ABSTRACT

This chapter considers some traditional formulations from the classical Poisson-Kirchhoff plate theory that reduces the bending of thin plates to boundary value problems formulated for the biharmonic equation. It explores the construction of influence functions and matrices for a variety of problems in mechanics of solids, which are modelled with either single partial differential equations of higher order or with systems of such equations. The chapter describes the influence function method to the mathematical formulation based on the so-called Reissner plate theory. It discusses some of the displacement formulations for isotropic and orthotropic media from the plane problem in theory of elasticity. The chapter shows that the elastic equilibrium of thin shells of revolution. The influence function method is extended to the mathematical formulation of thin plate problems based on the Reissner theory, which accounts for the effect of transverse normal stress and transverse shear deformation and admits any standard physically feasible boundary conditions.