Course on Theory of Elasticity

About Course

Theory of elasticity, also known as advanced mechanics of solids, is the branch of continuum mechanics which deals with the study/behaviour of deformable bodies. Theory of elasticity is an advanced subject in mechanical engineering and has also specific application in many other areas such as in health care/medical to understand the anatomy of living beings, dental prostheses and surgical implants. This basic study will be helpful for advance topics of solid mechanics such fatigue and fracture mechanics which deals with the initiation and propagation of cracks in solid materials. Thus, attending this course design engineers will gain theoretical knowledge of solid/continuum mechanics and solving methods in solid mechanics and interpret the results from the analysis.

Gain fundamental knowledge of mechanics of deformable solids.
Understand the basic field equations of linear elastic solids, force, stress, strain and equilibrium in solids.
Examine the properties of deformable bodies and apply the basic concepts and theoretical laws and derived formulas in solving solid/structural mechanics problem.
Use analytical techniques to predict deformation, internal force and failure of simple solids and structural components.
Check the sufficiency of the strength, stiffness and stability of structural and machine elements.

Course Content

Analysis of Stress

Analysis of Stress: Definition and notation of stress, Equations of equilibrium in differential form, Stresscomponents on an arbitrary plane, Equality of cross shear, Stress invariants, Principal stresses, Octahedral stress, Planes of maximum shear, Stress transformation, Plane state of stress, Mohr’s diagram for 3-dimensional state of stress.

Analysis of Strain

Stress – Strain Relations

Two-Dimensional classical elasticity

Investigation of Airy’s stress function

General equations in polar coordinates

Stress analysis in Axisymmetric body

Torsion

Thermal stress

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Course Content

Analysis of Stress

Analysis of Strain

Stress – Strain Relations

Stress – Strain Relations: Introduction,Generalized Hooke’s Lawfor Isotropic Materials, Relation between Young’s modulus E, Rigidity modulus G and Bulk Modulus K.

Two-Dimensional classical elasticity

Two-Dimensional classical elasticity: Cartesian co-ordinates, Relation between plane stress and plane strain,stress functions for plane stress and plane strain state, Airy’s stress functions,

Investigation of Airy’s stress function

General equations in polar coordinates

General equations in polar coordinates: stress distribution symmetrical about an axis, Thick wall cylinder subjected to internal and external pressures.

Stress analysis in Axisymmetric body

Stress analysis in Axisymmetric body: Stresses in rotating discs of uniform thickness and cylinders.Numerical Problems.

Torsion

Torsion: Torsion of circular, elliptical and triangular bars, Prandtl’s membrane analogy, Torsion of thin walled thin tubes, Torsion of thin walled multiple cell closed sections.

Thermal stress

Thermal stress: Thermo elastic stress strain relations, equations of equilibrium, thermal stresses in thin circular discs and in long circular cylinders.

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About Course

What Will You Learn?

Course Content

Analysis of Stress

Analysis of Strain

Stress – Strain Relations

Stress – Strain Relations: Introduction,Generalized Hooke’s Lawfor Isotropic Materials, Relation between Young’s modulus E, Rigidity modulus G and Bulk Modulus K.

Two-Dimensional classical elasticity

Two-Dimensional classical elasticity: Cartesian co-ordinates, Relation between plane stress and plane strain,stress functions for plane stress and plane strain state, Airy’s stress functions,

Investigation of Airy’s stress function

General equations in polar coordinates

General equations in polar coordinates: stress distribution symmetrical about an axis, Thick wall cylinder subjected to internal and external pressures.

Stress analysis in Axisymmetric body

Stress analysis in Axisymmetric body: Stresses in rotating discs of uniform thickness and cylinders.Numerical Problems.

Torsion

Torsion: Torsion of circular, elliptical and triangular bars, Prandtl’s membrane analogy, Torsion of thin walled thin tubes, Torsion of thin walled multiple cell closed sections.

Thermal stress

Thermal stress: Thermo elastic stress strain relations, equations of equilibrium, thermal stresses in thin circular discs and in long circular cylinders.

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