AS3020: Aerospace Structures
Jul-Nov, 2024
Table of Contents
Introduction
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Figure 1: Course Textbook: "Aircraft Structures for Engineering Students", T.H.G. Megson
Updates
- Module 4 Slide Errata: I-section idealization expressions updated. <2024-09-29 Sun>
Instructor, TA, and the basics
- Dr. Nidish Narayanaa Balaji
- nidish@iitm.ac.in, Room 139 AE building
- TA: Chris and Rohan
Textbook Reference: "Aircraft Structures for Engineering Students", T.H.G. Megson
Some Planning
The lectures will be split into eight modules:
SNo. Topic Lectures Assignments 1 Design of Aircrafts 3 1 2 Aircraft Materials 3 1 3 Elasticity 5 1 4 Bending of Beams 6 1 5 Torsion of Beams 5 1 6 2D Problems and Plate Bending 5 1 7 Structural Stability 3 1 8 Structural Vibrations 2 1 Total 32 8 - We have a total of 65 working days ahead of us. The weekly splitup is:
- 3 Lectures: ~39 in total
- 1 Tutorial With Faculty: ~13 in total
- 1 Extended Tutorial With TA: ~13 in total
Evaluation Rubrics
- One assignment will be given for each module due in one week from
the date of posting.
- Each assignment will include 2 numerical/analytical exercises and one reading exercise.
Two Quizzes and an End Sem occupy the examination portion.
Evaluation Assignments Quizzes End-Sem Weightage 30% 30% 40% - Project? No projects.
Policies
Honor Code Policy
You are required to sign an honor code for each submission, failing
which evaluation will not be done.
Honor Code
Upon my honor I state that I have received no unauthorized support and can attest that the submission reflects my understanding of the subject matter.
- Attendance Policy
- We will enforce the institute's 75% attendance policy.
- Noone will be turned away from class, but the time of entry will be logged in the attendance application.
- Attendance will be computed based on total minutes spent in class divided by 50 minutes.
- Late Submission Policy
- Late submissions will incur a penalty that linearly increases from the due date of the current assignment to that of the next.
- If you submit assignment \(n\) on or after the due date of assignment \(n+1\) then you get no credit.
- If you submit it \(d\) days after, with the next assignment's due date being \(D\) days after, the max. grade you can achieve is \(d/D\) times the full credit.
Useful Links
Module 1: Design of Aircrafts
Figure 2: Reference textbook for aircraft design overview
Overview
Figure 3: A400m structure
- Fuselage construction
- Stressed skin design
- monocoque, semi-monocoque, etc.
- Pressurized vs un pressurized design
- Stringers and stiffeners.
- Wing construction
- Shape requirements: lift generation from airfoil.
- Wing ribs, spars, etc.
- Loads on the different members.
- Load distribution. Discuss loads for different maneuvers.
- Load envelopes (V-n diagrams).
- Relate global loads to local loads on members.
- Airworthiness.
- Joining Processes
- Screwing, Bolting, Riveting, Welding.
- Rivets over bolts: blind riveting, resistance to vibration, "permanence", etc.
- Riveting process.
- Bolt-load distribution calculations.
- Other joining methods.
Tutorial Notes
- Bolted Joint Design
- Relevant pages from Shigley's
- I would also recommend Sec. 12.4 in your textbook (Aircraft Structures, Megson [1]).
Assignment
Useful Links
Fastening
Practice Problems
- Chapter 12 Problems in Megson.
- Aircraft FBD from Chapter 14 in Megson.
Module 2: Aircraft Materials
Overview
- Understanding the stress-strain curve.
- Elastic regime, plastic yield, proof load, failure, elongation at failure, toughness, etc.
- Strain hardening.
- The need for alloys.
- Show dramatic difference between raw Al and Al-alloy. Raw Fe & steels.
- Outline basic considerations.
- Examples of some common alloys with historical context.
- Aluminum Alloys
- Aluminum-Copper (Al-Cu) (High strength-to-weight ratio)
- Aluminum-Magnesium (Al-Mg) (Good corrosion resistance but cracks)
- Aluminum-Silicon (Al-Si) (Machinability)
- Titanium Alloys
- Titanium-Aluminum (Ti-Al) (High specific properties)
- Nickel-based Superalloys (High temperature components)
- Nickel-Chromium, Nickel-Aluminum
- Fatigue
- Failure at stress levels way below yield through repeated application.
- Show S-n curves. Contrast behavior of Steel and Al-alloys.
- Creep
- Gradual increase in strain for fixed load
- Fundamentally a high-temperature phenomenon
- Phase Diagrams
- Binary
- Cu-Ni
- Eutectic
- Pb-Sn
- The Iron-Carbon System
- Equilibrium phases: $α$-Ferrite, $γ$-Austenite, $δ$-ferrite, Cementite (Fe$3$C)
- Non-equilibrium phases: Bainite, Martensite
- Binary
Assignment
Useful Links
Practice Problems
- Only concepts. Chapters 11, 15 in Megson.
- Fe-C phase diagram.
Module 3: Elasticity
Overview
- Fundamentals
- Use the stress-strain curve and go into elasticity.
- Strain
- Introduce strain. Constitutive relationship.
- Strain compatibility.
- Stress
- Derive stress-balance => governing equations.
- Stress Mohr's circle.
- Constitutive Relationships
- Thermo-elasticity outline.
- Introduction to 2D Problems. Will revisit in Module 6.
Assignment
Practice Problems
- Chapter 1 problems in Megson.
- Chapter 1-3 problems from Sadd.
Module 4: Bending of Beams
Overview
Figure 4: An I-section beam subjected to 3-point bending
Figure 5: \(\sigma_{12}\) section strains for an I section under bending
Figure 6: \(\sigma_{13}\) section strains for an I section under bending
Figure 7: Analytical shear flow predictions for an I section beam
Figure 8: Shear flow and Shear Centre calculation for a C-sectino
- Motivate by applications (wings, wing spars, etc.).
- Beam theory assumptions and justifications (stringer-stiffeners, shape-preservation).
- Unsymmetrical bending of solid beams (wings).
- Shear of thin-walled beams (wing sections).
- Open sections, closed sections.
- Multi-cell closed/open combination sections.
Assignment
Useful Links
- Course Notes by Prof. Massoud Rais-Rohani
- CodeAster
- files/mod4/Isection.hdf: SalomeMeca file for 3-point bending analysis of an I-Section built using solid brick elements (to visualize shear flow).
- files/mod4/ShearLag1.hdf: SalomeMeca file for the shear lag examples with and without cutout.
- files/mod4/TSection.hdf: SalomeMeca file for a canilevered T-section beam built using plane stress elements (to visualize effects of tip point loads applied at shear center and at centroid).
Practice Problems
- Chapter 16, 17, 20 problems in Megson.
- Chapter 5 problems from CT Sun.
Module 5: Torsion of Beams
Overview
- Solid section torsion.
- Prandtl stress function.
- Warping of section.
- Discussion of physicality.
- Mention St. Venant's principle, will revisit in Module 6.
- Thin-walled torsion.
- Closed section, open section.
Assignment
Useful Links
- FreeFem++ Scripts numerically solving the Poisson problem for both
stress function and warping for different solid sections.
- aellipse.edp: Ellipse section
- brectangle.edp: Rectangle section
- ctriangle.edp: Triangle section
- gthinwalledrect.edp: (Closed) Thin-walled rectangular section
- hcsect.edp: (Open) C section
- CodeAster Tutorial for Solid Section Torsion
- ellbeam.hdf : HDF file for running the FEA
- Advanced Solid Mechanics Notes from Prof. U. Saravanan
- Structural Mechanics Notes, MIT AeroAstro
- Steel Construction Notes
Practice Problems
- Chapter 18, 19 problems from Megson.
- Chapter 4 problems from CT Sun.
Module 6: Variational Mechanics
Overview
- Principle of Virtual Work
- Primer on Calculus of Variations
Assignment
Practice Problems
- Chapter 4, 5 problems in Megson (only straight beam type).
Module 7: Structural Stability
Figure 9: Animation of post-buckling of pinned-pinned/roller supported beam.
Overview
- Column buckling.
- Derive governing equation for column-buckling.
- Sturm-Liouville ODE.
- Euler buckling analysis.
- Plate buckling.
- Write down governing equation (derivation left for self study).
- Show examples from aircrafts.
- Possibility and avenue for thermal buckling from governing equations.
Assignment
Useful Links
Practice Problems
- Chapter 7, 8, 9 problems from Megson (only whatever was covered in class).
- Class notes/assignment type problems.
Module 8: Structural Vibrations
This module will not be covered this semester.
- Dynamic elasticity equations.
- Dynamics of beams. Derive governing equations.
- Solve by method of variable separation.
- The Sturm-Liouville problem.
- Eigenfunctions and eigenvalues.
- Introduce a linear viscous damping to the PDE and show influence of damping on response.
- Visualize mode-shapes for realistic models and motivate the need for
fillets and chamfers from a fatigue standpoint.
- St. Venant doesn't help us for fatigue!
