Deduction by scaling: A unified approach to classic plate and rod theories

A method of formal scaling is presented that allows for a unified deduction from three-dimensional linear elasticity of the equations of structural mechanics, such as Reissner-Mindlin's equations for shearable plates and Timoshenko's equations for shearable rods. This method is based on the requirement that a scaled energy functional that may include second-gradient terms stay bounded in the limit of vanishing thickness.

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