First Principles Derivation of Differential Equations of Equilibrium of Anisotropic Rectangular Thin Plates on Elastic Foundations

In this paper, the partial differential equations of equilibrium for thin rectangular anisotropic plates resting on elastic foundations are derived from fundamental principles of the theory of elasticity. The derivations were done by simultaneous first principles consideration of the requirements of kinematic relations, material constitutive relations, and the differential equations of static equilibrium. The derivation considered transverse distributed load on the plate domain, and inplane loads. Orthotropic plate on elastic foundation equations and isotropic plate on elastic foundation equations were obtained as special cases of anisotropic plates on elastic foundations.

First Principles Derivation of Differential Equations of Equilibrium of Anisotropic Rectangular Thin Plates on Elastic Foundations Keywords:

Anisotropic plate , orthotropic plate , isotropic plate , elastic foundation