AS2070: Aerospace Structural Mechanics
Jan-May, 2026

Table of Contents

Introduction

Table 1: A few shortcuts to help navigate the site
n, p Next/Prev tab
<, > Scroll to top/bottom
j, k Incremental scroll
-, + Collapse/expand all
c, e Collapse/expand subheadings

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

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: 2026-02-11.