Feb. 25, 2008

AE xxx Aerospace Structural Mechanics 3 1 0 8

Prerequisite: AE xxx Solid Mechanics

Introduction to semi-monocoque aerospace structures: Loads and Design
considerations; aerospace structural construction concepts, layout and
nomenclature of parts, elementary ideas of load diffusion and structural
functions of the components of wing and fuselage structures; strength vs
stiffness based design.

Generalized (coupled) 1-d beam theory analysis including unsymmetric bending
and axial coupling, generalized expressions for direct and shear stresses
and deflection analysis.

Torsion of non-circular prismatic beams ~V importance of warping; St. Venant
or Prandtl~Rs formulation; Membrane analogy and its application to narrow
rectangular cross-section.

General formulation of Thin-Walled Beam (TWB) Theory (shell-beam analysis)
~V definitions, geometry & co-ordinate systems (Cartesian and midline
systems), basic assumptions for simplification of the displacement, stress
and strain fields (CSRD & thin-wall assumptions), general expressions for
dominant strain and stress fields, equilibrium equations in midline system,
stress resultants and general boundary conditions.

Analysis of bending and torsion of single and multicell open and closed
prismatic tubes - Bredt-Batho theory, shear flow, torsion constant, free
warping calculation, warp-less cross-sections, comparison between midline
and Prandtl~Rs analysis. Concept of center of twist. Equation of torsional
equilibrium for distributed loading, boundary conditions. Torsion of open
section TWBs without warp restraint - Midline analysis vs Prandtl analysis,
primary and secondary warping, torsion constant.
Thin-walled extension of elementary beam theory for uncoupled bending in
principal planes ~V axial stress, shear flow, displacement analysis, concept
and calculation of shear centre. Uncoupled bending of multi-cell TWBs.
Extension to general equations (non-principal coordinates). Torsion of open
section TWBs with primary warp restraint: concept of torsion bending,

general theory of torsion bending for open TWBs with warp restraint, axial
stress and shear flow computations, St. Venant and torsion bending
components of torsional stiffness, Torsion Bending constant. Secondary
warping restraint.

Buckling of TWBs: concept of structural instability, flexural buckling
analysis, bending of beams under combined axial and lateral loads ~V
beam-column formulation, Southwell plot, short column and inelastic
buckling. Pure torsional buckling and coupled flexural-torsional buckling of
open section TWBs. Introduction to the concept of buckling of plates, effect
of aspect ratio and boundary conditions on modes of buckling, concept of
local buckling of TWBs, local buckling of flanges vs webs, formulae for
local buckling. Introductory concepts in load carrying ability of stiffened
thin sheets in compression, introduction to buckling and post-buckling of
stiffened skin panels of wing structure, ultimate load carrying capacity of
a typical semimonocoque TW box-section of wing structure. Buckling of webs
in shear and introduction to tension-field beams.

Textbooks:
Aircraft Structures for Engineering Students,
by T. H. G. Megson, Butterworth-Heinemann, 4 edition, March 2007
Aircraft Structures, David J. Peery, McGraw-Hill Education, 1st Ed., January
1950
Analysis of Aircraft Structures (Cambridge Aerospace Series)
by Bruce K. Donaldson (Author), Cambridge University Press, 2nd edition,
March 2008.

References:
Mechanics of Aircraft Structures,
by C. T. Sun, Wiley-Interscience, March 1998.
Analysis and Design of Flight Vehicle Structures,
by E. F. Bruhn, Jacobs Pub, June 1973
Practical Stress Analysis for Design Engineers: Design & Analysis of
Aerospace Vehicle Structures, by Jean-Claude Flabel, Lake City Pub. Co.; 1st Ed. edition, November 1997
Airframe Stress Analysis & Sizing
by Michael Niu, Adaso Adastra Engineering Center, June 1998

Supplementary Reading:

Understanding Aircraft Structures,
by John Cutler, Jeremy Liber, WileyBlackwell, 4th Edition, Jan 2006
Aircraft Structures and Systems,
by R. Wilkinson, Mechaero Publishing; New Ed edition, Jul 2001

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July 18, 2007 (detailed lecturewise breakup)

Aerospace Structural Mechanics: 2 1 0 6

Introduction to semi-monocoque aerospace structures: Loads and Design considerations - sources/types of loads and environment; definition, basis and evolution of the semi-monoque stiffened shell-beam aircraft construction concepts; layout and nomenclature of parts, several examples showing details of the layout and construction of aircraft and space vehicle parts, elementary ideas of load diffusion and structural functions of the components of wing and fuselage structures; strength (limit & ultimate load) vs stiffness (buckling and aeroelastic considerations) based design; example V-n diagram; failure definition; aircraft materials. (5 hours)

Review of elasticity and 1-D beam theory. Generalized (coupled) 1-d analysis including unsymmetric bending and axial coupling, generalized expressions for direct and shear stresses and deflection analysis. (2 hours)

Torsion of non-circular prismatic beams – circular vs non-circular section, necessity of considering warping of the cross-section; St. Venant or Prandtl’s formulation – assumptions, co-ordinate systems, warping/stress function, equilibrium/compatibility, boundary conditions, torsion constant, warping pattern & shear stress distributions, example problems. Membrane analogy and its application to narrow rectangular cross-section. (4 hours)

General formulation of Thin-Walled Beam (TWB) Theory (shell-beam analysis) – definitions, geometry & co-ordinate systems (Cartesian and midline systems), basic assumptions for simplification of the displacement, stress and strain fields (CSRD & thin-wall assumptions), general expressions for the resulting simplified (dominant) displacement and strain fields, dominant stresses in the slender shell-beam, equilibrium equations in midline system, stress resultants and general boundary conditions. (4 hours)

Torsion of TWBs: Analysis of single cell closed prismatic tubes - Concepts of free and constrained warping, Bredt-Batho theory for closed single cell cross-sections (midline analysis) with free warping, concepts of shear flow, torsion constant, free warping calculation, warp-less cross-sections, comparison between midline and Prandtl’s analysis. Concept of center of twist. Analysis of multi-cell closed prismatic tubes – free warping analysis, junction equilibrium of shear flow, compatibility of warping displacement, reduced governing equations for shear flow, calculation of torsion constant and twist. Equation of torsional equilibrium for distributed loading, boundary conditions. Analysis of torsion of open section TWBs without warp restraint - Midline analysis vs Prandtl analysis (membrane analogy) narrow rectangular section, primary and secondary warping, torsion constant, extension to general thinwalled open sections including sections with junctions. (7 hours)

Bending of TWBs: Development of thin-walled extension (midline analysis) of elementary beam theory for uncoupled bending in principal planes – additional assumptions, axial stress, shear flow, displacement analysis, governing differential equations and boundary conditions for uncoupled bending, concept of shear centre, shear flow and shear centre calculations for open and closed single cell cross-sections. Extension to general equations for bending and shear in arbitrary (non-principal coordinates). Uncoupled bending of multi-cell TWBs – junction continuity and warping compatibility conditions, shear flow and shear centre calculations. (7 hours)

Torsion of open section TWBs with primary warp restraint: constraint on warping, axial constraint stresses, I beam example for illustration of axial constraint effects and introducing the concept of torsion bending, general theory of torsion bending for open TWBs with warp restraint, governing equations and boundary conditions, axial stress and shear flow computations, St. Venant and torsion bending components of torsional stiffness, Torsion Bending constant. Mention of secondary warping restraint and warping moments. (4 hours)

Buckling: Elementary beams under axial compressive loads, equilibrium, stability of equilibrium, restoring and disturbing moments, concept of buckling of straight beams, bifurcation buckling of ideal beams in flexure – governing equation, boundary conditions and solution of the eigenvalue problem, bending of beams under combined axial and lateral loads – beam-column formulation, Southwell plot. Mention of short column and inelastic buckling. Flexural buckling of TWBs. Concept of pure torsional buckling of open TWBs under axial compressive loads, analysis of uncoupled torsional and coupled flexural-torsional buckling of open section TWBs. Introduction to the concept of buckling of plates, effect of aspect ratio and boundary conditions on modes of buckling, concept of local buckling of TWBs, local buckling of flanges vs webs, formulae for local buckling. Introductory concepts in load carrying ability of stiffened thin sheets in compression, introduction to buckling and post-buckling of stiffened skin panels of wing structure, ultimate load carrying capacity of a typical semimonocoque TW box-section of wing structure. Buckling of webs in shear and introduction to tension-field beams. (7 hours)

Total 40-41 hours