ENGINEERING TRIPOS PART IIA – 2012/2013

Paper 3C7 - Mechanics of Solids

AIMS

The aim of the course is to provide students with an understanding of how the stresses and strains within engineering components are related to both the loads and displacements imposed at their boundaries and to any thermal or inertial loadings to which they are subjected.  Analytical methods will be introduced predominantly for two-dimensional geometries and both elastic and plastic responses will be considered.  The material will be illustrated by a number of engineering case studies.

SYLLABUS

Introduction (1L) Dr S D Guest

Two-Dimensional Elasticity (6L) Dr S D Guest

• Revision of stress and strain in 2D; Mohr's circle.
• Elastic constitutive relationship.
• Concepts of plane stress and plane strain.
• Equilibrium and compatibility equations in 2D; Cartesian and polar coordinates.
• Analysis of problems with circular symmetry: thick-walled tube, spinning disk, thermo-elastic problems.

Torsion, Stress Functions and Plasticity (3L) Dr S D Guest

• Elastic torsion of prismatic bars: Prandtl stress function.
• Plastic torsion of prismatic bars.
• Airy stress function in Cartesian and polar coordinates.
• Stress distribution in an infinite plate with a circular hole or crack.
• Analysis of contact stresses; half-plane under line and distributed loads.

Stress analysis in 3D and Plasticity (6L) Prof. J A Williams

• Stress analysis in 3D: principal stresses; stress invariants; hydrostatic and deviatoric stresses; deviatoric stress invariants.
• Yield locus, p -plane; symmetry; convexity; normality.
• Tresca and von Mises yield criteria; associated flow rules.
• Upper-Bound and Lower-Bound theorems.
• Applications of Upper-Bound and Lower-Bound theorems: thick-walled tubes; rotating disks.
• Revision of rigid block mechanisms: application to forming problems. Elasto-plastic analysis of a thick-walled tube.

EXAMPLES PAPERS

There will be four Examples Papers, directly related to the lectures.

COURSEWORK

Use the photo-elasticity method to determine stress concentration at the edge of a hole in a finite plate.

ASSESSMENT

REFERENCES

Please see the Booklist for Part IIA Courses for references for this module.