Elasticity Theory In Structural Mechanics

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

None

Course Contents

Indicial notation - Vector and tensor algebra - Transformation rules - Invariants - Eigen value and eigen vector problems - Some mathematical operators - Motion - Deformation - Strain tensor - Stress analysis - Linear elastic solid

Weekly Schedule

1) Indicial notation, Summation convention, Kronecker Delta, Permutation symbol, Dot and cross products.
2) Tensors, Product of a tensor and a vector, summation and product of two tensors, Identitiy tensor, Transpose of a tensor.
3) Transforms, Orthogonal transforms, Properties of orthogonal transforms, Orthogonal transforms of physical quantities.
4) Orthogonal transform of tensors, invariants under orthogonal transforms, First, second and thir invariants of a tensor.
5) Symmetric and antisymmetric tensors, Dual vector of an antisymmetric tensor, Eigen values and eigen vectors of a tensor.
6) Principal values and principal directions of a tensor, Characteristic equation and scalar invariants of a tensor.
7) Tensor functions with scalar variables, Scalar functions with vector variables, vector functions with vector variables (vector fields), grad, divergence, curl of a vector field, Laplacian of a Scalar field.
8) Midterm Exam
9) Motion, Material description, spatial description, Material derivative.
10) Deformation, Large deformations, Small deformations.
11) Strain tensor, Normal strain, shearing strain, Motion of points and infinitesimal vectors while deformation.
12) Stress, stress tensor, normal and shear stresses.
13) Components of a stress tensor, Stress Transformations, Force equilibrium and Principal of moment of momentum, relationships between components of a tensor.
14) Linear elastic solid, its properties and behaviour.
15) Material properties of linear elastic solid, Lamé's constants, Modulus of elasticity and Poisson's ratio.
16) Final Exam

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Self Study
6) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required