AS2070: Aerospace Structural Mechanics
Jan-May, 2026

Table of Contents

Introduction

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Instructor, TA, and the basics

  • Dr. Nidish Narayanaa Balaji
  • TA: Niranjan Gulla, Poorvika U.
  • Textbook References
    1. Module 1
      • Buckling of Bars, Plates and Shells (1975) by Brush and Almroth [1]
      • Theory of Elastic Stability (2009) by Stephen P. Timoshenko [2]
      • Aircraft Structures for Engineering Students (2013) by T. H. G. Megson [3]
    2. Module 2
      • Mechanics of Composite Structures (2003) by Kollar and Springer [4]
      • Principles of Composite Material Mechanics (2012) by Ronald F. Gibson [5]
    3. Module 3
      • Fracture Mechanics: An introduction (2005) by Gdoutos [6]
      • Elements of Fracture Mechanics (2009) by Kumar [7]
  • This website does have some notes that I have prepared, but note that these are more for my reference than yours.
    • You should assume that they come with mistakes that I will rectify as the semester progresses.
    • Your primary references must only be your textbooks.

Some Planning

  • The lectures will be split into three modules:

    Sno. Topic Lectures Assignments
    1 Elastic Stability 11 1-2
    2 Laminated Composites 11 1-2
    3 Introduction to Failure 11 1-2
      Total 33 3-6
    • The weekly split-up (nominally) is
      • 3 Lectures
      • 1 Tutorial

Grading Policy

  • The End Semester Examination will carry 40% weightage for the overall.
  • The quizzes (together) will carry 30% weightage.
  • The assignments (together) will carry 15% weightage.
  • A Course Project will carry 15% weightage.
  • The weighted overall grades will be scaled by the maximum score. A letter grade will be assigned based on the following rubric.

      [95, 100] [85, 95) [75, 85) [65, 75) [55, 65) [45, 55)
    Grade S A B C D E

Honor Code Policy

Honor Code Policy
You are required to sign an honor code for each submission, failing which evaluation will not be done.

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.

  • The honor code may be signed either by hand or just initials (in case of typed submission), but the key is that you should mean it.
  • Honor code violations will not be taken lightly.

Assignment Policy

  • Each module will have at least one assignment and at most 2.
  • Late Submission Policy
    • No late submissions will be encouraged. If you miss the deadline, you miss the submission.
    • Exceptions will be considered only if I receive written communication through Moodle before the submission date.

Course Project

  • The first week of classes will provide an executive overview of the three modules to be taught in the class.
  • You will be given one week's time to decide which module you want to work on for your project.
  • The problem statement for the project is:

    Develop an experimental demonstration of pedagogical value that highlights some of the concepts covered in class.

  • I will group you in teams of 5-6 based on your preferences.
  • The deliverables are:
    • a demonstration of the experiment.
    • a 15 minute presentation to class.
    • a 1-2 page summary (keep this very brief).

Attendance Policy

  • We shall try to use the DiGii app for attendance. If this does not work, I will be using an Attendance App on a tablet to record attendance.
    • My app logs the time of press also, so attendance will be computed as the ratio of the number of seconds spent in class and the total number of class hours.
  • Please be aware of institute policy regarding attendance matters, I can not provide any flexibility here.

Module 1: Elastic Stability

elstab.png

Figure 1: Table from [1]

bm_buckanim.gif

Figure 2: (Elastic) Post buckling of simply supported column

sdofsnap.png

Figure 3: Snap-through example from [8]

sdofsnapres_5.png

Figure 4: Load-deflection diagram for the SDoF snap-through example

Overview

  • What is stability?
  • Buckling of columns
  • Energy Perspectives to Stability
  • Snap-Through Buckling
  • Flat Plates

Class Slides

All Versions

Module 2: Laminated Composite Mechanics

comp.png

compt.png

Overview

  • Classification of composite materials
    1. Continuous fiber composite laminate
      • Interlaminar strength is matrix dominated.
    2. Woven fiber composites
      • Strength compromized but no risk of delamination.
    3. Chopped fiber composites
      • Poorer strength but cheaper.
    4. Hybrid composites
    5. Sandwich structure
      • High strength faces bonded through a lightweight foam/honeycomb core.
      • High flexural stiffness-to-weight ratios.
  • Materials in Composites
    1. Fibers
      • Fiberglass-Reinforced Plastics (FRPs)
        • Low cost, "basic" composites
      • "Advanced" composites: Carbon, SiC, aramid polymer, etc.
        • Higher modulus, strength; lower density.
      • Carbon Nanotubes, Nanofibres.
    2. Matrix, Filler
      • Polymers
        • Thermosets: Epoxy, Polyester, etc.
          • Highly cross-linked 3D molecular network which doesn't melt again.
        • Thermoplastics: Polyetherketone (PPEK), PolyPhenyl Sulphide (PPS), etc.
          • Polymer chains that do not cross-link. Will melt, can be reshaped.
      • Metal, ceramic, or carbon matrix for higher temperature applications.
  • Effective Moduli, Effective Strength.
  • Constitutive relationships.
  • Classical Laminate Theory (Subject to Time)

Class Slides

All Versions

Module 3: Introduction to Failure

fmods.png

sncurv.png

Overview

  • Structure of Materials
    • Lattice, Defects
  • Introduction to Fatigue
    • S-N Curve
    • Miner's Rule
    • Stress Concentration
  • Introduction to Fracture Mechanics
    • Modes of Fracture
    • Crack Growth

Class Slides

All Versions

Michell Solution

Box Beam Sizing Tutorial

Overview

This tutorial is meant as an introduction to the design process involving much of what is learnt in this class (specifically modules 1 and 3).

Course Project

a_groups.png

Instructions, Prompt, and Deliverables

All Versions

2026 Project Groups and Modules

ID Group Module
ae24b008 1 1
ae24b001 1 1
ae24b021 1 1
ae24b017 1 1
ae24b003 1 1
Group 1
  • Project Module: Module 1
  • Project Title: TBD
ID Group Module
ae24b022 2 3
ae24b027 2 3
ae24b023 2 3
ae24b016 2 3
ae24b024 2 3
Group 2
  • Project Module: Module 3
  • Project Title: TBD
ID Group Module
ae24b002 3 2
ae24b012 3 2
ae24b011 3 2
ae24b020 3 2
ae24b007 3 2
Group 3
  • Project Module: Module 2
  • Project Title: TBD
ID Group Module
ae24b019 4 1
ae24b005 4 1
ae24b018 4 1
ae24b009 4 1
ae24b013 4 1
Group 4
  • Project Module: Module 1
  • Project Title: TBD
ID Group Module
ae24b026 5 2
ae24b010 5 2
ae24b028 6 2
ae24b030 5 2
ae24b004 5 2
Group 5
  • Project Module: Module 2
  • Project Title: TBD
ID Group Module
ae24b006 6 3
ae24b015 6 3
ae24b029 6 3
ae22b105 6 3
Group 6
  • Project Module: Module 3
  • Project Title: TBD

The process of group sorting

  • I created an undirected graph by symmetrizing the adjacency preferences. 0.5 weight for a given student student wanting to work with another, and 0.5 weight for any student to want to work with the given student.
  • I computed the eigenvectors of the associated graph Laplacian and conducted hierarchical clustering in the spectral space (I used 3 eigenvectors for this, second to fourth).
    • I cut the resulting dendrogram tree to get 6 clusters in total.
    • This already yielded 3 groups of 5 members each, so I froze these.
  • Next I used the remaining nodes and computed the graph Laplacian again (within each other). Using the signs of the components of the Fiedler vector (leading eigenvector), I was able to obtain one group of 5 members.
  • With the remaining (9), I once again constructed a Fiedler vector and used its value to sort the nodes. The nodes with the smallest 4 values are assigned to be one group, and the remaining 5 nodes are assigned another.

    a_groups.png

    Figure 5: Adjacency graph plotted using the the spring/repulsion model of Fruchterman and Reingold (1991, doi 10.1002/spe.4380211102). Plotted below are the module preferences.

Past Project Reports

The reports and presentation (where available) of projects from past semesters are documented here. Do have a look and reach out to your seniors to understand what they would do differently, given their experience.

Jan - May 2025

A.jpg

Group A: Thin Plate Buckling under Simply Supported Conditions   Stability

B.jpg

Group B: Snap-Through Buckling of Link-Arch Model   Stability

G.jpg

Group G: Estimation of Critical Buckling Load Using Southwell's Plot   Stability

C.jpg

Group C: Experimental Verification of Rule of Mixtures   Composites

D.jpg

Group D: Tensile & Creep Testing of Composite   Composites

E.jpg

Group E: Crack Propagation in Double Cantilever Beam   Failure

F.jpg

Group F: Area Dependence of Failure in Fibers   Failure

H.jpg

Group H: Failure Analysis: The Role of Surface Roughness   Failure

References

[1]
D. O. Brush and B. O. Almroth, Buckling of Bars, Plates, and Shells. McGraw-Hill, 1975.
[2]
S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability. Courier Corporation, 2009.
[3]
T. H. G. Megson, Aircraft Structures for Engineering Students. Elsevier, 2013.
[4]
L. P. Kollár and G. S. Springer, Mechanics of Composite Structures. Cambridge: Cambridge University Press, 2003. doi: 10.1017/CBO9780511547140.
[5]
R. F. Gibson, Principles of composite material mechanics, 3rd ed. in Dekker mechanical engineering. Boca Raton, Fla: Taylor & Francis, 2012.
[6]
Fracture Mechanics: An Introduction, Second Edition. in Solid Mechanics and Its Applications, no. 123. Dordrecht: Springer Netherlands, 2005. doi: 10.1007/1-4020-3153-X.
[7]
P. Kumar, Elements of Fracture Mechanics, 1st Edition. McGraw-Hill Education, 2009.
[8]
R. Wiebe, L. Virgin, I. Stanciulescu, and S. Spottswood, “On Snap-Through Buckling,” in 52Nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado: American Institute of Aeronautics and Astronautics, Apr. 2011. doi: 10.2514/6.2011-2083.

Created using Emacs 30.2 (Org mode 9.7.11).

Last updated: 2026-04-17.