Mechanics of Plates: Curvature, Bending, and Stretching Energy

Related lectures (32)

Covers the equations of plates, bending and stretching energy, von Karman equations, and buckling of plates.

Investigates post-buckling deformation behavior, bending energy derivation, and in-plane stretching energy considerations in square plates.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Discusses Kirchhoff-Love Classical Plate theory for laminates and the relationship between displacements and strains.

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Covers the mechanics of slender structures, focusing on nonlinear curved beams.

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Covers the calculation of curvature in beams and the design of beams for stress considerations.

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