A thin circular plate is a flat, circular object with a small thickness in comparison to its diameter. It is commonly used in engineering and mechanics applications, such as in the design of pressure vessels and heat exchangers.
Pure bending is a type of deformation that occurs when a material is subject to a bending moment, causing it to bend without any accompanying shear forces. This results in a change in the shape of the material, but not in its volume.
A thin circular plate in pure bending can be modeled using the theory of elasticity, which takes into account the material properties, applied forces, and geometry of the plate. It can also be modeled using finite element analysis, which uses numerical methods to solve for the stresses and strains in the plate.
The main assumptions made in the analysis of a thin circular plate in pure bending are that the material is homogenous and isotropic, the plate is thin with a constant thickness, and the applied load is perpendicular to the plane of the plate. These assumptions allow for simplified equations to be used in the analysis.
The stress distribution in a thin circular plate in pure bending is parabolic, with maximum stresses at the edges of the plate and zero stresses at the center. This is due to the bending moment causing tensile stresses on the outer surface and compressive stresses on the inner surface of the plate.
