Solid Mechanics Course

Lesson 1 • Concept of Strain

Introduces engineering and tensorial strain measures for small deformations, including shear strain and volumetric strain. Links displacement fields to measurable deformation quantities.

Lesson 2 • Mathematical Preliminaries

Reviews vectors, tensors, index notation, and coordinate transformations essential for stress and strain analysis. Provides the mathematical language used throughout the course.

Lesson 3 • Concept of Stress

Defines the Cauchy stress tensor, traction vectors, and sign conventions for normal and shear components. Connects internal force resultants to the continuum stress state.

Lesson 4 • Introduction to Deformable Bodies

Distinguishes rigid-body assumptions from deformable-body reality and motivates the need for solid mechanics. Sets the conceptual stage for all subsequent stress-strain analysis.

Lesson 1 • Anisotropic and Orthotropic Materials

Extends linear elasticity to materials with directional stiffness properties, including composites and wood. Introduces the full compliance and stiffness matrix representations.

Lesson 2 • Introduction to Inelastic Behavior

Surveys plasticity, viscoelasticity, and creep as departures from linear elasticity. Gives students conceptual awareness of material nonlinearity before advanced topics.

Lesson 3 • Thermal and Hygroscopic Effects

Incorporates temperature and moisture changes into the constitutive equations as additional strain sources. Prepares students to solve thermomechanical coupling problems.

Lesson 4 • Linear Elastic Behavior

Presents Hooke's law in one and three dimensions, introducing elastic moduli and their physical meaning. Forms the constitutive backbone for all linear elastic analyses in the course.

Lesson 1 • Stress Transformation in 2D

Derives transformation equations for plane stress states and identifies principal planes. Directly enables analysis of critical stress orientations in structural components.

Lesson 2 • Three-Dimensional Stress Transformation

Extends transformation to full 3D stress states using eigenvalue analysis of the stress tensor. Identifies absolute maximum shear stress critical for failure assessment.

Lesson 3 • Mohr's Circle for Stress

Constructs and interprets Mohr's circle as a graphical tool for 2D stress transformation. Reinforces transformation equations with a visual method widely used in practice.

Lesson 4 • Strain Transformation and Mohr's Circle

Applies the same transformation framework to the strain tensor, yielding principal strains and maximum shear strains. Connects to strain gauge rosette data reduction in experimental work.

Lesson 1 • Bending Stress in Beams

Derives the flexure formula from Euler-Bernoulli beam kinematics and applies it to symmetric and unsymmetric cross-sections. Introduces the section modulus for design.

Lesson 2 • Axially Loaded Members

Derives normal stress and deformation in bars under axial force, including statically indeterminate cases. Introduces the concept of thermal mismatch in axial members.

Lesson 3 • Shear Stress in Beams

Derives the shear formula for transverse shear stress distribution and identifies the shear centre for thin-walled sections. Connects shear flow to fastener design in built-up beams.

Lesson 4 • Torsion of Circular Shafts

Develops the torsion formula for solid and hollow circular cross-sections using the kinematic assumption of plane sections. Covers power transmission and angle-of-twist calculations.

Lesson 1 • Moment-Area Method

Uses the two moment-area theorems to determine slopes and deflections graphically from the M/EI diagram. Offers a rapid method for beams with variable cross-sections.

Lesson 2 • Energy Methods for Deflections

Applies Castigliano's theorem and the unit-load method to compute deflections and rotations in beams and frames. Bridges constitutive energy concepts to structural analysis.

Lesson 3 • Analysis of Statically Indeterminate Beams

Solves propped cantilevers and continuous beams using compatibility equations and the force method. Demonstrates how redundant reactions are found from deformation constraints.

Lesson 4 • Differential Equation of the Elastic Curve

Establishes the governing ODE relating beam curvature to bending moment and integrates it for deflection. Applies boundary and continuity conditions to determine integration constants.

Lesson 1 • Fatigue Failure Fundamentals

Introduces S-N curves, endurance limits, and the mechanisms of crack initiation and propagation under cyclic loading. Establishes the basis for fatigue life prediction methods.

Lesson 2 • Fatigue Life Prediction Methods

Applies Goodman, Gerber, and Soderberg diagrams to combined mean and alternating stress states. Introduces Miner's rule for variable-amplitude fatigue damage accumulation.

Lesson 3 • Static Failure Theories for Ductile Materials

Presents the maximum shear stress and distortion energy (von Mises) criteria for ductile material failure. Compares predictions and identifies when each criterion is most appropriate.

Lesson 4 • Stress Concentration Factors

Defines theoretical stress concentration factor Kt and demonstrates its use with charts for common geometries. Explains how notch sensitivity reduces effective concentration in ductile materials.

Lesson 1 • Inelastic Buckling and Column Curves

Addresses buckling of intermediate columns where stresses exceed the proportional limit using tangent-modulus theory. Introduces empirical column curves used in engineering standards.

Lesson 2 • Eccentrically Loaded Columns

Analyses columns with eccentric axial loads using the secant formula and amplification factors. Demonstrates how eccentricity dramatically reduces load-carrying capacity.

Lesson 3 • Energy Methods in Stability Analysis

Applies the Rayleigh-Ritz method and potential energy criterion to estimate critical loads for complex geometries. Connects stability to the second variation of total potential energy.

Lesson 4 • Buckling of Plates and Shells

Extends stability analysis to thin plates under in-plane compression and cylindrical shells under axial load. Introduces buckling coefficients and imperfection sensitivity.

Lesson 1 • Torsion by the Prandtl Membrane Analogy

Uses the membrane analogy to visualise and solve torsion problems for arbitrary cross-sections. Extends understanding beyond circular and thin-walled sections covered earlier.

Lesson 2 • Two-Dimensional Elasticity

Formulates plane stress and plane strain problems using the Airy stress function and biharmonic equation. Solves classical problems including thick-walled cylinders and stress around holes.

Lesson 3 • Introduction to Finite Element Concepts

Presents the displacement-based finite element method as a numerical extension of energy principles in solid mechanics. Prepares students to critically interpret FEA results in practice.

Lesson 4 • Contact Mechanics and Hertzian Contact

Analyses stress fields generated by contact between curved elastic bodies using Hertz contact theory. Applies results to bearing, gear, and rail-wheel contact design.