Syllabus
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Course Code: MMATH20 -205 Course Name: Mechanics of Solids |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Tensor Algebra: Coordinate-transformation, Cartesian Tensors of different order. Properties of tensors. Isotropic tensors of different orders and relation between them. Symmetric and skew symmetric tensors. Tensor invariants. Deviatoric tensors. Eigen-values and eigenvectors of a tensor. Tensor Analysis: Scalar, vector, tensor functions, Comma notation. Gradient, divergence and curl of a vector / tensor field. (Relevant portions of Chapters 2 and 3 of book by D.S. Chandrasekharaiah and L.Debnath) Affine transformation, Infinitesimal affine deformation. (Relevant portions of Chapter 1 of the book by I.S. Sokolnikoff). |
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| 2 | Analysis of Strain: Strain tensor, Geometrical Interpretation of strain components. Strain quadric
of Cauchy. Principal strains, Invariants, General infinitesimal deformation. Examples of strain,
Equations of compatibility. (Relevant portions of Chapter 1 of the book by I.S. Sokolnikoff). Analysis of Stress : Stress Vector, Stress tensor, Equations of equilibrium, Transformation of coordinates. Stress quadric of Cauchy, Principal stresses. Maximum normal and shear stresses. Mohr’s circles. Examples of stress. |
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| 3 | Equations of Elasticity: Generalised Hooke’s Law, Anisotropic symmetries, Homogeneous
Isotropic media. Elasticity moduli for Isotropic media. Equilibrium and dynamic equations for an
isotropic elastic solid. Strain energy function and its connection with Hooke’s Law. Beltrami-Michell compatibility equations. Uniqueness of solution. Clapeyron’s theorem. SaintVenant's principle. |
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| 4 | Variational Methods: Variational problems and Euler’s Equations, Theorem of minimum potential energy. Theorem of minimum complementary energy. Reciprocal theorem of Betti and Rayleigh. Ritz method: one and two dimensional cases. Galerkin method. Method of Kantorovich. | |
