On a General Nonlinear Theory of Plates and Shells: Formulation and Applications (Structures).

A consistent and efficient nonlinear theory for shell-type structures undergoing large deformations and rotations as well as large strains is presented. The formulation is valid for a broad class of rate independent constitutive equations. Starting from the governing equations of a three-dimensional solid in a full Lagrangian description and adopting only one consistent kinematical approximation, a director type of shell theory is derived in its most general tensorial form employing curvilinear coordinates. Consequently, the effect of transverse and normal strains are incorporated in a natural way in the proposed shell theory. The behavior of plates subjected to finite pure bending, to a uniformly distributed transverse load and to a linearly distributed shear load are analysed successively by employing both the proposed theory as well as the exact three dimensional formulation. Two classes of constitutive laws are utilized in order to assess the validity of the theory in the nonlinear regime: a hyperelastic model and a hypoelastic model. The problems considered in the present work are solved analytically and numerically. The results are overall very encouraging and indicate that the proposed approximation is adequate for describing the deformations of shells well into the nonlinear (both kinematically and materially) range.PhDAerospace engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/160184/1/8422289.pd