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

Article type: Research Article

Authors: Miara, B. | Podio-Guidugli, P.

Affiliations: Laboratoire de Modélisation et Simulation Numérique, ESIEE, 2, Boulevard Blaise Pascal, 93160 Noisy-Le-Grand, France E-mail: [email protected] | Dipartimento di Ingegneria Civile, Università di Roma TorVergata, Via del Politecnico 1, I-00133 Roma, Italy E-mail: [email protected]

Abstract: 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.

Journal: Asymptotic Analysis, vol. 51, no. 2, pp. 113-131, 2007