Lectures related to Mechanics of Continuous Media: Stress and Strain

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

3D Linear Elasticity & Beams

Covers 3D linear elasticity, stress, strain, beams' behavior under loads, and torsion.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Equilibrium Extension Analysis

Discusses equilibrium, extension analysis, stress distribution, and strain components' compatibility for a valid solution.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Linear Elasticity: Equations of Linear Elasticity

Covers the equations of linear elasticity for static problems with small strain, emphasizing uniqueness of solutions and Navier's Equations.

Continuum Mechanics: Forces and Deformation

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

Introduction to Structural Mechanics: Stress and Strain

Covers stress equilibrium, strain, and constitutive equations in 2D and 3D.

Elasticity Basics: Vibrational Modes Description

Covers the theory of elasticity to describe vibrational modes of mechanical resonators.

Linear Elasticity: Cylindrically-symmetric Problems

Covers linear elasticity, focusing on cylindrically-symmetric problems and the simplification of Hooke's Law for axially-symmetric cases.

Compatibility of Stress and Strain: Form Expressions

Explores stress and strain compatibility, closed-form expressions, and constant strain components.

Stiffness vs Strength: Deformation and Load

Covers stiffness, strength, strain, stress, and strain measurement in structural mechanics.

Finite Element Method: Linear Statics

Explores the Finite Element Method applied to linear statics of deformable solids.

Normal Stresses: Internal Stress and Strain

Introduces internal stress and strain, material properties, and design considerations for axial loads and direct shear.

Fluid Dynamics: Differential Conservation Laws and Equations

Covers the differential approach to fluid dynamics, focusing on conservation laws and the Cauchy stress tensor.

Equilibrium in Tension: Verification and Compatibility

Covers the verification of equilibrium equations and compatibility in tension scenarios, ensuring uniform stress distribution.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Stress and Strain: Generalization to 3D

Covers stress equilibrium, strain, and the generalization of stress to 3D, introducing Hooke's Law and analyzing structures with axial loads.

Solid Mechanics II + Material Models

Explores material models for elastic objects, including inverse shape optimization and hyperelasticity.

Deformations and Constraints

Covers relative deformations, flexibility matrix, stress relations, and internal forces in structures.