http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Improved analysis of laminated heterogeneous beams and associated formulation of a new finite element method
Kirchhoff's theory for plates and Bernouilli-Euler's theory for beams ignore the effects of transverse shear and normal deformations on stresses and displacements. Various subsequent theories have incorporated these effects by using an assumed displacement field. But these theories do not satisfy all the necessary elasticity equations. Kozik's kinematics-based equation provides an exact displacement within the limitation of linear theory of elasticity. By discretizing a beam through the thickness into hypothetical layers, this study determines explicit relations between transverse strains and inter-layer transverse stresses. An expression for the displacement field is then obtained using Kozik's equation. The resulting displacement and strain fields are functions of the reference surface displacements and transverse inter-layer stresses. The constitutive relations and the equations of equilibrium for each layer are utilized in an anlytical solution employed to determine the inter-layer stresses. As an alternative approach, a finite element method based on a modified form of the Hu-Washizu variational principle is formulated. In this formulation the derived displacement field is employed. Further modifications of this principle, were necessary in order to adjust the special features of the displacement field. This research also includes several case studies of homogeneous and heterogeneous beams. The results for displacement and stress fields closely approximate exact solutions for both homogeneous and heterogeneous beams. The bending stresses in heterogeneous beams are especially accurate as compared to values obtained by either classical or ad-hoc beam theories.
"Major subject: Mechanical Engineering."