Shape Change and Polar Decomposition

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3D Linear Elasticity & Beams

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

Mechanics of Slender Structures: Final Review and Overview

Covers the main learning objectives of ME-411, focusing on dimensional analysis, scalings, and mechanical elements.

Mechanics of Slender Structures: Elasticity & Buckling

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.

Structural Mechanics: Beam Bending and Boundary Conditions

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

Finite & Infinite Deformation: Key Distinction

Explains the geometric interpretation of eigen vectors and values in material deformation.

Polar Decomposition Theorem

Explores the Polar Decomposition Theorem, decomposing deformations into stretches and rotations, discussing uniqueness and implications in continuum mechanics.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Continuum Mechanics: Forces and Deformation

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

Transformation Laws: Diagonalization of Symmetric Tensors

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.

Spectral Decomposition and SVD

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.