Lectures related to Compatibility of Stress and Strain: Form Expressions

Equilibrium Extension Analysis

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

Poincaré - Friedrichs: Theorem and Kernel Inequality

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Linear Elasticity: Cylindrically-symmetric Problems

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

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.

Equilibrium in Tension: Verification and Compatibility

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

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.

Structural Mechanics: Beam Bending and Boundary Conditions

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

Mechanics of Continuous Media: Stress and Strain

Explores stress and strain in continuous media, emphasizing the Cauchy stress tensor and boundary conditions.

Internal Heat Transfer Effects

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Mechanics of Kirchhoff Rods II

Explores the mechanics of Kirchhoff rods, focusing on 3D kinematics and twisted solutions.

Axial Deformation in Elasticity: Fundamentals

Explores equilibrium equations, strain linearity, Hooke's law, and boundary conditions.

Elasticity Basics: Vibrational Modes Description

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

Electric Displacement in Dielectrics: Gauss's Law and Boundary Conditions

Introduces the concept of electric displacement vector D and explores boundary conditions in dielectrics.

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.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Continuum Mechanics: Forces and Deformation

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

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Thermal Diffusion: Conservation and Fourier Law

Explains conservation of energy and Fourier's law in thermal diffusion.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.