Mar. 6, 2008

AE xxx Solid Mechanics 3 1 0 8

Prerequisite: AE xxx, Solid Mechanics

Introduction: Engg. Statics vs Solid Mechnics, Solid as a continuum,
statement of a general solid mechanics problem.

Elements of 2-D & 3-D Elasticity: stress/strain field, components of stress
& strain, stress/strain transformation, principal stresses, plane
stress/strain and Mohr~Rs circle, equilibrium, strain displacement
relations, compatibility conditions, natural & kinematic boundary
conditions. Stress-strain relations ~V Generalized Hooke~Rs Law, isotropy,
orthotropy, anisotropy, homogeneous and nonhomogeneous materials.
Displacement and force methods of analysis. Concepts of linear and nonlinear
problems. Illustration of linear elasticity solutions ~V problems in 2-D
(rectangular and polar co-ordinates), stress function approach. End effects
 St. Venant's principle.

Material behaviour: metallic and non-metallic materials of aerospace
interest, bulk material properties - elastic properties, strength, other
mechanical properties of structural interest, awareness/overview of
structure of materials and origin of elastic properties. concepts and
properties of ductile, brittle, elasto-plastic and viscoelastic material
behaviour. Materials selection. Failure of engineering materials ~V failure
theories, elementary concepts of fatigue and fracture.

1-D structural analysis: slender structural elements, assumptions
simplifying the general (3-d) stress, strain and deformation fields for
uncoupled axial deformation, uncoupled bending, and uncoupled twisting of
slender 1-D elements and development of corresponding elementary theories
(Elementary Beam Theory, Elementary Torsion theory),
idealization/conceptualization of general loads into axial forces, bending
moments, shear forces and torque distributions, deflection and stress
analysis of rods, beams and circular shafts. Applications of these concepts
and analyses through a number of example problems.

Measurement of strain and displacement. Measurement of elastic and strength
properties. ASTM standards.

Texts:

Gere, J.M. ``Mechanics of Materials'',
Thomson, sixth edition (India Edition) 2007.

Crandall, S.H., Dahl, N.C. and Lardner, T.J.
``An Introduction to the Mechanics of Materials'',
McGraw-Hill Book Company, International Edition, 1978

Timoshenko, S.P. and Goodier, J.N. ``Theory of Elasticity'',
McGraw-Hill Book Company, International Edition, 1970

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July 18, 2007 (detailed lecturewise breakup)

Solid Mechanics 3 1 0 8

Introduction – What is Solid mechnics?. Engg. Statics vs Solid Mechnics, Solid as a continuum, need/importance of solid mechanics from an application perspective through examples, statement of a general structural analysis problem. (1-2 hours)

Elements of 2-D & 3-D Elasticity – Concept and definition of stress/strain at a point and stress/strain field, components of stress & strain: direct (extensional) and shear, notation (indicial), stress/strain transformation, principal stresses, plane stress/strain and Mohr’s circle, differential equations of equilibrium of stresses, strain displacement relations, compatibility conditions, natural & kinematic boundary conditions. Measurement of strain and displacement. (12 hours)

Material behaviour: Classes of materials – metallic and non-metallic of aerospace interest, definitions and characteristics of bulk material properties - elastic properties, strength, other mechanical properties of structural interest (thermal, hardness etc.), awareness/overview of structure of materials and origin of elastic properties (atomic & crystal levels). Stress-strain relations – Generalized Hooke’s Law, isotropy, orthotropy, anisotropy, homogeneous and nonhomogeneous materials, linear and nonlinear materials, concepts and properties of ductile, brittle, elasto-plastic and viscoelastic material behaviour, introductory concepts of fibre reinforced composite materials. Materials selection. Measurement of elastic and strength properties. Failure of engineering materials – failure theories, elementary concepts of fatigue and fracture. (10 hours)

Formulation of the general solid mechanics problem: displacement and force methods. Concepts of linear and nonlinear problems. Illustration of linear elasticity solutions – one or two problems in 2-D (rectangular and polar co-ordinates, stress function). End effects – St. Venant’s principle. (5 hours)

1-D structural elements: slender structural elements, idealization/conceptualization of general loads into axial forces, bending moments, shear forces and torque distributions, assumptions simplifying the general (3-d) stress, strain and deformation fields for uncoupled axial deformation, uncoupled bending, and uncoupled twisting of slender 1-D elements and development of corresponding elementary theories (Elementary Beam Theory, Elementary Torsion theory), deflection and stress analysis of rods, beams and circular shafts, Applications of these concepts and analyses through a large number of example problems. (12 hours)

Total 52-53 hours

Notes: The elasticity element is strengthened and 3-d elasticity, covered earlier in the 2^nd course on structures, is integrated into the above syllabus, now called as Solid Mechanics, instead of Aerospace Structures I. Material aspects are strengthened, since there is no course on materials in the new curriculum. Buckling/structural instability is shifted to the Aerospace Structural Mechanics course (the 2^nd structures course in the new curriculum) as many other aspects of instability are covered in the earlier version of that course (Aerospace Structures III). Unsymmetric bending and generalized (coupled) 1-D analysis and St. Venants torsion theory (noncircular sections) will be covered in the Aerospace Structures course.