of utilization of the structure (or the critical section)
critical temperature.
protection design & final check.
3. Design the column fire protection
for the required fire resistance under the quasi- permanent load combination (optional: accounting for the effect of the thermal elongation of the beam).
suggested steps: design load under fire
thermal elongation of the beam assessment of the equivalent. uniform moment critical temperature (spreadsheet file)
protection design & final check
If needed, the member cross-sections designed at room temperature may be adjusted in order to meet the required fire resistance (parts 2 and 3)
Fire Resistance of Materials & Structures - Analysing the Concrete StructureArshia Mousavi
Analysing the concrete structure for the following aims:
(a) Design the critical beam sections at room temperature, by determining the reinforcement, and then evaluate the fire endurance of the beam (with reference to the fire scenario studied in Homework 2) by means of the 500°C isotherm method. Both the static and the kinematic approach should be applied, and the differences between the two should be commented.
To ensure the ductility requirements at room temperature, the relative depth of the compression zone must not be larger than x/d = 0.40.
* Let us assume that the central column is removed: the new section and the corresponding structural scheme are indicated in the figure below. The total depth h2 becomes 60 cm.
(b) Repeat step (a) for the new section and structural scheme, and comment on the possible interaction with the boundaries.
Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'...Franco Bontempi
Lezione su applicazioni dell'ottimizzazione strutturale a casi reali di strutture per l'ingegneria civile tenuta nell'ambito del corso di dottorato sull'ottimizzazione strutturale, Roma 21 maggio 2015.
Bike Share Webinar Presentation July 2015 Dr Elliot FishmanDr. Elliot Fishman
This presentation acts as the foundation for a webinar on international bike share. It covers the history of bike share, impact analysis, as well as barriers and facilitators to use.
Advice is provided for cities looking to establish bike share, as well as for those looking to boost the performance of existing ones.
Fire Resistance of Materials & Structures - Analysing the Steel StructureArshia Mousavi
A library room, whose structural steel members are to be checked in fire conditions (in terms of bearing capacity, R criterion).
The aims of this project are as follows:
1. Design of the beam and the column at room temperature
a) design the beam capacity at the ULS and the check the deflection at the SLS (d ≤ L1/250 in the rare combination) b) design the column for its buckling resistance.
2. Design the beam fire protection (boards) for the required fire resistance under the quasi-permanent load
the combination and assuming a three-sided exposure (concrete deck on top)
suggested steps: design load under fire
ultimate load of the beam at time = 0
ductility class
global failure or just a critical section?
increased capacity of the critical sections by the adaptation factors degree of utilization of the structure (or the critical section)
critical temperature.
protection design & final check.
3. Design the column fire protection
for the required fire resistance under the quasi- permanent load combination (optional: accounting for the effect of the thermal elongation of the beam).
suggested steps: design load under fire
thermal elongation of the beam assessment of the equivalent. uniform moment critical temperature (spreadsheet file)
protection design & final check
If needed, the member cross-sections designed at room temperature may be adjusted in order to meet the required fire resistance (parts 2 and 3)
Fire Resistance of Materials & Structures - Analysing the Concrete StructureArshia Mousavi
Analysing the concrete structure for the following aims:
(a) Design the critical beam sections at room temperature, by determining the reinforcement, and then evaluate the fire endurance of the beam (with reference to the fire scenario studied in Homework 2) by means of the 500°C isotherm method. Both the static and the kinematic approach should be applied, and the differences between the two should be commented.
To ensure the ductility requirements at room temperature, the relative depth of the compression zone must not be larger than x/d = 0.40.
* Let us assume that the central column is removed: the new section and the corresponding structural scheme are indicated in the figure below. The total depth h2 becomes 60 cm.
(b) Repeat step (a) for the new section and structural scheme, and comment on the possible interaction with the boundaries.
Spring 2015 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
TINCE2016 - Estimate of cracking and leaking rate of VERCORS mock-up - R. Vé...Gildas POTIN
The VERCORS project (French acronym for “Realistic verification of the behaviour of reactor containments”) consists in designing and building a 1/3 scaled mock-up of the inner containment of a French nuclear reactor of type “P’4”. The mock-up is a prestressed-concrete building dedicated to research purposes. Its overall dimensions are: height 25 m, diameter 15m, thickness of cylinder wall 0.40 m.
A first benchmark was organized by EDF with three themes proposed:
1. Early-age behaviour of gusset zone of the containment;
2. Containment history: prediction of deformations, stresses and cracking history of the whole containment during prestressing and first pressure test;
3. Leakage: estimate of air leakage during pressure test at the pressure peak of 5,2 bars absolute
The paper deals with calculations carried out by Tractebel Engie – Coyne et Bellier for themes 2 and 3. As regards results, we focus on cracking and leaking rate.
Spring 2014 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
Reinforced concrete Course Assignments, 2023.
Educational material for the RCS course. Design examples for reinforced concrete structures regarding beams and mast columns.
Spring 2016 problems for the course Rak-43.3110 Prestressed and precast concrete. Problems include
-Working stress design
-Ultimate strength design
-Loadbalancing
-Prestress losses
-Composite structures
Fatigue life predictions analysis should be performed according to standards in order to avoid uncertainties regarding assumptions for loads and component capacity.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
More Related Content
Similar to MSc thesis presentation - Aerospace Structures - July 2015
Spring 2015 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
TINCE2016 - Estimate of cracking and leaking rate of VERCORS mock-up - R. Vé...Gildas POTIN
The VERCORS project (French acronym for “Realistic verification of the behaviour of reactor containments”) consists in designing and building a 1/3 scaled mock-up of the inner containment of a French nuclear reactor of type “P’4”. The mock-up is a prestressed-concrete building dedicated to research purposes. Its overall dimensions are: height 25 m, diameter 15m, thickness of cylinder wall 0.40 m.
A first benchmark was organized by EDF with three themes proposed:
1. Early-age behaviour of gusset zone of the containment;
2. Containment history: prediction of deformations, stresses and cracking history of the whole containment during prestressing and first pressure test;
3. Leakage: estimate of air leakage during pressure test at the pressure peak of 5,2 bars absolute
The paper deals with calculations carried out by Tractebel Engie – Coyne et Bellier for themes 2 and 3. As regards results, we focus on cracking and leaking rate.
Spring 2014 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
Reinforced concrete Course Assignments, 2023.
Educational material for the RCS course. Design examples for reinforced concrete structures regarding beams and mast columns.
Spring 2016 problems for the course Rak-43.3110 Prestressed and precast concrete. Problems include
-Working stress design
-Ultimate strength design
-Loadbalancing
-Prestress losses
-Composite structures
Fatigue life predictions analysis should be performed according to standards in order to avoid uncertainties regarding assumptions for loads and component capacity.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
MSc thesis presentation - Aerospace Structures - July 2015
1. Static and free-vibration analysis of damaged
metallic and composite aerospace structures
through advanced beam models
Alessandro Rosati
POLITECNICO DI TORINO
I Facoltà di Ingegneria
Tesi di laurea magistrale in Ingegneria Aerospaziale
Prof. Erasmo Carrera
Dott. Marco Petrolo
Dott. Alfonso Pagani
Relatori:
22 luglio 2015
2. 1D Beam models
Politecnico di Torino
Tesi 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
3. Carrera Unified Formulation (CUF)
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 3
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:
4. Modelli CUF 1D Taylor e Lagrange
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 4
Carrera Unified Formulation
TE models:
LE models:
Timoshenko classical model, obtained as a particular case of N = 1
L9 isoparametric polynomial:
5. Component–Wise (CW)
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 5
Carrera Unified Formulation
Each component of the structure is modelled via beams only!
6. Present work outlines
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 6
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 CUF
capabilities to deal with non-destructive testing of structures
7. Damage Modelling
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 7
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)
8. Progressive Failure Analysis
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 8
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 each
component of the structure has to be
studied
failure criteria have to be defined
The ultimate load is intended as the maximum external load at which the structure
collapse and it is no more able to perform its duties
9. Failure Criteria
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 9
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
10. Procedure and Assumptions
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 10
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
11. Isotropic material definition
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 11
Failure Analysis
An isotropic aluminium alloy material has been adopted for every component
of the studied structures:
E is the elastic modulus of the material,
ν the Poisson ratio,
ρ the density,
Yield stress
E = 75 GPa
ν = 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
12. Ultimate load evaluation: 4-stringers wing-box
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 12
Failure Analysis: 4-stringers wing-box
b = 1 m
h = 0.5 m
t = 2 × 10−3 m
L = 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
13. Ultimate load evaluation: 6-stringers wing-box
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 13
Failure Analysis: 6-stringers wing-box
• 10 B4 element mesh along the y−axis
• Clamped in y = 0
• Fz applied at [b/2, L, h/2]
• Resistant panels
b = 1 m
h = 0.5 m
t = 2 × 10−3 m
L = 3 m
As = 1.6 × 10−3 m2
14. Initial damages: 6-stringers wing-box
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 14
Failure Analysis: 6-stringers wing-box
Ultimate Load × 10-5 N
15. Shear-instabilities: 6-stringers wing-box
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 15
Failure Analysis: 6-stringers wing-box
• onset of instability phenomena on panels
• the instability condition modelled as a damage
Critical shear tension:
16. Multi wing-boxes
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 16
Failure Analysis: multi wing-boxes
• 30 B4 element mesh along the y−axis
• Clamped in y = 0
• Fz applied at [b/2, L, h/2]
• Resistant panels
b = 1 m
h = 0.5 m
t = 2 × 10−3 m
L = 9 m
ℓ = 3 m
As = 1.6 × 10−3 m2
17. Free-vibration analysis
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 17
Free-vibration analysis
• Isotropic, orthotropic and composite
materials 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 damaged
structure
Objectives:
to understand the dynamic behaviour of structures
in response to the introduction of damages
18. Sandwich beam
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 18
Free-vibration analysis
• clamped-clamped
• face sheets (f) bonded to a core (c)
• 10 B4 element mesh along the y−axis
• isotropic material
L = 1 m
hc = 0.16 m
hf = 0.02 m
Ef = 68.9 GPa
Ec = 179.1 MPa
ρ f = 2687.3 kg/m3
ρ c = 119.69 kg/m3
ν f = ν c = 0.3
19. Sandwich beam
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 19
Free-vibration analysis
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
20. Damages : bottom face-sheet
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 20
Free-vibration analysis
d* = 0.5
21. MAC evaluation
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 21
Free-vibration analysis
Undamaged - d* = 0.1Undamaged - d* = 0.5Undamaged - d* = 0.9
CW solutions, comparisons in mode shapes
of undamaged and damaged structure
22. MAC evaluation
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 22
Free-vibration analysis
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
23. Composite-type Longeron
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 23
Free-vibration analysis
• clamped-free
• 16 B4 along the y−axis
• total length: 1 m
UD and -45/45 layers:
ORTHOTROPIC
EL = 40 GPa
ET = 4 GPa
GLT = GTT = 1 GPa
ν LT = ν TT = 0.25
Foam:
ISOTROPIC
E = 50 MPa
ν = 0.25
24. Damages: bottom UD layer
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 24
Free-vibration analysis
d* = 0.5
25. MAC evaluation, UD layer
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 25
Free-vibration analysis
Undamaged - d* = 0.1Undamaged - d* = 0.5Undamaged - d* = 0.9
CW solutions, comparisons in mode shapes
of undamaged and damaged structure
26. MAC evaluation, UD layer
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 26
Free-vibration analysis
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
27. Damages: internal -45/45 thin layer
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 27
Free-vibration analysis
d* = 0.5
28. MAC evaluation, thin layer
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 28
Free-vibration analysis
Undamaged - d* = 0.1Undamaged - d* = 0.5Undamaged - d* = 0.9
CW solutions, comparisons in mode shapes
of undamaged and damaged structure
29. Conclusions
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 29
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
30. Conclusions
Politecnico di Torino
Tesi di laurea magistrale in Ingegneria Aerospaziale 30
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: