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Lecture

Laminate Analysis: Kirchhoff-Love Plate Theory

In course

ME-437: Advanced solid mechanics

Description

This lecture covers the Kirchhoff-Love Classical Plate theory, focusing on laminates made of thin plates. The theory's main assumptions include the use of plane stress approximation due to the finite thickness of the plates. It discusses the displacement vector components and the kinematic assumptions for plate bending. The lecture also explains the neglect of deflection dependence on the z-coordinate and the treatment of only bending problems. The strain components, stresses, curvatures, and equilibrium conditions are detailed, emphasizing the relationship between displacements and strains. The lecture concludes with the application of Hooke's law and the equilibrium conditions for moments applied to the plate.

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Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

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In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point. At each point p of a differentiable surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal plane at p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section.

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