Lecture

Topics: Linear elasticity, Tensor, Continuum mechanics Pages: 9 (753 words) Published: September 9, 2013
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ME321: Advanced Mechanics of Solids

Sumit Basu Room no NL 211 Department of Mechanical Engng IIT Kanpur Email: sbasu@iitk.ac.in Ph: +91 (0) 512 259 7506 (O) +91 (0) 512 259 8511 (R)

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ME321: Advanced Mechanics of Solids

Course Objectives

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• Learn to handle the mechanics of deformable bodies, as opposed to rigid body mechanics. • Build on what we have learnt in ESO204. Local approach vs global approach, forces and displacements vs stress and strain See deformation! Learn to design experiments (both real and computational) to measure deformation and its effects.

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ME321: Advanced Mechanics of Solids

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Course Outline

Language of tensor algebra and calculus. Measuring deformation Concept of stress Techniques for measuring deformation Techniques for ‘seeing’ stress in action Constitutive equations of elasticity Boundary value problems in linear elasticity and some techniques for solving them Energy methods in elasticity

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Hands on part of the course

A combined computational+experimental project on measuring deformations. Demonstrations on how materials are tested, deformations are measured and stresses are seen A project on photoelasticity and strain gauges Using a commercial software (ABAQUS) to solve an elastic boundary value problem. Course details on Google calender: https://www.google.com/calendar/render?tab=wc&pli=1

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ME321: Advanced Mechanics of Solids

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Books

Martin H. Sadd: Elasticity: Theory, Applications, and Numerics, Elsevier, 2009

Allan F Bower, Applied Mechanics of Solids 1st Edition, CRC Press, 2009. Also http://www.solidmechanics.org Coursenotes and assignments available on Brihaspati.

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Evaluation

4 Hands-on Projects: 50%+upto 20% bonus marks 1 Mid Semester Examination: 20% End Semester Examination: 30% About 5 Assignments to be given. No need to submit. Just for your practise. Attendance will not be monitored but not attending classes regularly will have its consequences.

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Experiments

4 hands-on projects to be executed. 2 completely experimental, 1 completely computational and 1 involves experiments and simulations. Form teams of at most 11 people. Decide on 3 team leaders for the experimental, computational and combined parts. Team leaders will decide division of labour. They will also report problems, bottlenecks to the concerned people. We will adopt a zero-tolerance policy to unfair practises

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ME321: Advanced Mechanics of Solids

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QIP Course on Recent trends in Nano-composites, IIT Kanpur November, 2006 ME321: Advanced Mechanics of Solids

IIT Kanpur

Kronecker delta

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ME321: Advanced Mechanics of Solids

Symmetry and skew-symmetry

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Symmery or skew symmetry reduces the number of independent components of the tensor.

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ME321: Advanced Mechanics of Solids

Summation convention

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Summation over repeated indices obviates the need to use the summation symbol.

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The exercise is equivalent to writing:

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Tensor sum

Contraction

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ME321: Advanced Mechanics of Solids

Permutation symbol 1 3 2

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Permutations Clockwise: even Counter clockwise: odd

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ME321: Advanced Mechanics of Solids

inner 18 outer

i n

j

k
first

i

m

second

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ME321: Advanced Mechanics of Solids

Second order tensors

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ME321: Advanced Mechanics of Solids

Components of the second order tensor

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